<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0" xmlns:itunes="http://www.itunes.com/dtds/podcast-1.0.dtd" xmlns:googleplay="http://www.google.com/schemas/play-podcasts/1.0"><channel><title><![CDATA[RevealedEye: Alternative Energy]]></title><description><![CDATA[This section explores the archives of forgotten blueprints and sidelined inventions that promised to revolutionize the world but never reached the public. We dive into the stories of pioneers whose breakthroughs in propulsion, materials, and efficiency were allegedly buried by corporate competition or national security interests.]]></description><link>https://www.revealedeye.com/s/alternative-energy</link><image><url>https://substackcdn.com/image/fetch/$s_!xq8z!,w_256,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fbucketeer-e05bbc84-baa3-437e-9518-adb32be77984.s3.amazonaws.com%2Fpublic%2Fimages%2F4c0731e9-c4c8-4eb4-bd8a-c0ce61e96bb2_640x640.png</url><title>RevealedEye: Alternative Energy</title><link>https://www.revealedeye.com/s/alternative-energy</link></image><generator>Substack</generator><lastBuildDate>Sat, 16 May 2026 01:08:57 GMT</lastBuildDate><atom:link href="https://www.revealedeye.com/feed" rel="self" type="application/rss+xml"/><copyright><![CDATA[RevealedEye]]></copyright><language><![CDATA[en]]></language><webMaster><![CDATA[revealedeye@substack.com]]></webMaster><itunes:owner><itunes:email><![CDATA[revealedeye@substack.com]]></itunes:email><itunes:name><![CDATA[RevealedEye]]></itunes:name></itunes:owner><itunes:author><![CDATA[RevealedEye]]></itunes:author><googleplay:owner><![CDATA[revealedeye@substack.com]]></googleplay:owner><googleplay:email><![CDATA[revealedeye@substack.com]]></googleplay:email><googleplay:author><![CDATA[RevealedEye]]></googleplay:author><itunes:block><![CDATA[Yes]]></itunes:block><item><title><![CDATA[The Divine Proportion: Golden (Phi)nomena of Nature]]></title><description><![CDATA[Discover why Phi (1.618) is called the Divine Proportion. From sacred geometry and Fibonacci sequences to the "Phiveness" of life, explore how this golden ratio acts as the universal blueprint for beauty, nature, and the fabric of reality.]]></description><link>https://www.revealedeye.com/p/the-divine-proportion-golden-phi-nomena-of-nature</link><guid isPermaLink="false">https://www.revealedeye.com/p/the-divine-proportion-golden-phi-nomena-of-nature</guid><dc:creator><![CDATA[RevealedEye]]></dc:creator><pubDate>Tue, 14 Apr 2026 15:03:16 GMT</pubDate><enclosure url="https://substack-post-media.s3.amazonaws.com/public/images/df8c46d1-f0eb-4aad-a6ad-dbbe9ffd9961_1200x630.png" length="0" type="image/jpeg"/><content:encoded><![CDATA[<p>There is one proportion that is divine. A ratio of two numbers, the simplest of which being one. Paired with unity, there is only one number that is capable of fractal expansion and contraction. By using the four operations of mathematics: addition, subtraction, multiplication, and division, this golden number (1.6180339..) is the key to understanding fractality, holograms, life, and the nature of reality. This is the number (or ratio) the universe uses to become more aware of itself. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!Rt0H!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!Rt0H!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!Rt0H!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!Rt0H!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!Rt0H!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!Rt0H!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;golden number phi calipers&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:false,&quot;topImage&quot;:true,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="golden number phi calipers" title="golden number phi calipers" srcset="https://substackcdn.com/image/fetch/$s_!Rt0H!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!Rt0H!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!Rt0H!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!Rt0H!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3bf9fef7-66cc-43c1-b744-739ddf8785d4_900x707.jpeg 1456w" sizes="100vw" fetchpriority="high"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>The divine proportion is the only mathematical ratio that the Universe needs to intelligently design all life. Phi, aka the Golden Ratio, is a truly divine number. It&#8217;s quite a <em>phi</em>nomenon. Along with unity this number creates the perfect proportion. Let&#8217;s demysti<em>phi</em> some of the more esoteric geometric concepts attributed to this golden proportion. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!-GkJ!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!-GkJ!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg 424w, https://substackcdn.com/image/fetch/$s_!-GkJ!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg 848w, https://substackcdn.com/image/fetch/$s_!-GkJ!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!-GkJ!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!-GkJ!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg" width="900" height="506" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/a62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:506,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phi Compilation&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:false,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phi Compilation" title="Phi Compilation" srcset="https://substackcdn.com/image/fetch/$s_!-GkJ!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg 424w, https://substackcdn.com/image/fetch/$s_!-GkJ!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg 848w, https://substackcdn.com/image/fetch/$s_!-GkJ!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!-GkJ!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa62d54a0-639c-4438-8c47-323d28213eca_900x506.jpeg 1456w" sizes="100vw"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><em>Geometric constructions of Phi, the Golden Number (explored in detail later)</em></figcaption></figure></div><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!qxec!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!qxec!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg 424w, https://substackcdn.com/image/fetch/$s_!qxec!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg 848w, https://substackcdn.com/image/fetch/$s_!qxec!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!qxec!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!qxec!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg" width="900" height="510" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:510,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Fibonacci 1&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:false,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Fibonacci 1" title="Fibonacci 1" srcset="https://substackcdn.com/image/fetch/$s_!qxec!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg 424w, https://substackcdn.com/image/fetch/$s_!qxec!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg 848w, https://substackcdn.com/image/fetch/$s_!qxec!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!qxec!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9836aa39-46c0-4465-8f27-ff0bfc75b0de_900x510.jpeg 1456w" sizes="100vw"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Phi is found everywhere and yet nobody talks about it. It&#8217;s missing from the calculator. Its importance remains hidden even from the most hard-core math geeks. Most mathematicians have heard of it, but the mystery surrounding its existence is ineffable, and the complete understanding of it, perhaps insurmountable.</p><div class="callout-block" data-callout="true"><p><em>The <a href="https://www.mathsisfun.com/numbers/golden-ratio.html">Golden Ratio</a> is a universal law in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form.</em><br><em>&#8211;Adolf Zeising</em></p><p><em>&#8220;Geometry has two great treasures: one is the theorem of Pythagoras; the other the division of a line into extreme and mean ratio. The first we may compare to a measure of Gold; the second we may name a precious jewel.&#8221; -Johannes Kepler</em></p></div><p>This ratio is also known as the divine cut, golden mean or golden section. Other names include Phi, extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, and golden number. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!vggj!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!vggj!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg 424w, https://substackcdn.com/image/fetch/$s_!vggj!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg 848w, https://substackcdn.com/image/fetch/$s_!vggj!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!vggj!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!vggj!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg" width="881" height="900" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:900,&quot;width&quot;:881,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;phi fibonacci&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:false,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="phi fibonacci" title="phi fibonacci" srcset="https://substackcdn.com/image/fetch/$s_!vggj!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg 424w, https://substackcdn.com/image/fetch/$s_!vggj!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg 848w, https://substackcdn.com/image/fetch/$s_!vggj!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!vggj!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F61f819ef-9bce-4eaa-9822-1f60670d58ab_881x900.jpeg 1456w" sizes="100vw"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><em>(a+b is to a, as a is to b)</em></figcaption></figure></div><blockquote><p><em>A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser. -Euclid</em></p></blockquote><p>With the golden ratio the whole line is to the large line; as the large line is to the small line. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!3Itb!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!3Itb!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!3Itb!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!3Itb!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!3Itb!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!3Itb!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phi Lines&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phi Lines" title="Phi Lines" srcset="https://substackcdn.com/image/fetch/$s_!3Itb!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!3Itb!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!3Itb!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!3Itb!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F18f132dd-0950-4533-bf94-fac08dee80f0_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><blockquote><p><em>&#8220;Like God, the Divine Proportion is always similar to itself.&#8221; &#8211;Fra Luca Pacioli</em></p></blockquote><p>If we were to take a line and divide it, there is only one place where the two separate lines would be in golden proportion with each other. One side would be 1 and the other, 1.618. Or one side would be .618 (1/&#248;) and the other 1. This is the only ratio that works this way. It is the only ratio in geometric and mathematical progression. It&#8217;s perfect!</p><p>Phi (1.618..) and phee(.618..) are the numbers of fractal expansion and contraction. Like male and female, these two energies spiral around unity, creating life as we know it. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!cDHG!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!cDHG!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!cDHG!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!cDHG!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!cDHG!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!cDHG!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Caduceus Phiral&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Caduceus Phiral" title="Caduceus Phiral" srcset="https://substackcdn.com/image/fetch/$s_!cDHG!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!cDHG!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!cDHG!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!cDHG!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0b5d8f87-9c00-4bb4-923e-8476a2f07954_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><div class="captioned-image-container"><figure><a class="image-link image2" target="_blank" href="https://substackcdn.com/image/fetch/$s_!Mw4J!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2b498cc1-e6a5-4262-b298-7f8a01aceeed_297x88.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!Mw4J!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2b498cc1-e6a5-4262-b298-7f8a01aceeed_297x88.gif 424w, https://substackcdn.com/image/fetch/$s_!Mw4J!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2b498cc1-e6a5-4262-b298-7f8a01aceeed_297x88.gif 848w, 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https://substackcdn.com/image/fetch/$s_!BIdq!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6b242c71-4eff-459d-8746-5f537889e44b_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!BIdq!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6b242c71-4eff-459d-8746-5f537889e44b_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!BIdq!