{"id":21787,"date":"2013-10-04T21:35:41","date_gmt":"2013-10-04T21:35:41","guid":{"rendered":"http:\/\/thomasjpitts.co.uk\/wp\/?p=21787"},"modified":"2013-10-04T21:35:41","modified_gmt":"2013-10-04T21:35:41","slug":"day-277-a-lazy-caterer","status":"publish","type":"post","link":"https:\/\/thomasjpitts.co.uk\/wordpress\/2013\/10\/04\/day-277-a-lazy-caterer\/","title":{"rendered":"Day 277: A Lazy Caterer"},"content":{"rendered":"<p>The <a class=\"zem_slink\" title=\"Lazy caterer's sequence\" href=\"http:\/\/en.wikipedia.org\/wiki\/Lazy_caterer%27s_sequence\" target=\"_blank\" rel=\"wikipedia\">lazy caterer&#8217;s sequence<\/a> is used to work out the maximum number of pieces of a <a class=\"zem_slink\" title=\"Pancake\" href=\"http:\/\/en.wikipedia.org\/wiki\/Pancake\" target=\"_blank\" rel=\"wikipedia\">pancake<\/a> or pizza (anything circular) that can be made with a given number of straight cuts.<\/p>\n<p>3 cuts can create 6 pieces if all cuts meet at a single point, but 7 if they don&#8217;t.<\/p>\n<p>It isn&#8217;t actually called the lazy caterer&#8217;s sequence at all &#8211; it is really the central <a class=\"zem_slink\" title=\"Polygonal number\" href=\"http:\/\/en.wikipedia.org\/wiki\/Polygonal_number\" target=\"_blank\" rel=\"wikipedia\">polygonal number<\/a> sequence. In three dimensions, it is known as\u00a0the <a class=\"zem_slink\" title=\"Cake number\" href=\"http:\/\/en.wikipedia.org\/wiki\/Cake_number\" target=\"_blank\" rel=\"wikipedia\">cake number<\/a>.<\/p>\n<p>Its formula is:<\/p>\n<p><img decoding=\"async\" alt=\"p=frac{n^2+n+2}{2}\" src=\"http:\/\/thomasjpitts.co.uk\/wp\/wp-content\/uploads\/2013\/10\/gif.latexpfracn^2+n+22\" align=\"absmiddle\" \/><\/p>\n<p><em>p<\/em> is the number of pieces, <em>n<\/em> is the number of cuts used.<\/p>\n<p>Sticking 23 in the equation provides:<\/p>\n<p><img decoding=\"async\" alt=\"p=frac{23^2+23+2}{2}=frac{529+23+2}{2}=frac{554}{2}=277\" src=\"http:\/\/thomasjpitts.co.uk\/wp\/wp-content\/uploads\/2013\/10\/gif.latexpfrac23^2+23+22frac529+23+22frac5542277\" align=\"absmiddle\" \/><\/p>\n<p>That then, is why I&#8217;m writing about it today.<\/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>The lazy caterer&#8217;s sequence is used to work out the maximum number of pieces of a pancake or pizza (anything circular) that can be made with a given number of straight cuts. 3 cuts can create 6 pieces if all cuts meet at a single point, but 7 if they don&#8217;t. It isn&#8217;t actually called [&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":[349,630,784,2281,2523],"class_list":["post-21787","post","type-post","status-publish","format-standard","hentry","category-2","category-maths","tag-baking-powder","tag-central-polygonal-numbers","tag-cook","tag-pancake","tag-recreation","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-5Fp","jetpack-related-posts":[],"builder_content":"","_links":{"self":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/21787","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=21787"}],"version-history":[{"count":0,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/21787\/revisions"}],"wp:attachment":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/media?parent=21787"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/categories?post=21787"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/tags?post=21787"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}