{"id":1282,"date":"2013-06-15T10:32:57","date_gmt":"2013-06-15T17:32:57","guid":{"rendered":"http:\/\/theoryofeverything.org\/MyToE\/?p=1282"},"modified":"2017-10-01T11:54:50","modified_gmt":"2017-10-01T18:54:50","slug":"connecting-the-octonion-fano-plane-to-the-atomic-elements","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2013\/06\/15\/connecting-the-octonion-fano-plane-to-the-atomic-elements\/","title":{"rendered":"Connecting the Octonion Fano Plane to the Atomic Elements"},"content":{"rendered":"<p>There are <a href=\"https:\/\/en.wikipedia.org\/wiki\/Fano_plane\" title=\"Fano plane\">28 octonion Fano plane triangles<\/a> that correspond directly to the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Bitangents_of_a_quartic\" title=\"Trott curve bitangents\">28 Trott quartic curve bitangents<\/a>. These bitangents are directly related to the Legendre functions used in the Shroedinger spherical harmonic electron orbital probability densities. Shown below is a graphic of these overlaid onto the n=5, l=2, m=1 element, which is assigned to <a href=\"https:\/\/en.wikipedia.org\/wiki\/File:Stowe-Janet-Scerri_PeriodicTable.svg\" title=\"Stowe-Janet-Scerri periodic table\">gold (Au)<\/a>. When using an algorithm based on the <a href=\"https:\/\/en.wikipedia.org\/wiki\/E8_%28mathematics%29\" title=\"E8\">E8 positive algebra root assignments<\/a>, the &#8220;flipped&#8221; Fano plane has E8 algebra root number 79 (the atomic number of Au) and split real even group number of 228 (in Clifford\/Pascal triangle order). For more information, please see the complete list of <a href=\"http:\/\/theoryofeverything.org\/MyToE\/?p=1232\" title=\"Fano inices\">integrated Fano indices here<\/a> with <a href=\"http:\/\/theoryofeverything.org\/MyToE\/?p=1258\" title=\"explanation\">full explanation of the layout here<\/a>.<\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=1298\" rel=\"attachment wp-att-1298\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2013\/06\/FanoLegendre.jpg\" alt=\"FanoLegendre\" width=\"500\" class=\"alignnone size-full wp-image-1298\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>There are 28 octonion Fano plane triangles that correspond directly to the 28 Trott quartic curve bitangents. These bitangents are directly related to the Legendre functions used in the Shroedinger spherical harmonic electron orbital probability densities. Shown below is a graphic of these overlaid onto the n=5, l=2, m=1 element, which is assigned to gold &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2013\/06\/15\/connecting-the-octonion-fano-plane-to-the-atomic-elements\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Connecting the Octonion Fano Plane to the Atomic Elements<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[24,19,20,25],"class_list":["post-1282","post","type-post","status-publish","format-standard","hentry","category-personal","tag-chemistry","tag-fano","tag-octonion","tag-periodic-table"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/1282","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/comments?post=1282"}],"version-history":[{"count":1,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/1282\/revisions"}],"predecessor-version":[{"id":4645,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/1282\/revisions\/4645"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=1282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=1282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=1282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}