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6b242c71-4eff-459d-8746-5f537889e44b_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/6b242c71-4eff-459d-8746-5f537889e44b_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phi Phormulas&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phi Phormulas" title="Phi Phormulas" srcset="https://substackcdn.com/image/fetch/$s_!BIdq!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6b242c71-4eff-459d-8746-5f537889e44b_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!BIdq!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6b242c71-4eff-459d-8746-5f537889e44b_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!BIdq!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6b242c71-4eff-459d-8746-5f537889e44b_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!BIdq!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6b242c71-4eff-459d-8746-5f537889e44b_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><em>Powers of Phi</em></figcaption></figure></div><p>The powers of Phi work just like the Fibonacci sequence. 1 + Phi = Phi squared. Phi + Phi squared = Phi cubed, and so on. This is the only number that does this. Phi is the only number where its square is exactly 1 number larger. It&#8217;s also unique in that its reciprocal (1/Phi) is one less than Phi, which we&#8217;ll call phee (0.618..) </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!m1zc!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!m1zc!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!m1zc!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!m1zc!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!m1zc!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!m1zc!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/ce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phibonacci Ratios&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phibonacci Ratios" title="Phibonacci Ratios" srcset="https://substackcdn.com/image/fetch/$s_!m1zc!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!m1zc!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!m1zc!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!m1zc!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fce371157-afa3-4223-b42e-b98563a2df88_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><em>Phi is the only number that can do this. Perfect fractal geometric and mathematic expansion and contraction</em></figcaption></figure></div><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!0Bpj!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!0Bpj!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!0Bpj!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!0Bpj!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!0Bpj!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!0Bpj!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Earth Moon and Phi&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Earth Moon and Phi" title="Earth Moon and Phi" srcset="https://substackcdn.com/image/fetch/$s_!0Bpj!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!0Bpj!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!0Bpj!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!0Bpj!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0a2cb42c-d436-46be-bb72-0ff3c4cc7afd_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><div><hr></div><p>Jonathan Quinton made this video that beautifully displays the nature of the Golden Ratio. </p><div class="native-video-embed" data-component-name="VideoPlaceholder" data-attrs="{&quot;mediaUploadId&quot;:&quot;5789f8e7-43a3-4d06-8b28-878c866b0982&quot;,&quot;duration&quot;:null}"></div><div><hr></div><h3>Geometric Constructions of the Divine Proportion </h3><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!5vDs!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!5vDs!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!5vDs!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!5vDs!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!5vDs!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!5vDs!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/a24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phi from Triangle Geometry&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phi from Triangle Geometry" title="Phi from Triangle Geometry" srcset="https://substackcdn.com/image/fetch/$s_!5vDs!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!5vDs!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!5vDs!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!5vDs!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa24fd572-5b08-4e5a-941f-34667b6a41ad_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Phi arises out of simple <a href="http://www.goldennumber.net/geometry/">geometries</a>. Take three lines of equal length and at their midpoints arrange them in this manner. Phi originates from the square root of five. (&#248; = (&#8730;5 +1/2). Being the number of life, <a href="http://www.goldennumber.net/five-phi/">Five</a> is closely connected to Phi. Even here the midpoints are .5 their full length. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!ryVw!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!ryVw!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!ryVw!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!ryVw!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!ryVw!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!ryVw!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Square Roots and the Golden Proportion&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Square Roots and the Golden Proportion" title="Square Roots and the Golden Proportion" srcset="https://substackcdn.com/image/fetch/$s_!ryVw!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!ryVw!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!ryVw!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!ryVw!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3134fb7d-9c27-42ca-8e8c-b094ad82a108_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>The square root of five is the cross section of the double square as seen above in blue. The square root of 4 (or 2) is the length of the double square. The square root of three comes from the vesica piscis. If the circle&#8217;s radius is one, the vertical length where they connect is the square root of three. Phi (seen in gold) arises from the relationship shown. The radius of the blue circle is the square root of five divided by two, or 1.180339&#8230; which is also Phi minus one half. The diameter of the blue circle is the square root of five. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!BW3R!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fefb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!BW3R!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fefb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!BW3R!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fefb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!BW3R!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fefb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!BW3R!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fefb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!BW3R!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fefb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/efb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Golden George Odom&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Golden George Odom" title="Golden George Odom" srcset="https://substackcdn.com/image/fetch/$s_!BW3R!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fefb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!BW3R!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fefb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!BW3R!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fefb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!BW3R!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fefb732cf-171b-4ae8-94ae-24dd6e1eaee3_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>This construction was developed by George Odom and published in American Mathematics Monthly in 1983. A circle with the simplest shape inside it reveals golden ratios, both in linear and curvilinear representations. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!jWFy!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!jWFy!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!jWFy!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!jWFy!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!jWFy!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!jWFy!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/e1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phiangle Schneider&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phiangle Schneider" title="Phiangle Schneider" srcset="https://substackcdn.com/image/fetch/$s_!jWFy!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!jWFy!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!jWFy!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!jWFy!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe1cdbfce-d23b-483a-8908-c82c42bb2b58_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>&#8220;Phiangle&#8221; further expanded upon by <a href="http://www.constructingtheuniverse.com/">Michael S. Schneider</a> </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!kwRu!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!kwRu!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!kwRu!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!kwRu!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!kwRu!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!kwRu!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Divine Proportion Phi Guy&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Divine Proportion Phi Guy" title="Divine Proportion Phi Guy" srcset="https://substackcdn.com/image/fetch/$s_!kwRu!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!kwRu!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!kwRu!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!kwRu!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F30a20624-eff2-4213-b0ab-c84a8d676838_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Starting with the circle on the right, divine proportions are derived in this way. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!xyG7!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!xyG7!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!xyG7!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!xyG7!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!xyG7!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!xyG7!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/d5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phi Circle Square&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phi Circle Square" title="Phi Circle Square" srcset="https://substackcdn.com/image/fetch/$s_!xyG7!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!xyG7!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!xyG7!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!xyG7!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd5ade970-be61-4ede-b1ab-ff7f1bfb68fb_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>A very basic construction of Phi. The arc of the circle is needed to create it. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!-3Gw!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!-3Gw!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!-3Gw!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!-3Gw!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!-3Gw!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!-3Gw!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phi from Square&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phi from Square" title="Phi from Square" srcset="https://substackcdn.com/image/fetch/$s_!-3Gw!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!-3Gw!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!-3Gw!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!-3Gw!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3469adf3-42c0-4b89-985e-e542290fd17f_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Phi constructed from three circles. John Michell gets credit for this one. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!SQJ4!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!SQJ4!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!SQJ4!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!SQJ4!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!SQJ4!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!SQJ4!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Pentagon Phormation phi&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Pentagon Phormation phi" title="Pentagon Phormation phi" srcset="https://substackcdn.com/image/fetch/$s_!SQJ4!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!SQJ4!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!SQJ4!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!SQJ4!