{"id":27668,"date":"2021-04-21T13:46:50","date_gmt":"2021-04-21T17:46:50","guid":{"rendered":"https:\/\/blog.carlrobitaille.org\/?p=27668"},"modified":"2021-04-21T14:07:02","modified_gmt":"2021-04-21T18:07:02","slug":"universal-parabolic-constant","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=27668","title":{"rendered":"Universal Parabolic Constant"},"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\">Everyone knows that all circles are similar. But did you know that all parabolas are similar?<br><br>The ratio of the red parabolic arc length and the blue focal parameter is<br>\u221a2 + log(1+\u221a2) = 2.29558&#8230;<br>for any parabola. This is the universal parabolic constant, the \u201c\u03c0 of parabolas\u201d. <a href=\"https:\/\/t.co\/JntitYWd7q\">pic.twitter.com\/JntitYWd7q<\/a><\/p>&mdash; Tam\u00e1s G\u00f6rbe (@TamasGorbe) <a href=\"https:\/\/twitter.com\/TamasGorbe\/status\/1246014582113492994?ref_src=twsrc%5Etfw\">April 3, 2020<\/a><\/blockquote><script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<\/div><\/figure>\n\n\n\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\">Pick uniformly distributed random points in a 6\u00d76 square. The average distance from the centre is<br>\u221a2 + log(1+\u221a2) = 2.29558&#8230;<br><br>It&#39;s the universal parabolic constant! How crazy is that\u203d Where is the parabola in this problem about random points in a square??? <a href=\"https:\/\/t.co\/AOnYPFNubR\">pic.twitter.com\/AOnYPFNubR<\/a><\/p>&mdash; Tam\u00e1s G\u00f6rbe (@TamasGorbe) <a href=\"https:\/\/twitter.com\/TamasGorbe\/status\/1246347195718262785?ref_src=twsrc%5Etfw\">April 4, 2020<\/a><\/blockquote><script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<\/div><\/figure>\n\n\n\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\">A final surprise! We can connect e, \u03c0, and the universal parabolic constant.<br><br>Plot the function y=exp(-x) over the positive x-axis and rotate the graph about the x-axis. The surface you get has area \u03c0 \u00d7 the parabolic constant. <a href=\"https:\/\/t.co\/jL13wWpRBv\">pic.twitter.com\/jL13wWpRBv<\/a><\/p>&mdash; Tam\u00e1s G\u00f6rbe (@TamasGorbe) <a href=\"https:\/\/twitter.com\/TamasGorbe\/status\/1246444915162148864?ref_src=twsrc%5Etfw\">April 4, 2020<\/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-27668","post","type-post","status-publish","format-standard","hentry","category-mathematiques"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/27668","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=27668"}],"version-history":[{"count":3,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/27668\/revisions"}],"predecessor-version":[{"id":27671,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/27668\/revisions\/27671"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=27668"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=27668"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=27668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}