{"id":5237,"date":"2018-12-31T11:24:14","date_gmt":"2018-12-31T18:24:14","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=5237"},"modified":"2019-01-02T10:02:49","modified_gmt":"2019-01-02T17:02:49","slug":"latest-paper-even-fibbinary-numbers-and-the-golden-ratio","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2018\/12\/31\/latest-paper-even-fibbinary-numbers-and-the-golden-ratio\/","title":{"rendered":"Latest paper: Even FibBinary Numbers and the Golden Ratio"},"content":{"rendered":"

Please see my latest paper here<\/a>.<\/p>\n

It adds information related to my previous blog post here<\/a>. <\/p>\n

Abstract: Previously, a determination of the relationship between the Natural numbers (N) and the n’th odd fibbinary number has been made using a relationship with the Golden ratio phi=(Sqrt[5]+1}\/2 and tau=1\/phi. Specifically, if the n’th odd fibbinary equates to the j’th N, then j=Floor[n phi^2 – 1]. This note documents the completion of the relationship for the even fibbinary numbers, such that if the n’th even fibbinary equates to the j’th N, then j=Floor[n phi]-1, starting at j=0 for n=1. Alternatively, starting at j=2 for n=1, then j=Floor[n phi + tau].<\/p>\n

Title:<\/strong>Even FibBinary Numbers and the Golden Ratio
\nAuthors:<\/strong> J Gregory Moxness<\/a>
\nComments:<\/strong> Dec 31 2018, 5 pages, 4 Figures.
\nSubjects:<\/strong> Combinatorics<\/p>\n

Below is a listing of the N integers represented by their 38 odd FibBinaries, along with the binary and Gray code Compositions.
\n\"\"<\/p>\n

Below is a listing of the first 63 N integers represented by their even FibBinaries, along with the binary and Gray code Compositions.
\n\"\"<\/p>\n

Code output examples:
\n\"\"<\/p>\n

Mathematica Code Snippets:
\n\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

Please see my latest paper here. It adds information related to my previous blog post here. Abstract: Previously, a determination of the relationship between the Natural numbers (N) and the n’th odd fibbinary number has been made using a relationship with the Golden ratio phi=(Sqrt[5]+1}\/2 and tau=1\/phi. Specifically, if the n’th odd fibbinary equates to … Continue reading Latest paper: Even FibBinary Numbers and the Golden Ratio<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[14],"class_list":["post-5237","post","type-post","status-publish","format-standard","hentry","category-physics","tag-math"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5237","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=5237"}],"version-history":[{"count":5,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5237\/revisions"}],"predecessor-version":[{"id":5261,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5237\/revisions\/5261"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=5237"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=5237"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=5237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}