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1b521040-efe8-48f0-a0da-7890e7307ef9_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Phi springs to life from the geometry of five. Golden proportions are ubiquitous in the pentagons and pentagrams. It is this &#8220;phiveness&#8221; that brings Phi to life. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!Gk6F!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!Gk6F!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!Gk6F!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!Gk6F!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!Gk6F!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!Gk6F!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Pentagon Decagon&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Pentagon Decagon" title="Pentagon Decagon" srcset="https://substackcdn.com/image/fetch/$s_!Gk6F!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!Gk6F!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!Gk6F!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!Gk6F!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F437d7f0a-59d0-4527-80d1-cd08d10e5d24_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Robert Lawlor, in his book &#8216;Sacred Geometry&#8217;, shows Phi proportions with a circle split into 5&#215;2 sections. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!GM0g!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!GM0g!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!GM0g!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!GM0g!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!GM0g!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!GM0g!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Pentagram Phi 2&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Pentagram Phi 2" title="Pentagram Phi 2" srcset="https://substackcdn.com/image/fetch/$s_!GM0g!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!GM0g!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!GM0g!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!GM0g!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F77ee43ed-5e07-4412-9e6c-9f8c6ef6564a_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><blockquote><p><em>&#8220; Where plants have five-fold patterns, a consideration of their souls is in place. For patterns of five appear in the regular solids, and so involve the ratio called the Golden Section, which results from a self-developing series that is an image of the faculty of propagation in plants. Thus the flower carries the authentic flag of this faculty, the pentagon.&#8221; &#8211; Johannes Kepler</em></p></blockquote><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!jVZc!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!jVZc!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!jVZc!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!jVZc!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!jVZc!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!jVZc!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Traffic Light Phi&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Traffic Light Phi" title="Traffic Light Phi" srcset="https://substackcdn.com/image/fetch/$s_!jVZc!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!jVZc!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!jVZc!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!jVZc!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F00d872ec-0fdf-49a2-8728-6d8be499f005_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><em>The traffic lights, they turn blue tomorrow..</em></figcaption></figure></div><p>In 2006 Bengt Erik Erlandsen showed that Phi can be represented simply in this way. Whenever you drive down the street you are subconsciously experiencing golden ratios. Again, with the appearance of five. This time the circles on the top and bottom are cut in half (or .5) </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!Un_B!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!Un_B!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!Un_B!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!Un_B!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!Un_B!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!Un_B!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/e31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Divine Proportion!&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Divine Proportion!" title="Divine Proportion!" srcset="https://substackcdn.com/image/fetch/$s_!Un_B!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!Un_B!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!Un_B!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!Un_B!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fe31ed62b-560a-404a-b30b-4fff6aed9424_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><em>Phi is phound in the phabric of sacred and secular geometry.</em></figcaption></figure></div><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!yE44!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!yE44!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!yE44!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!yE44!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!yE44!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!yE44!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Eye of Phi&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Eye of Phi" title="Eye of Phi" srcset="https://substackcdn.com/image/fetch/$s_!yE44!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!yE44!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!yE44!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!yE44!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6622d197-ad4a-4af0-a13c-fa138dbb4e2b_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>In 2002 Kurt Hofstetter published this construction in Forum Geometricorum. The vesica piscis (the two smaller circles) in combination with circles around the &#8220;bladder of the fish&#8221;, created phi proportions. He struck gold on this one.  </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!JRHP!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!JRHP!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!JRHP!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!JRHP!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!JRHP!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!JRHP!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/d6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Penitent Man Will Pass&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Penitent Man Will Pass" title="Penitent Man Will Pass" srcset="https://substackcdn.com/image/fetch/$s_!JRHP!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!JRHP!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!JRHP!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!JRHP!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fd6434587-ef37-4a47-a740-332e547ddab7_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Constructing the pentagram using circles and phi ratios: Starting with the green square, circles are extended out which define the points of the pentagram. The radius of the green circle is 1, the yellow 1.618.., and the magenta 1.23.. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!MMZE!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!MMZE!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!MMZE!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!MMZE!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!MMZE!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!MMZE!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Vesica Phiscis&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Vesica Phiscis" title="Vesica Phiscis" srcset="https://substackcdn.com/image/fetch/$s_!MMZE!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!MMZE!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!MMZE!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!MMZE!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F6c09be25-1206-4653-92ab-d6f19fc4e559_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Vesica Phiscis, well not quite. The name may be a play on words, but the golden proportion inherent in this geometry is forever accurate. Phi seems to come up a lot analyzing circles. It may seem odd then that Phi is not encoded into the relationship of a circle&#8217;s circumference to its diameter, (&#960;). Pi is well-known. It even has its own day.</p><p>Why then, is Phi not encoded into the ratio known as Pi? Well some mathematicians think it is. Australian mathemagician <a href="http://www.jainmathemagics.com/">Jain108</a> has concluded that the ratio of a circle&#8217;s circumference to its diameter IS linked to Phi. He goes on to show that &#960; = 4/&#8730;&#248;. Four divided by the square root of Phi, which is a little over the accepted value today. (3.1446..) More on this in an upcoming article. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!nicf!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!nicf!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!nicf!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!nicf!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!nicf!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!nicf!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/c4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Vesica Phiscis lawlor&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Vesica Phiscis lawlor" title="Vesica Phiscis lawlor" srcset="https://substackcdn.com/image/fetch/$s_!nicf!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!nicf!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!nicf!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!nicf!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc4261d42-4f6e-4234-97a8-99fc190e45f1_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>The green and red circles are in golden proportion with each other. The blue square and circle have the same perimeters. Thus Phi encodes the solution to &#8220;squaring the circle&#8221;. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!jlCW!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!jlCW!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!jlCW!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!jlCW!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!jlCW!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!jlCW!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phi Ratios Circle and Square3&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phi Ratios Circle and Square3" title="Phi Ratios Circle and Square3" srcset="https://substackcdn.com/image/fetch/$s_!jlCW!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!jlCW!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!jlCW!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!jlCW!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1342787e-9c29-45d1-8281-2f99c6410f5b_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Blue is to Red; as Magenta is to Green. Isn&#8217;t that phinomenal?! </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!3FW7!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!3FW7!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!3FW7!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!3FW7!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!3FW7!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!3FW7!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Pentagram Phi Magic&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Pentagram Phi Magic" title="Pentagram Phi Magic" srcset="https://substackcdn.com/image/fetch/$s_!3FW7!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!3FW7!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!3FW7!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!3FW7!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2bbecbe3-5b82-41bf-9115-b7453744f6cf_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>The Pentagram and the many manifestations of Phi. One is always needed in between to transition from the higher powers of Phi into the lesser. These golden numbers Phi and phee, 1.618 and .618, are never without the presence of ONE. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!_NgO!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Feece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!_NgO!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Feece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!_NgO!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Feece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!_NgO!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Feece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!_NgO!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Feece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!_NgO!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Feece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/eece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Pentagram Phi Cubed&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Pentagram Phi Cubed" title="Pentagram Phi Cubed" srcset="https://substackcdn.com/image/fetch/$s_!_NgO!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Feece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!_NgO!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Feece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!_NgO!