{"id":22323,"date":"2013-12-09T22:37:28","date_gmt":"2013-12-09T22:37:28","guid":{"rendered":"http:\/\/thomasjpitts.co.uk\/wp\/?p=22323"},"modified":"2013-12-09T22:37:28","modified_gmt":"2013-12-09T22:37:28","slug":"day-343-just-geeky-mathsness","status":"publish","type":"post","link":"https:\/\/thomasjpitts.co.uk\/wordpress\/2013\/12\/09\/day-343-just-geeky-mathsness\/","title":{"rendered":"Day 343: Just Geeky Mathsness"},"content":{"rendered":"<p>Nothing much happened today, but 343 is an interesting number in many ways.<\/p>\n<ul>\n<li>343 = 7<sup>3<\/sup><\/li>\n<li>343 is a\u00a0<a title=\"Day 289: Geeky Maths Things \u2013 Friedman Numbers\" href=\"http:\/\/thomasjpitts.co.uk\/wp\/2013\/10\/day-289-geeky-maths-things-friedman-numbers\/\">Friedman number<\/a>\u00a0since 343 = (3 + 4)<sup>3<\/sup>.<\/li>\n<li>It&#8217;s the only known example of x<sup>2<\/sup>+x+1 = y<sup>3<\/sup>, in this case, x=18, y=7.<\/li>\n<li>It is z in a triplet (x,y,z) such that x<sup>5<\/sup>\u00a0+ y<sup>2<\/sup>\u00a0= z<sup>3<\/sup>.<\/li>\n<li>The\u00a0<a class=\"zem_slink\" title=\"Speed of sound\" href=\"http:\/\/en.wikipedia.org\/wiki\/Speed_of_sound\" target=\"_blank\" rel=\"wikipedia\">speed of sound<\/a>\u00a0in dry air at\u00a020 \u00b0C is 343\u00a0m\/s.<\/li>\n<\/ul>\n<p>There aren&#8217;t many numbers I know that have such varied properties.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"zemanta-pixie\" style=\"margin-top: 10px; height: 15px;\"><a class=\"zemanta-pixie-a\" title=\"Enhanced by Zemanta\" href=\"http:\/\/www.zemanta.com\/?px\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"zemanta-pixie-img\" style=\"border: none; float: right;\" alt=\"Enhanced by Zemanta\" src=\"https:\/\/i0.wp.com\/img.zemanta.com\/zemified_e.png?w=1165\" \/><\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Nothing much happened today, but 343 is an interesting number in many ways. 343 = 73 343 is a\u00a0Friedman number\u00a0since 343 = (3 + 4)3. It&#8217;s the only known example of x2+x+1 = y3, in this case, x=18, y=7. It is z in a triplet (x,y,z) such that x5\u00a0+ y2\u00a0= z3. The\u00a0speed of sound\u00a0in dry [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[2,18],"tags":[149,812,1636,1801,1909,2523,2825,3038],"class_list":["post-22323","post","type-post","status-publish","format-standard","hentry","category-2","category-maths","tag-343-industries","tag-creative-director","tag-josh-holmes","tag-linkedin","tag-math","tag-recreation","tag-specific-numbers","tag-tomb-raider","has-post-title","has-post-date","has-post-category","has-post-tag","has-post-comment","has-post-author",""],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6OeSW-5O3","jetpack-related-posts":[],"builder_content":"","_links":{"self":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/22323","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/comments?post=22323"}],"version-history":[{"count":0,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/22323\/revisions"}],"wp:attachment":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/media?parent=22323"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/categories?post=22323"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/tags?post=22323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}