{"id":29127,"date":"2022-01-12T09:44:23","date_gmt":"2022-01-12T14:44:23","guid":{"rendered":"https:\/\/blog.carlrobitaille.org\/?p=29127"},"modified":"2022-01-12T09:44:26","modified_gmt":"2022-01-12T14:44:26","slug":"leibnizs-harmonic-triangle-1673","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=29127","title":{"rendered":"Leibniz\u2019s harmonic triangle (1673)"},"content":{"rendered":"\n<figure class=\"wp-block-embed is-type-rich is-provider-twitter wp-block-embed-twitter\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"twitter-tweet\" data-width=\"550\" data-dnt=\"true\"><p lang=\"en\" dir=\"ltr\">Leibniz\u2019s harmonic triangle (1673). Each little threesome of unit fractions satisfies the \u201cblue rule\u201d below. Leibniz used this construction to calculate certain infinite sums as telescoping series. E.g., the red sum is 1\/2 of the sum of reciprocal triangular numbers. <a href=\"https:\/\/t.co\/fDYO3mCLyn\">pic.twitter.com\/fDYO3mCLyn<\/a><\/p>&mdash; Steven Strogatz (@stevenstrogatz) <a href=\"https:\/\/twitter.com\/stevenstrogatz\/status\/1481267202389155847?ref_src=twsrc%5Etfw\">January 12, 2022<\/a><\/blockquote><script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-29127","post","type-post","status-publish","format-standard","hentry","category-mathematiques"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/29127","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=29127"}],"version-history":[{"count":1,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/29127\/revisions"}],"predecessor-version":[{"id":29128,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/29127\/revisions\/29128"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=29127"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=29127"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=29127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}