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Feece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!_NgO!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Feece977f-645b-4f9b-8802-3ef620bf2d1a_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>My friend Rhuben Neal made this construction. If the diameter of the blue circle is 1, the diameter of the golden circle is Phi cubed. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!Bj4J!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!Bj4J!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!Bj4J!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!Bj4J!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!Bj4J!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!Bj4J!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/c1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phi circles Kutler&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phi circles Kutler" title="Phi circles Kutler" srcset="https://substackcdn.com/image/fetch/$s_!Bj4J!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!Bj4J!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!Bj4J!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!Bj4J!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc1a38476-46ba-43c8-bb03-9cf49a362084_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Fibonacci Circles. Original construction by Sam Kutler. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!0EpX!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!0EpX!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!0EpX!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!0EpX!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!0EpX!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!0EpX!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Phi Map Meisner&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Phi Map Meisner" title="Phi Map Meisner" srcset="https://substackcdn.com/image/fetch/$s_!0EpX!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!0EpX!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!0EpX!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!0EpX!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F08d103e4-646b-4769-94e4-4bcd043c8e92_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p><a href="http://www.goldennumber.net/golden-section/">Gary Meisner&#8217;s</a> website <a href="http://www.goldennumber.net/circles/">GoldenNumber.net</a> explores Phi in depth.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!YfoK!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!YfoK!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!YfoK!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!YfoK!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!YfoK!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!YfoK!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;The Golden One Phi!&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="The Golden One Phi!" title="The Golden One Phi!" srcset="https://substackcdn.com/image/fetch/$s_!YfoK!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!YfoK!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!YfoK!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!YfoK!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F2799ca32-2298-4316-9d70-af3f70a196d0_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><em>Phi, The Golden Ratio, is the most perfect number in existence.</em></figcaption></figure></div><p>Phee Phi Pho Phum, I smell the blood of the Golden One.</p><blockquote><p><em>&#8220;Neglect of mathematics work injury to all knowledge, since he who is ignorant of it cannot know the other sciences or things of this world. And what is worst, those who are thus ignorant are unable to perceive their own ignorance, and so do not seek a remedy.&#8221; &#8213; Roger Bacon, Mathematics</em></p></blockquote><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!ekoA!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!ekoA!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!ekoA!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!ekoA!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!ekoA!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!ekoA!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/a2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;The Golden Section!&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="The Golden Section!" title="The Golden Section!" srcset="https://substackcdn.com/image/fetch/$s_!ekoA!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!ekoA!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!ekoA!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!ekoA!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa2826abc-7cb2-4f4b-8d52-90144466ce43_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><em>The Making of the Divine Proportion</em></figcaption></figure></div><p>This simple drawing reveals a lot, but like Hermes put it, <em>The lips of wisdom are closed, except to the ears of Understanding. </em>Or in this case, eyes. The length of the square, in green, is one. The hypotenuse in magenta is &#8730;5 or 2.2360679.. The blue line is double the green. In red is &#8216;phee&#8217; sometimes labeled lowercase phi. In Gold, Phi. The circle, as it seems in these drawings, is vital to the existence of this divine proportion.</p><p>The double square encodes Phi with the help of the circle. If the length of one square is one, the double-square&#8217;s perimeter is six, and the cross section(in magenta) is the square root of five. This relationship of 5 to 6 is encoded into the fabric of our reality. Five is the number of life, and Six the number of structure. These two archetypes combine to construct our numerical universe. </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!TTkF!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!TTkF!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!TTkF!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!TTkF!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!TTkF!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!TTkF!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;Fractal Phi&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="Fractal Phi" title="Fractal Phi" srcset="https://substackcdn.com/image/fetch/$s_!TTkF!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!TTkF!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!TTkF!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!TTkF!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F429a7aea-5b4a-45ea-b91f-75bacb1c1b5c_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p><em>&#8221;He who joins the hexagram and pentagram has solved half of the sacred secret.&#8221; &#8211;<a href="http://en.wikipedia.org/wiki/Eliphas_Levi">Eliphas Levi</a> (19th century magician)</em></p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!wnDr!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!wnDr!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg 424w, https://substackcdn.com/image/fetch/$s_!wnDr!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg 848w, https://substackcdn.com/image/fetch/$s_!wnDr!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!wnDr!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!wnDr!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg" width="900" height="850" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:850,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;George Leoniak Phi Construction&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="George Leoniak Phi Construction" title="George Leoniak Phi Construction" srcset="https://substackcdn.com/image/fetch/$s_!wnDr!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg 424w, https://substackcdn.com/image/fetch/$s_!wnDr!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg 848w, https://substackcdn.com/image/fetch/$s_!wnDr!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!wnDr!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F1a5fbac8-8ea7-4278-b06f-e2829be6bd7d_900x850.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Another phi construction ^ via George Leoniak </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!s8Ty!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!s8Ty!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg 424w, https://substackcdn.com/image/fetch/$s_!s8Ty!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg 848w, https://substackcdn.com/image/fetch/$s_!s8Ty!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!s8Ty!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!s8Ty!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg" width="900" height="526" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:526,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!s8Ty!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg 424w, https://substackcdn.com/image/fetch/$s_!s8Ty!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg 848w, https://substackcdn.com/image/fetch/$s_!s8Ty!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!s8Ty!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b39361a-1be9-4f44-89a1-4ce7749a8760_900x526.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Elliot McGucken discovered a Phi relationship between the 3, 4 &amp; 5 sided polygons^ <a href="https://www.cut-the-knot.org/do_you_know/Elliot2.shtml">https://www.cut-the-knot.org/do_you_know/Elliot2.shtml</a></p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!9G5d!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!9G5d!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg 424w, https://substackcdn.com/image/fetch/$s_!9G5d!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg 848w, https://substackcdn.com/image/fetch/$s_!9G5d!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!9G5d!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!9G5d!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg" width="900" height="496" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/a67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:496,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!9G5d!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg 424w, https://substackcdn.com/image/fetch/$s_!9G5d!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg 848w, https://substackcdn.com/image/fetch/$s_!9G5d!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!9G5d!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa67d7151-bd61-4f7c-9f50-bc0bc1f22863_900x496.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!an0l!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8d68194a-e766-4546-956b-f763400614df_900x526.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!an0l!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8d68194a-e766-4546-956b-f763400614df_900x526.jpeg 424w, https://substackcdn.com/image/fetch/$s_!an0l!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8d68194a-e766-4546-956b-f763400614df_900x526.jpeg 848w, https://substackcdn.com/image/fetch/$s_!an0l!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8d68194a-e766-4546-956b-f763400614df_900x526.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!an0l!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8d68194a-e766-4546-956b-f763400614df_900x526.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!an0l!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8d68194a-e766-4546-956b-f763400614df_900x526.jpeg" width="900" height="526" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/8d68194a-e766-4546-956b-f763400614df_900x526.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:526,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!an0l!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8d68194a-e766-4546-956b-f763400614df_900x526.jpeg 424w, https://substackcdn.com/image/fetch/$s_!an0l!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8d68194a-e766-4546-956b-f763400614df_900x526.jpeg 848w, https://substackcdn.com/image/fetch/$s_!an0l!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8d68194a-e766-4546-956b-f763400614df_900x526.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!an0l!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8d68194a-e766-4546-956b-f763400614df_900x526.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p><a href="https://math.stackexchange.com/questions/1798843/new-very-simple-golden-ratio-construction-incorporating-a-triangle-square-and">https://math.stackexchange.com/questions/1798843/new-very-simple-golden-ratio-construction-incorporating-a-triangle-square-and</a></p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!H3Hx!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!H3Hx!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg 424w, https://substackcdn.com/image/fetch/$s_!H3Hx!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg 848w, https://substackcdn.com/image/fetch/$s_!H3Hx!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!H3Hx!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!H3Hx!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg" width="900" height="526" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/a64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:526,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!H3Hx!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg 424w, https://substackcdn.com/image/fetch/$s_!H3Hx!