{"id":20074,"date":"2013-05-28T21:55:43","date_gmt":"2013-05-28T21:55:43","guid":{"rendered":"http:\/\/thomasjpitts.co.uk\/wp\/?p=20074"},"modified":"2013-05-28T21:55:43","modified_gmt":"2013-05-28T21:55:43","slug":"geeky-maths-things-148-heptagonal-numbers","status":"publish","type":"post","link":"https:\/\/thomasjpitts.co.uk\/wordpress\/2013\/05\/28\/geeky-maths-things-148-heptagonal-numbers\/","title":{"rendered":"Geeky Maths Things: 148 – Heptagonal Numbers"},"content":{"rendered":"

Day 148 of my 365 project reminds me about heptagonal numbers.<\/p>\n

148 is a good example of a heptagonal number<\/a> because it fits two of the three heptagonal number categories: heptagonal numbers, centred heptagonal numbers and centred heptagonal primes.<\/p>\n

\"The<\/a>
The first five heptagonal numbers [via Wikipedia<\/a>]<\/figcaption><\/figure>
\nAs you can see, these numbers make heptagons<\/a>. The first few heptagonal numbers are 1,\u00a07,\u00a018,\u00a034,\u00a055,\u00a081,\u00a0112,\u00a0148… and are found using the formula\u00a0\"frac{5n^{2}-3n}{2}\".<\/p>\n

Centred heptagonal numbers are similar, except the heptagons grow around a central point. 148 is the second number to be in both the sequence of heptagonal numbers and centred heptagonal numbers.<\/p>\n

\"Centred<\/a>
Centred heptagonal number sample (figurate numbers), 8, 22, 43, 71 points. [via Wikipedia]<\/figcaption><\/figure>The first few centred heptagonal numbers are:\u00a01,\u00a08,\u00a022,\u00a043,\u00a071,\u00a0106,\u00a0148… Centred heptagonal numbers are of the form\u00a0\"frac{7n^{2}-7n+2}{2}\".<\/p>\n

 <\/p>\n

\"Enhanced<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"

Day 148 of my 365 project reminds me about heptagonal numbers. 148 is a good example of a heptagonal number because it fits two of the three heptagonal number categories: heptagonal numbers, centred heptagonal numbers and centred heptagonal primes. As you can see, these numbers make heptagons. The first few heptagonal numbers are 1,\u00a07,\u00a018,\u00a034,\u00a055,\u00a081,\u00a0112,\u00a0148… and […]<\/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":[18],"tags":[1409,1410,1909,2199,3251],"class_list":["post-20074","post","type-post","status-publish","format-standard","hentry","category-maths","tag-heptagon","tag-heptagonal-number","tag-math","tag-number-theory","tag-wikipedia","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-5dM","jetpack-related-posts":[],"builder_content":"","_links":{"self":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/20074","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=20074"}],"version-history":[{"count":0,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/20074\/revisions"}],"wp:attachment":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/media?parent=20074"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/categories?post=20074"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/tags?post=20074"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}