{"id":19715,"date":"2019-12-16T09:45:12","date_gmt":"2019-12-16T14:45:12","guid":{"rendered":"https:\/\/blog.carlrobitaille.org\/?p=19715"},"modified":"2019-12-16T09:45:15","modified_gmt":"2019-12-16T14:45:15","slug":"osgood-curves","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=19715","title":{"rendered":"Osgood curves"},"content":{"rendered":"\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Osgood_curve\">Osgood curves<\/a><\/p>\n\n\n\n<figure class=\"wp-block-embed-twitter wp-block-embed is-type-rich is-provider-twitter\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"twitter-tweet\" data-width=\"550\" data-dnt=\"true\"><p lang=\"en\" dir=\"ltr\">There is no injective space-filling curve. However, there do exist injective curves with nonzero area. These are called Osgood curves<a href=\"https:\/\/t.co\/ezeQejes8n\">https:\/\/t.co\/ezeQejes8n<\/a> <a href=\"https:\/\/t.co\/h8tBSiwECj\">pic.twitter.com\/h8tBSiwECj<\/a><\/p>&mdash; Akiva Weinberger (@akivaw) <a href=\"https:\/\/twitter.com\/akivaw\/status\/1206343211226161153?ref_src=twsrc%5Etfw\">December 15, 2019<\/a><\/blockquote><script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Osgood curves<\/p>\n","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-19715","post","type-post","status-publish","format-standard","hentry","category-mathematiques"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/19715","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=19715"}],"version-history":[{"count":1,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/19715\/revisions"}],"predecessor-version":[{"id":19716,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/19715\/revisions\/19716"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=19715"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=19715"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=19715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}