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg 848w, https://substackcdn.com/image/fetch/$s_!H3Hx!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!H3Hx!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa64f0c42-f33b-45e6-89d8-512206beb3ef_900x526.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Here shows the edge relationships of regular polygons from a triangle to the hexagon inscribed in the same size 1 radius circle. [Credit to Hunter Hughes]</p><p>The following construction was made by George Leoniak </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!dySG!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!dySG!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg 424w, https://substackcdn.com/image/fetch/$s_!dySG!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg 848w, https://substackcdn.com/image/fetch/$s_!dySG!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!dySG!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!dySG!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg" width="900" height="732" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:732,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!dySG!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg 424w, https://substackcdn.com/image/fetch/$s_!dySG!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg 848w, https://substackcdn.com/image/fetch/$s_!dySG!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!dySG!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9c58534b-f81d-4719-95ae-de4aff81eda8_900x732.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!HvuV!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!HvuV!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg 424w, https://substackcdn.com/image/fetch/$s_!HvuV!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg 848w, https://substackcdn.com/image/fetch/$s_!HvuV!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!HvuV!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!HvuV!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg" width="900" height="488" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:488,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!HvuV!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg 424w, https://substackcdn.com/image/fetch/$s_!HvuV!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg 848w, https://substackcdn.com/image/fetch/$s_!HvuV!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!HvuV!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F7001acef-9a7f-401b-ad66-33de793bbfac_900x488.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>constructed by Hunter Hughes</p><div class="callout-block" data-callout="true"><p><em>&#8220;Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.&#8221; -Mario Livio </em></p></div><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!SSAj!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!SSAj!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!SSAj!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!SSAj!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!SSAj!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!SSAj!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg" width="900" height="707" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:707,&quot;width&quot;:900,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:&quot;fruit of phi joedubs&quot;,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="fruit of phi joedubs" title="fruit of phi joedubs" srcset="https://substackcdn.com/image/fetch/$s_!SSAj!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg 424w, https://substackcdn.com/image/fetch/$s_!SSAj!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg 848w, https://substackcdn.com/image/fetch/$s_!SSAj!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg 1272w, https://substackcdn.com/image/fetch/$s_!SSAj!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d148344-12fb-45f5-a1f7-7c3fcd9206fe_900x707.jpeg 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p><em>Courtesy: JoeDubs</em></p><div><hr></div><p>More articles on this topic are coming. I hope you&#8217;ll subscribe and stay tuned. And I&#8217;d really appreciate it if you considered becoming a paid subscriber to support my work.</p><p class="button-wrapper" data-attrs="{&quot;url&quot;:&quot;https://www.revealedeye.com/subscribe?&quot;,&quot;text&quot;:&quot;Subscribe now&quot;,&quot;action&quot;:null,&quot;class&quot;:null}" data-component-name="ButtonCreateButton"><a class="button primary" href="https://www.revealedeye.com/subscribe?"><span>Subscribe now</span></a></p><p><em>To see how readers have benefited from this publication and the community it has built, you can view their feedback <a href="https://revealedeye.substack.com/p/reader-feedback">here</a>.</em></p>]]></content:encoded></item><item><title><![CDATA[A DIY Guide to Free Energy Conversions : This report explains how to use high-frequency pulses to turn ordinary 'Tap Water' into a powerful 'WaterFuel' for your engine.]]></title><description><![CDATA[A complete walkthrough of the waterfuel conversion process, featuring the diagrams and circuit designs for a DIY free energy system. We examine how nested electrodes and specific electronic frequencies can replace gasoline with a high-energy hydrogen-oxygen mixture.]]></description><link>https://www.revealedeye.com/p/water-as-fuel-a-diy-guide-to-free-energy</link><guid isPermaLink="false">https://www.revealedeye.com/p/water-as-fuel-a-diy-guide-to-free-energy</guid><dc:creator><![CDATA[RevealedEye]]></dc:creator><pubDate>Tue, 31 Mar 2026 17:02:35 GMT</pubDate><enclosure url="https://substack-post-media.s3.amazonaws.com/public/images/c6cbe103-3256-4352-b5f0-045d76ab3f3b_1200x630.png" length="0" type="image/jpeg"/><content:encoded><![CDATA[<p><em>Below, I have reposted the complete text and diagrams of a paper titled &#8220;The Freedom Reclamation Project&#8221; which was faxed (Jan. 7, 2002) to list owner Geoff Egel of Energy 2000 (&lt;energy2000@yahoogroups.com&gt;), a chat list devoted to free energy ideas. The author who assembled this paper wishes to remain anonymous, but whoever he is, we all owe him our gratitude. </em></p><div><hr></div><p>To help speed up your orientation and understanding of what&#8217;s explained in the paper, I&#8217;ll give the reader a brief overview of how the system works first and will later add a parts list, telling you where you can obtain the needed parts. I realize that it&#8217;s easy for those with a background in electronics to build the controller circuit, but not so easy for non techies. With that in mind, I&#8217;ll probably assemble a ready made kit which will include the controller circuit, and perhaps the reaction chamber, the dash gauges, etc. to simplify running around on your part. If you have the ability and time though, the necessary info is included in this paper to assemble everything yourself.</p><h3>Introduction &amp; Overview</h3><p>This WaterFuel system is adapted to an ordinary internal combustion engine found in most cars. Rather than use vaporized gasoline as the fuel, this system uses a hydrogen/oxygen gas mixture (along with some water vapor) which is ignited in the engine&#8217;s combustion chamber in the same way that gasoline vapor is ignited. According to this paper, water stores more latent energy than gasoline, so you can get expect better performance, better mileage, and zero pollution using water as a fuel. It is not necessary to dismantle your car&#8217;s existing gasoline fuel system. You can leave everything in place and use your gasoline when and if you find it necessary. The parts required to build this WaterFuel system are not very expensive and can be readily obtained from off the shelf suppliers.</p><h3>Overview</h3><p>Since you are now using water as a fuel, you need a <strong>Water Tank</strong> to hold it and enough tubing to deliver it to the <strong>Reaction Chamber</strong> located under the hood (bonnet for Aussie, UK readers). The Reaction Chamber contains two stainless steel cylinders, one nested inside the other. The gap between these two cylinders must be between 1-5 mm, with a 1 mm gap producing the best results. These two cylinders are functioning as two electrodes which &#8220;vibrate&#8221; under the influence of the electronic pulse signal coming from the <strong>Controller. </strong>The particular frequency and special shape of this electronic pulse<strong> </strong>will break the water down into hydrogen and oxygen gases. The gas mixture is then delivered to the carburetor where it enters the combustion chamber within the cylinder and explodes just like gasoline.</p><p>You need a few <strong>Monitoring Gauges </strong>mounted to the dashboard area of your car to tell you </p><ol><li><p>the level of water in the Water Tank and </p></li><li><p>the level of water in your Reaction Chamber. You need another gauge to tell you </p></li><li><p>the temperature of the cylinder heads and you should have a dash gauge to tell you </p></li><li><p>the pressure inside the Reaction Chamber.</p></li></ol><p>You&#8217;ll need to install a variable control device (10 k ohm potentiometer) to the existing accelerator pedal or install a second accelerator pedal for this control mechanism. This accelerator control is connected to the <strong>Controller </strong>box and allows you to vary the width of the pulse going to the stainless steel electrodes inside the Reaction Chamber. By &#8216;widening&#8217; the width of the electronic pulse, the electrodes can produce more hydrogen/oxygen gas which in turn will allow the car to go faster when the accelerator pedal is pushed down. To start the process, you need an on/off switch mounted on the dash to send battery power to the Controller to start the Reaction Chamber producing the hydrogen/oxygen gas mixture. Once the gas pressure inside the Reaction Chamber gets up to 30 pounds per square inch, you can turn on the ignition key and crank the engine to start it.</p><p>For safety, you need to install a <strong>safety relief valve</strong> in the Reaction Chamber in case the pressure within the chamber exceeds the upper specified limit of 75 pounds per square inch (psi.). To prevent rusting, the cylinders, the piston heads, the exhaust system piping, and the valves need to made rust proof. You replace the existing valves and the existing exhaust system with stainless steel and coat the inside of the cylinders and the piston heads with ceramic to prevent the water vapor from rusting the iron. To prevent a flashback explosion in the Reaction Chamber from the carb/intake manifold/cylinder combustion area, you need a <strong>Flashback Arrestor</strong> made of copper mesh connected to the flexible stainless steel tubing going from the Reaction Chamber into the carburetor .</p><p>If your engine develops knock, you can install an optional donut shaped stainless steel coil around the electrode cylinders inside the Reaction Chamber along with an extra controller circuit called a <strong>Prahydogen Enhancement</strong></p><p>That&#8217;s about it in a nut shell.</p><p>After you read through the paper a couple of times, you&#8217;ll see how the system goes together and understand the process with greater clarity. This is a rather easy project to construct, so don&#8217;t sit on your hands. You can do it. After building this system for your car, you can also consider other uses for your hydrogen/oxygen gas mixture which you can now produce in unlimited quantities. How about using it for heating water? Or your house? Or run an electric generator? Or your boat&#8217;s outboard motor? Get the idea? </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!1UTr!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!1UTr!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif 424w, https://substackcdn.com/image/fetch/$s_!1UTr!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif 848w, https://substackcdn.com/image/fetch/$s_!1UTr!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif 1272w, https://substackcdn.com/image/fetch/$s_!1UTr!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!1UTr!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif" width="774" height="327" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/a6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:327,&quot;width&quot;:774,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!1UTr!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif 424w, https://substackcdn.com/image/fetch/$s_!1UTr!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif 848w, https://substackcdn.com/image/fetch/$s_!1UTr!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif 1272w, https://substackcdn.com/image/fetch/$s_!1UTr!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fa6cfed33-aa0f-44af-8e8f-a2beff5dcc69_774x327.gif 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p><strong>The Freedom Reclamation Project</strong></p><p>CONVERT YOUR ENGINE TO BURN HYDROGEN AND OXYGEN</p><p>VAPOR FROM WATER ON DEMAND + POLLUTION-FREE</p><p>ZPV: ZERO POLLUTON VEHICLE</p><p>VIRTUALLY FREE ENERGY</p><p>FREEDOM FROM GA$OLINE</p><p>SIMPLE AND INEXPENSIVE CONVERSION</p><p>ON DEMAND&#8217; VAPOR RATE (i.e. THROTTLE )</p><p>EAST TO FOLLOW DO-IT-YOURSELF PLANS</p><p>HELP CLEAN THE AIR WHILE YOU SAVE MONEY</p><p>IMPORTANT INFORMATION </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!gmUm!