{"id":3063,"date":"2015-04-22T08:14:38","date_gmt":"2015-04-22T15:14:38","guid":{"rendered":"http:\/\/theoryofeverything.org\/MyToE\/?p=3063"},"modified":"2015-04-22T08:14:38","modified_gmt":"2015-04-22T15:14:38","slug":"pascal-triangle-and-mod-2-9-sierpinski-maps","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2015\/04\/22\/pascal-triangle-and-mod-2-9-sierpinski-maps\/","title":{"rendered":"Pascal Triangle and Mod 2-9 Sierpinski Maps"},"content":{"rendered":"<p>I decided to take a quick dive into an interesting idea from <a href=\"http:\/\/naturalnumber.com\">Peter Williams<\/a> related to how the modulus of binomial numbers are related to the Pascal Triangle. I&#8217;ve added this to the VisibLie_E8 viewer as well.<\/p>\n<p>Here is a screenshot:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3142\" rel=\"attachment wp-att-3142\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/Pascal-snap.png\" alt=\"Pascal-snap\" width=\"500\" class=\"alignnone size-full wp-image-3142\" \/><\/a><\/p>\n<p>Here is the code I wrote to produce the output below:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3130\" rel=\"attachment wp-att-3130\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/Pascal-Sierpinski-Mods-32.png\" alt=\"Pascal-Sierpinski Mods-3\" width=\"500\" class=\"alignnone size-full wp-image-3130\" \/><\/a><\/p>\n<p>Mod 9:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3131\" rel=\"attachment wp-att-3131\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/Pascal-Binary-Mod9-e.png\" alt=\"Pascal-Binary-Mod9-e\" width=\"500\" class=\"alignnone size-full wp-image-3131\" \/><\/a><\/p>\n<p>Mod 8:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3132\" rel=\"attachment wp-att-3132\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/Pascal-Binary-Mod8-e.png\" alt=\"Pascal-Binary-Mod8-e\" width=\"500\" class=\"alignnone size-full wp-image-3132\" \/><\/a><\/p>\n<p>Mod 7:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3133\" rel=\"attachment wp-att-3133\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/Pascal-Binary-Mod7-e.png\" alt=\"Pascal-Binary-Mod7-e\" width=\"500\" class=\"alignnone size-full wp-image-3133\" \/><\/a><\/p>\n<p>Mod 6:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3134\" rel=\"attachment wp-att-3134\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/Pascal-Binary-Mod6-e.png\" alt=\"Pascal-Binary-Mod6-e\" width=\"500\" class=\"alignnone size-full wp-image-3134\" \/><\/a><\/p>\n<p>Mod 5:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3135\" rel=\"attachment wp-att-3135\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/Pascal-Binary-Mod5-e.png\" alt=\"Pascal-Binary-Mod5-e\" width=\"500\" class=\"alignnone size-full wp-image-3135\" \/><\/a><\/p>\n<p>Mod 4:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3136\" rel=\"attachment wp-att-3136\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/Pascal-Binary-Mod4-e.png\" alt=\"Pascal-Binary-Mod4-e\" width=\"500\" class=\"alignnone size-full wp-image-3136\" \/><\/a><\/p>\n<p>Mod 3:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3137\" rel=\"attachment wp-att-3137\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/Pascal-Binary-Mod3-e.png\" alt=\"Pascal-Binary-Mod3-e\" width=\"500\" class=\"alignnone size-full wp-image-3137\" \/><\/a><\/p>\n<p>Mod 2:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3138\" rel=\"attachment wp-att-3138\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/Pascal-Binary-Mod2-e.png\" alt=\"Pascal-Binary-Mod2-e\" width=\"500\" class=\"alignnone size-full wp-image-3138\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I decided to take a quick dive into an interesting idea from Peter Williams related to how the modulus of binomial numbers are related to the Pascal Triangle. I&#8217;ve added this to the VisibLie_E8 viewer as well. Here is a screenshot: Here is the code I wrote to produce the output below: Mod 9: Mod &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2015\/04\/22\/pascal-triangle-and-mod-2-9-sierpinski-maps\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Pascal Triangle and Mod 2-9 Sierpinski Maps<\/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":[3],"tags":[11,14,16],"class_list":["post-3063","post","type-post","status-publish","format-standard","hentry","category-physics","tag-2d","tag-math","tag-physics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/3063","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=3063"}],"version-history":[{"count":0,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/3063\/revisions"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=3063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=3063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=3063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}