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!gmUm!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif 424w, https://substackcdn.com/image/fetch/$s_!gmUm!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif 848w, https://substackcdn.com/image/fetch/$s_!gmUm!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif 1272w, https://substackcdn.com/image/fetch/$s_!gmUm!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!gmUm!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif" width="560" height="391" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:391,&quot;width&quot;:560,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!gmUm!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif 424w, https://substackcdn.com/image/fetch/$s_!gmUm!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif 848w, https://substackcdn.com/image/fetch/$s_!gmUm!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif 1272w, https://substackcdn.com/image/fetch/$s_!gmUm!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F8b65ea5e-a56b-46c8-8c68-8526220585a6_560x391.gif 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>RUN YOUR CAR / TRUCK / RV / MOTORCYCLE / AIRPLANE (ETC) ON TAP WATER! </p><div class="captioned-image-container"><figure><a class="image-link image2" target="_blank" href="https://substackcdn.com/image/fetch/$s_!-Q7B!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!-Q7B!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif 424w, https://substackcdn.com/image/fetch/$s_!-Q7B!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif 848w, https://substackcdn.com/image/fetch/$s_!-Q7B!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif 1272w, https://substackcdn.com/image/fetch/$s_!-Q7B!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!-Q7B!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif" width="774" height="173" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:173,&quot;width&quot;:774,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!-Q7B!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif 424w, https://substackcdn.com/image/fetch/$s_!-Q7B!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif 848w, https://substackcdn.com/image/fetch/$s_!-Q7B!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif 1272w, https://substackcdn.com/image/fetch/$s_!-Q7B!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F4ad289a9-a01c-460d-a83f-9b0ed8d0802b_774x173.gif 1456w" sizes="100vw" loading="lazy"></picture><div></div></div></a></figure></div><h3>Introduction</h3><p>Are you fed up with ga$oline price$ and THE POLLUTION?</p><p>Would you like to do something about it besides complain and wait?</p><p>Are you still CHOKING on the whole idea of fossil fuel CON$UMPTION? WHY?</p><p>Wouldn&#8217;t you like to free yourself from centrally-controlled or imported fuel?</p><p>Do you have a 2nd vehicle you don&#8217;t use every day?</p><p>Now there is something we can actually do about it, as individuals willing to help clean the environment, and travel at lower cost to both you and your environment. Do-it-yourself plans allow the individual (that&#8217;s you and me, folks) to make a difference.</p><p>This is the easiest and lowest cost way to convert your car to run on (relatively) free energy. Now with existing technology, anyone can stand up and make a difference by reducing the local automotive pollution, eliminate ga$oline expen$e$, help restore our atmosphere, and breathe a little easier. You will be making use of your entire existing system, except the fuel tank and catalytic converter.</p><h3>The Plan:</h3><p>Know the Truth and set yourself FREE. Set a good example for the World you choose to create. Exercise your own Free Will. Live cleaner and healthier.</p><p>Build and install a low-cost alternative method for running your vehicle (internal combustion) engine on TAP WATER, using off-the-shelf components. This is simply an efficient way to convert ordinary tap water into gaseous Hydrogen and Oxygen, and then burn these vapours in the engine, instead of that $melly, $tinky, expen$ive &#8216;other $tuff.</p><p>This &#8216;minisystem&#8217; runs easily from your existing battery and electrical system, and it plugs into your carburetor with simple off-the-shelf fittings. You will be installing a plastic water tank, a control circuit, a reaction chamber, a hi-pressure carb/FI fitting, and 3 gauges (see Figure 1), and then hooking into your existing carb/FI.</p><p>The SIMPLICITY comes from being an &#8216;on-demand&#8217; system requiring no fancy storage, or plumbing. You crank the gas pedal or throttle and you electrically create more vapour for immediate consumption, on demand; Lo - Hi Flow Rate as needed from idle - max power. The only real change is that you are using tap water as fuel, instead of the traditional petroleum-based fuel. Given, a choice, which way would you choose?</p><h3>FAQs</h3><p>Q: Does it really work?</p><p>A: Yes; this is well-established technology dating back to stainless steel. But be sure to follow these instructions using the proper mechanical and electrical assembly techniques, as it incorporates the best qualities of several techniques.</p><p>Q: How does it qualify as &#8216;free energy&#8217;?</p><p>A: If you&#8217;re paying someone for the water you use, then it is not strictly &#8216;free&#8217;. But, the alternative is to keep buying into the expen$ive ga$oline and re$ultant hydrocarbon pollution.</p><p>Q: ls it Safe?</p><p>A: Technically, it is safer than running on fossil fuel, because you are no longer choking on your own emissions (health-wise), but in general it is practically as safe as your current gasoline arrangement. You will be installing a few simple safety devices, using current automotive standards.</p><p>Q: What kind of performance can I expect?</p><p>A: Properly adjusted, your modified vapour-only fuel system will run cooler, and at a modestly higher power level. The mileage performance expected from this design ranges from 50-300 mpg, depending on your adjusting skills.</p><p>Q: Can I do the modification myself?</p><p>A: Why not? If you know someone with basic mechanical and/or electrical skills, you can even delegate some of the construction. If you are using a fuel-injected engine, you may have to get a mechanic&#8217;s opinion.</p><p>0: What is the environmental impact that my vehicle will have?</p><p>A: It will be producing H20 steam and unburnt 02, hence it will be cleaning the environment, rather than dumping nauseous toxins into it. Plus you will be helping to save our dwindling supply of atmospheric oxygen. Any excess vapour in the reaction becomes either steam or oxygen. You can also expect to be receiving more than casual interest from those around you.</p><p>Q: Is this really a steam engine?</p><p>A: No; really. Exceedingly hi temp &amp; pressure are not used. This is strictly an internal combustion engine (burning orthohydrogen) with residual steam in the exhaust as a by product. </p><div class="captioned-image-container"><figure><a class="image-link image2" target="_blank" href="https://substackcdn.com/image/fetch/$s_!Kz-f!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!Kz-f!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif 424w, https://substackcdn.com/image/fetch/$s_!Kz-f!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif 848w, https://substackcdn.com/image/fetch/$s_!Kz-f!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif 1272w, https://substackcdn.com/image/fetch/$s_!Kz-f!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!Kz-f!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif" width="700" height="133" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:133,&quot;width&quot;:700,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!Kz-f!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif 424w, https://substackcdn.com/image/fetch/$s_!Kz-f!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif 848w, https://substackcdn.com/image/fetch/$s_!Kz-f!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif 1272w, https://substackcdn.com/image/fetch/$s_!Kz-f!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F97314f3b-4023-4d30-844e-46016bb90ffb_700x133.gif 1456w" sizes="100vw" loading="lazy"></picture><div></div></div></a></figure></div><p>0. Gasoline as a fuel is NOT NECESSARY; it is optional.</p><p>1. ORIGIN - In the 19th century, the gasoline portion of the refining process, was first considered to be a &#8216;waste&#8217; product of extracting the purified crude oil. Later on, it was discovered that it could be $old as fuel, instead of just dumping it back in the hole as had been the tradition.</p><p>2. CONSUMPTION RATE - The gasoline consumption rate for every mass-produced car has been carefully &#8216;designed in&#8217; as a market asset. As an indication, simply observe how quickly and closely ALL the local different gas stations adjust their prices. Even the hybrid cars which use electric motors still consume a designed amount of gasoline, and their price tags are prohibitively high.</p><p>3. EFFICIENCY - There is a lot of thermochemical energy in gasoline, but there is even more energy in water. The DOE has quoted about 40%, 50 it is probably much more than that. Most people are unaware that &#8216;internal combustion&#8217; is DEFINED as: a thermo-vapour process; as in &#8216;no liquid in the reaction&#8217;; AND most of the gasoline in a standard internal combustion engine, is ACTUALLY CONSUMED cooked and finally broken down) IN THE CATALYTIC CONVERTER, which happens AFTER the fuel has been not-so-burnt in the engine. Sadly, this means that most of the fuel we use in this way, is used only to cool down the combustion process, rather than using a cleaner and more efficient means to do so.</p><p>4. ADDITIVES - Also sadly, we are told by &#8216;authorities&#8217; that some of the many gasoline additives are in the mix to increase performance; but because of its current overly-complex molecular structure, the real built-in function of the gasoline formula is to slow down the combustion so that only so much is actually consumed in the cylinder, and the liquid balance goes to the catalytic converter. As a further insult, the additives are also there to clog and prevent the use of the Pogue-style carburetors, designed to get 200-300 mpg.</p><p>5. PROFIT- Of course the oil companies are making a huge profit. It is by design. What do you suppose the Gulf War was about? Just look at where the crude oil comes from and where the money is flowing. Rest assured that the oil companies do NOT want you to know how to make use of this water-fuel technology. They have been making money on our ignorance, dis-empowerment, and willingness to follow along in a mindless &#8216;comfort-zone&#8217; of toxic waste, suppression, resentment, and apathy: WHO NEEDS IT?</p><p>Let us proceed to set a good example and do it right, do it clean.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!0NTE!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fdc5e13d7-9c54-4e4b-9260-a60d9802c5f5_495x552.png" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!0NTE!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fdc5e13d7-9c54-4e4b-9260-a60d9802c5f5_495x552.png 424w, https://substackcdn.com/image/fetch/$s_!0NTE!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fdc5e13d7-9c54-4e4b-9260-a60d9802c5f5_495x552.png 848w, https://substackcdn.com/image/fetch/$s_!0NTE!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fdc5e13d7-9c54-4e4b-9260-a60d9802c5f5_495x552.png 1272w, https://substackcdn.com/image/fetch/$s_!0NTE!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fdc5e13d7-9c54-4e4b-9260-a60d9802c5f5_495x552.png 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!0NTE!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fdc5e13d7-9c54-4e4b-9260-a60d9802c5f5_495x552.png" width="495" height="552" 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srcset="https://substackcdn.com/image/fetch/$s_!0NTE!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fdc5e13d7-9c54-4e4b-9260-a60d9802c5f5_495x552.png 424w, https://substackcdn.com/image/fetch/$s_!0NTE!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fdc5e13d7-9c54-4e4b-9260-a60d9802c5f5_495x552.png 848w, https://substackcdn.com/image/fetch/$s_!0NTE!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fdc5e13d7-9c54-4e4b-9260-a60d9802c5f5_495x552.png 1272w, https://substackcdn.com/image/fetch/$s_!0NTE!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fdc5e13d7-9c54-4e4b-9260-a60d9802c5f5_495x552.png 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Exceedingly simple. Water is pumped as needed to replenish and maintain the liquid level in the chamber. The electrodes are vibrated with a 0.5-SA electrical pulse which breaks 2(H20) ---&gt; 2H2 + 02. When the pressure reaches say 30-60 psi, you turn the key and go. You step on the pedal, you send more energy to the electrodes, and thus more vapour to the cylinders; i.e. fuel vapour on demand. You set the idle -max flow rate to get the most efficient use of power, and you&#8217;re off to the races.</p><p>In the BIG picture, your Free Energy is coming from the tap water, in an open system, as the latent energy in the water is enough to power the engine, and hence drive the alternator and whatever belt-driven accessories; AND the alternator is efficient enough to run the various electrical loads (10-20 amps), including the additional low current to run this vapour reaction. No extra batteries are required<em>.</em></p><div class="subscription-widget-wrap-editor" data-attrs="{&quot;url&quot;:&quot;https://www.revealedeye.com/subscribe?&quot;,&quot;text&quot;:&quot;Subscribe&quot;,&quot;language&quot;:&quot;en&quot;}" data-component-name="SubscribeWidgetToDOM"><div class="subscription-widget show-subscribe"><div class="preamble"><p class="cta-caption">This Substack is reader-supported. To receive new posts and support my work, consider becoming a free or paid subscriber.</p></div><form class="subscription-widget-subscribe"><input type="email" class="email-input" name="email" placeholder="Type your email&#8230;" tabindex="-1"><input type="submit" class="button primary" value="Subscribe"><div class="fake-input-wrapper"><div class="fake-input"></div><div class="fake-button"></div></div></form></div></div><h3>Step-by-Step Construction </h3><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!5YjT!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!5YjT!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif 424w, https://substackcdn.com/image/fetch/$s_!5YjT!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif 848w, https://substackcdn.com/image/fetch/$s_!5YjT!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif 1272w, https://substackcdn.com/image/fetch/$s_!5YjT!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!5YjT!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif" width="599" height="792" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/b3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:792,&quot;width&quot;:599,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!5YjT!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif 424w, https://substackcdn.com/image/fetch/$s_!5YjT!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif 848w, https://substackcdn.com/image/fetch/$s_!5YjT!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif 1272w, https://substackcdn.com/image/fetch/$s_!5YjT!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3021fa5-3dfb-417a-bca9-ae2b5b121143_599x792.gif 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p><strong>Overview</strong><em>- Here is the suggested sequence of steps:</em></p><p>0. Install the CHT (or EGT) gauge and measure your current operating temp range (gasoline), for comparison.</p><p>1. Build &amp; test the controller to verify the correct pulse output.</p><p>2. Build the reaction chamber &amp; test it w. the controller (i.e pressure out).</p><p>3. Install the tank, controller, chamber, and pressure fittings.</p><p>4. Run engine &amp; Adjust the control circuit as necessary for best performance.</p><p>5. Install the stainless steel valves and get the pistons/cylinders coated with ceramic.</p><p>6. Coat the exhaust system with ceramic without the catalytic converter OR let it rust out and replace the whole dang thang with stainless steel pipe sections.</p><p><strong>You Will Need</strong></p><p>- plastic water tank with pump and level sensor.</p><p>- control circuit, wiring, connectors, and epoxy.</p><p>- reaction chamber with electrodes and fittings.</p><p>- 3/8&#8221; stainless steel flex-tubing, fittings and clamps.</p><p>- carb/FI vapor-pressure fitting kit. - pressure, CHT (or EGT), &amp; level gauges.</p><p>- stainless steel valves.</p><p>- copper mesh junction.</p><p>- ceramic surface treatment for cylinders &amp; pistons.</p><p>- stainless steel or ceramic treated exhaust assembly.</p><p><strong>Basics tools</strong></p><p>- drill, screwdriver and pliers</p><p>- hole cutter</p><p>- wire-wrap, solder-iron and clippers</p><p>- DVM and oscilloscope.</p><p><strong>Reaction Chamber</strong></p><p>Construct as shown in Figure 2. Use a section of 4&#8221; PVC waste pipe with a threaded screw-cap fitting on one end and a standard end-cap at the other.</p><p>Make sure to drill-and-epoxy or tap threads through the PVC components for all fittings. Set and control the water level in the chamber so that it well submerses the pipe electrodes; yet leave some headroom to build up the hydrogen/oxygen vapour pressure. Use stainless steel wires inside the chamber or otherwise use a protective coating; use insulated wires outside. Ensure that the epoxy perfects the seal, or otherwise lay down a bead of water-proof silicone that can hold pressure.</p><p>The screw fitting may require soft silicone sealant, or a gasket; its purpose is to hold pressure and allow periodic inspection of the electrodes. No leaks, no problems. Make sure you get a symmetric 1-5mm gap between the 2 stainless steel pipes. The referenced literature suggests that the closer to 1mm you get, the better. You WILL want to get your chamber level sensor verified BEFORE you epoxy the cap on.</p><p>Make your solder connections at the wire/electrode junctions nice, smooth, and solid; then apply a water-proof coating, e.g. the epoxy you use for joining the pipes to the screw cap.</p><p>This epoxy must be water-proof and be capable of holding metal to plastic under pressure.</p><p>You WILL want to get your chamber level sensor verified BEFORE you epoxy the cap on.</p><p><strong>Control Circuit </strong></p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!3b1z!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!3b1z!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif 424w, https://substackcdn.com/image/fetch/$s_!3b1z!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif 848w, https://substackcdn.com/image/fetch/$s_!3b1z!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif 1272w, https://substackcdn.com/image/fetch/$s_!3b1z!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!3b1z!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif" width="593" height="792" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:792,&quot;width&quot;:593,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!3b1z!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif 424w, https://substackcdn.com/image/fetch/$s_!3b1z!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif 848w, https://substackcdn.com/image/fetch/$s_!3b1z!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif 1272w, https://substackcdn.com/image/fetch/$s_!3b1z!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F35fe2eb7-7b89-4ce9-8963-c22ce4559387_593x792.gif 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>Figures 3 &amp; 4 show a simple circuit to control and drive this mini-system. You are going to make a &#8216;square-pulse&#8217; signal that &#8216;plays&#8217; the electrodes like a tuning fork; which you can watch on an oscilloscope. The premise given by the literature is:</p><p>The faster you want do go down the road, the &#8216;fatter&#8217; you make the pulses going into the reaction chamber. Duty cycle will vary with the throttle in the vicinity of </p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!gEle!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!gEle!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif 424w, https://substackcdn.com/image/fetch/$s_!gEle!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif 848w, https://substackcdn.com/image/fetch/$s_!gEle!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif 1272w, https://substackcdn.com/image/fetch/$s_!gEle!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!gEle!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif" width="1121" height="1542" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:1542,&quot;width&quot;:1121,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!gEle!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif 424w, https://substackcdn.com/image/fetch/$s_!gEle!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif 848w, https://substackcdn.com/image/fetch/$s_!gEle!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif 1272w, https://substackcdn.com/image/fetch/$s_!gEle!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F850d7109-76ee-4ae4-ac9a-32af44348ec6_1121x1542.gif 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>90% MARK 10% SPACE (OFF/ON).</p><p>There is nothing sacred about how the pulse waveform is generated; there are many ways to generate pulses, and the attached diagrams show a few. Figure 4 gives the NE555-circuit approach from the referenced patent. The output switching transistor must be rated for</p><p>1-5 amps @ I2VDC(in saturation).</p><p>Go with a plan that works for you or your friendly neighborhood technoid or mechanic, and go get all the circuit elements from your local electronics store, such as Radio-Shack or Circuits-R-Us, including the circuit board, IC sockets, and enclosure/box.</p><p>DigiKey has better selection, service, and knowledge; plus they have no minimum order crap. Be sure to use a circuit board with a built-in ground plane, and to accommodate room for mounting 2 or 3 of the gauges. Mounting the reaction chamber in the engine compartment will require running a stub to your pressure gauge where you can watch it.</p><div class="captioned-image-container"><figure><a class="image-link image2" target="_blank" href="https://substackcdn.com/image/fetch/$s_!Qe2i!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!Qe2i!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif 424w, https://substackcdn.com/image/fetch/$s_!Qe2i!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif 848w, https://substackcdn.com/image/fetch/$s_!Qe2i!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif 1272w, https://substackcdn.com/image/fetch/$s_!Qe2i!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!Qe2i!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif" width="84" height="77.53846153846153" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:120,&quot;width&quot;:130,&quot;resizeWidth&quot;:84,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!Qe2i!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif 424w, https://substackcdn.com/image/fetch/$s_!Qe2i!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif 848w, https://substackcdn.com/image/fetch/$s_!Qe2i!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif 1272w, https://substackcdn.com/image/fetch/$s_!Qe2i!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F3d43a03b-9618-460a-ab9d-bad4f9fc6b71_130x120.gif 1456w" sizes="100vw" loading="lazy"></picture><div></div></div></a></figure></div><p>You can easily make 30-gauge wire-wrap connections between the socket pins and through-hole discrete components having wire leads. Also make sure to get spec sheets on any IC you use. More details of the best circuits to use will be announced pending prototype testing. You WILL want to get your chamber level sensor verified BEFORE you epoxy the cap on.  </p><p class="button-wrapper" data-attrs="{&quot;url&quot;:&quot;https://www.revealedeye.com/subscribe?&quot;,&quot;text&quot;:&quot;Subscribe now&quot;,&quot;action&quot;:null,&quot;class&quot;:null}" data-component-name="ButtonCreateButton"><a class="button primary" href="https://www.revealedeye.com/subscribe?"><span>Subscribe now</span></a></p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!vrai!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!vrai!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif 424w, https://substackcdn.com/image/fetch/$s_!vrai!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif 848w, https://substackcdn.com/image/fetch/$s_!vrai!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif 1272w, https://substackcdn.com/image/fetch/$s_!vrai!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!vrai!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif" width="1121" height="1537" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:1537,&quot;width&quot;:1121,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!vrai!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif 424w, https://substackcdn.com/image/fetch/$s_!vrai!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif 848w, https://substackcdn.com/image/fetch/$s_!vrai!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif 1272w, https://substackcdn.com/image/fetch/$s_!vrai!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F857fb348-4be8-4ff3-a46d-781e96269ec5_1121x1537.gif 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p><strong>Throttle Control. </strong></p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!cEw7!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!cEw7!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif 424w, https://substackcdn.com/image/fetch/$s_!cEw7!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif 848w, https://substackcdn.com/image/fetch/$s_!cEw7!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif 1272w, https://substackcdn.com/image/fetch/$s_!cEw7!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!cEw7!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif" width="1121" height="1548" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:1548,&quot;width&quot;:1121,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!cEw7!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif 424w, https://substackcdn.com/image/fetch/$s_!cEw7!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif 848w, https://substackcdn.com/image/fetch/$s_!cEw7!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif 1272w, https://substackcdn.com/image/fetch/$s_!cEw7!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F44859f96-18ae-4da6-af09-a02853bcd79f_1121x1548.gif 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><p>If you have a throttle position sensor, you should be able to access the signal from the sensor itself OR from the computer connector. This signal is input to the circuit as the primary control (i.e. throttle level pulse width = vapour rate).</p><p>If you don&#8217;t have such a signal available, you will have to rig a rotary POT (variable resistor) to the gas linkage (i.e. coupled to something at the gas pedal or throttle cable running to the carb or Fl. If you make the attachment at the cart/Fl, be sure to use a POT that can handle the engine temp cycles. Don&#8217;t use a cheezy-cheapy POT; get one rated for long life and mechanical wear; mount it securely to something sturdy and stationary that will not fall apart when you step on the gas.</p><p>Control Range.</p><p>The full throttle RANGE (idle-max) MUST control the vapour rate, i.e. pulse-width (duty). The resistor values at the throttle signal must allow the throttle signal voltage, say 1-4 Volt swing, to drive the VAPOR RATE. You will be using this voltage swing to generate a 10% ON &#8216;square&#8217; pulse.</p><p>The patent implies using a &#8216;resonant&#8217; pulse in the 10-250 KHz frequency range; but it is not explicitly stated so. In this circuit, you will simply tune to whatever frequency makes the most efficient vapour conversion. You will have to get into the specs for each IC you use, to insure you connect the right pins to the right wires, to control the frequency and pulse width.</p><p>You can use spare sockets to try out different discrete component values. Just keep the ones that are spec-compatible in the circuit, and get the job done.</p><p>You crank up the throttle signal and put more electrical energy (fatter pulses) into the electrodes; verify you can get 10% duty on the scope (2 - 100 usec on the horizontal time-base). Your averaging DVM will display the 90%-I 0% DC voltage across the output transistor (Vce or Vds or Output to Ground). Set and connect DVM in the supply current and measure .5 - 5 amps, without blowing the DVM fuse. Now verify that you got everything you wanted.</p><p>Verify your wiring connections using your DVM as a continuity detector. Check your wiring 1 at a time and yellow line your final schematic as you go. You can best use board-mount miniature POTs for anything you want to set-and-forget. The LEDs are there to give you a quick visual check of normal vs abnormal operation of your new creation. You WILL want to get your chamber level sensor verified BEFORE you epoxy the cap on (see Figures 2 &amp; 4).</p><p>CARB/FI CONNECTION &#8211;</p><p>Figure 2 also shows that fittings are required to the carb/FI I. There are ready-made kits (such as by Impco) available for making your pressure fittings to the carburetor or fuel-injector as the case may be. You will necessarily be sealing the built in vents and making a 1-way air-intake.</p><p>The copper mesh comprises the inadvertent backfire&#8217; protection for the reaction chamber. Make sure that all vapor/duct junctions are air-tight and holding full pressure without leakage. Your new &#8216;system&#8217; is considered successful and properly adjusted when you get the full power range at lower temp and minimum vapor flow without blowing the pressure safety valve.</p><p><em>CHT (or EGT)</em>- Monitor your engine temp with the CHT (cylinder head temp) or EGT (exhaust gas temp) instead of your original engine temp indicator (if any). Your existing gauge is TOO SLOW for this application and will not warn you against overheating until after you have burnt something.</p><p>Make sure that your engine RUNS NO HOTTER than in the gasoline arrangement. VDO makes a CHT gauge with a platinum sensor that fits under your spark plug against the cylinder head (make sure it is REAL CLEAN before you reinstall your spark plug (as this is also an electrical ground).</p><p>ENGINE/EXHAUST TREATMENT &#8211;</p><p>Get the valves replaced with stainless steel ones AND get the pistons/cylinders ceramic-treated ASAP when you have successfully converted and run your new creation. Do not delay as these items WILL RUST, either by sheer use or by neglect (i.e. letting it sit). You could make max use of your current exhaust system by using it with your new deal until it rusts through, then have your mechanic or welder friend to fit a stainless steel exhaust pipe (no catalytic converter is required). But it could be ea$ier to send your existing exhaust system out for the ceramic treatment, and then simply re-attach it to the exhaust ports.</p><p>GENERAL</p><p>1. Do not discard or remove any of the old gasoline set up components, e.g. tank, carb/FI, catalytic converter, unless necessary. Better to always leave an easy way to revert back to something that at least runs, just in case. Some people are leaving their gasoline set up completely intact, and switching back and forth at will, just to have a backup plan.</p><p>2. Set your throttle circuit so that you get minimum vapour flow at IDLE, and maximum vapour flow at FULL POWER without blowing the pressure relief valve. In this way, you control how &#8216;lean&#8217; your mixture is by the strength of the pulse (i.e. &#8216;fatness&#8217; at the optimum pulse frequency).</p><p>3. If you just don&#8217;t get enough power (at any throttle setting), it means that you need to (1) change the pulse frequency, (2) change the gap between the electrodes, (3) change the size (bigger) electrodes, OR (4) make a higher output pulse voltage (last resort). Always use an output transistor, such as a MOSFET, that is rated for the voltage and current you need to get the job done. OK so you might have to play around with it some. Isn&#8217;t that where all the Fun is anyhow?</p><p>4. If you get ANY engine knock our loud combustions (not compensated by adjusting the timing), it means that you need to install an additional coil in the chamber, and drive the coil with an additional pulse signal (about 19 Hz on the .lsec time base) (see Figure 5). </p><div class="captioned-image-container"><figure><a class="image-link image2" target="_blank" href="https://substackcdn.com/image/fetch/$s_!fL4m!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!fL4m!,w_424,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif 424w, https://substackcdn.com/image/fetch/$s_!fL4m!,w_848,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif 848w, https://substackcdn.com/image/fetch/$s_!fL4m!,w_1272,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif 1272w, https://substackcdn.com/image/fetch/$s_!fL4m!,w_1456,c_limit,f_webp,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!fL4m!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif" width="712" height="125" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:125,&quot;width&quot;:712,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:null,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:null,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!fL4m!,w_424,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif 424w, https://substackcdn.com/image/fetch/$s_!fL4m!,w_848,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif 848w, https://substackcdn.com/image/fetch/$s_!fL4m!,w_1272,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif 1272w, https://substackcdn.com/image/fetch/$s_!fL4m!,w_1456,c_limit,f_auto,q_auto:good,fl_lossy/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F9d105b7f-97ce-4ff0-81da-38c6fea34c00_712x125.gif 1456w" sizes="100vw" loading="lazy"></picture><div></div></div></a></figure></div><p>Here,you will be slowing down the burn rate just enough so that the vapours burn throughout the power stroke of the piston. Be sure to include a board-mount POT to set the correct strength of this 2nd pulse signal into the coil. This is a stainless steel coil of about 1500 turns (thin wire) that you can arrange like a donut around the center pipe (but NOT touching either electrode), directly over the circular 1-5mm gap. You want NO KNOCKING at any power/throttle setting; smooth power only, but also no excess hydrogen leftover from the combustion.</p><p>5. Build the canister(s) as tall as you can without compromising your ability to mount them conveniently near the dash panel, or in the engine compartment, as the case may be. This way, you can always make the electrodes bigger, if necessary without undue hardship. Remember that anything in the engine compartment should be mounted in a bullet-proof, vibration and temperature tolerant fashion.</p><p>6. If you have to drill a through-hole for wiring or plumbing through metal, make sure to also install a grommet for protection against chafing. Always watch your chamber pressure range from</p><p><em>IDLE (15-25 psi) - FULL POWER (30-60 psi)</em>. Set your safety-pressure relief-valve to 75 psi and make sure it&#8217;s rated for much higher.</p><p>7. Shut OFF the power switch and pull over if there is any MALFUNCTION of the system. Your engine will last longest when it still develops FULL POWER+ at some minimum temperature that we are sure you can find, by leaning back the Royal Vapour Flow and/or by making use of the water-vapour cooling technique (see Figure 7). Keep good mpg performance records, and periodic maintenance/inspection. Keep it clean; save some money; clean the air; heal the planet; happy motoring; tell a friend; enjoy your freedom and self-empowerment; haul ass.</p><p>8. There lacks documented material for perfecting this vapour system through a fuel injector; there may be some details you will discover on your own as working prototypes progress. For example, you may be restricted to inject the hydrogen/oxygen vapour WITHOUT ANY water vapour, as it may rust the injectors. If engine temp and CHT is a problem, then you will want to re-think your plan, e.g. ceramic-coating the injectors. There is always &#8216;replacing the Fl system with a Carb&#8217;.</p><p>9. If you install the water-vapour system (for lower operating temp/stress), you will want to lean the mixture (vapour/air) for minimum vapour flow rate to achieve any given throttle position (idle - max). Make sure that you get a minimum flow for IDLE an a modestly sufficient flow for MAX, that does the cooling job without killing the combustion.</p><p>10. If you cannot find stainless steel pipe combinations that yield the 1-5mm gap, you can always regress back to alternating plates of +/- electrodes.</p><p>11. If you are concerned about the water freezing in your system, you can (a) add some 98% isopropyl alcohol and re-adjust the pulse frequency accordingly; or (b) install some electric heating coils.</p><p>12. Do not let ANYONE ever compromise your dream, your freedom, your independence, your truth.</p><p><strong>References</strong></p><ol><li><p><em>Stephen Chambers &#8216;Apparatus for Producing Orthohydrogen and/or Parahydrogen&#8217; US Patent 6126794, uspto.gov</em></p></li><li><p><em>Stanley Meyer &#8216;Method for the Production of a Fuel Gas&#8217; US Patent 4936961, uspto. gov</em></p></li><li><p><em>Creative Science &amp; Research, &#8216;Fuel From Water&#8217;, fuelless.com</em></p></li><li><p><em>Carl Celia &#8216;A Water-Fuelled Car&#8217; Nexus Magazine Oct-Nov 1996</em></p></li><li><p><em>Peter Lindemann &#8216;Where in the World is All the Free Energy&#8217;, free-energy.cc</em></p></li><li><p><em>George Wiseman &#8216;The Gas-Saver and HyCO Series&#8217; eagle-research.com</em></p></li><li><p><em>C. Michael Holler &#8216;The Dromedary Newsletter&#8217; and &#8216;SuperCarb Techniques&#8217;</em></p></li><li><p><em>Stephen Chambers &#8216;Prototype Vapor Fuel System&#8217;, xogen.com</em></p></li></ol><p><strong>Disclaimer: </strong>The author of this document assumes no liability for the use or misuse if this information, which is made available as public-domain information, for the purposes of education, ecology, health, well-being, freedom, liberty, and pursuit of happiness.</p><div><hr></div><div class="community-chat" data-attrs="{&quot;url&quot;:&quot;https://open.substack.com/pub/revealedeye/chat?utm_source=chat_embed&quot;,&quot;subdomain&quot;:&quot;revealedeye&quot;,&quot;pub&quot;:{&quot;id&quot;:941403,&quot;name&quot;:&quot;RevealedEye&quot;,&quot;author_name&quot;:&quot;RevealedEye&quot;,&quot;author_photo_url&quot;:&quot;https://substackcdn.com/image/fetch/$s_!HuHP!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fbucketeer-e05bbc84-baa3-437e-9518-adb32be77984.s3.amazonaws.com%2Fpublic%2Fimages%2F4ca260d4-8699-4037-a80e-838f224f9b5e_640x640.jpeg&quot;}}" data-component-name="CommunityChatRenderPlaceholder"></div><div class="subscription-widget-wrap-editor" data-attrs="{&quot;url&quot;:&quot;https://www.revealedeye.com/subscribe?&quot;,&quot;text&quot;:&quot;Subscribe&quot;,&quot;language&quot;:&quot;en&quot;}" data-component-name="SubscribeWidgetToDOM"><div class="subscription-widget show-subscribe"><div class="preamble"><p class="cta-caption">This Substack is reader-supported. 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