{"id":2069,"date":"2008-07-08T20:43:14","date_gmt":"2008-07-09T04:43:14","guid":{"rendered":"http:\/\/www.ogre.nu\/wp\/?p=2069"},"modified":"2008-07-08T20:43:14","modified_gmt":"2008-07-09T04:43:14","slug":"looking-for-sanity-checks-in-an-insane-world","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=2069","title":{"rendered":"looking for sanity checks in an insane world"},"content":{"rendered":"<p>Some years ago, using basic theorems of hyperbolic trigonometry, I worked out a conformal representation of the hyperbolic plane which preserves one line &ndash; analogous to the Mercator projection of the sphere, a conformal map which preserves one great circle.  (At that time, I had a mistaken notion of the Mercator rule, so I didn&#8217;t know until later how strong the analogy is.)  Unfortunately I&#8217;ve utterly forgotten how I worked it out; and I need to try again; because, now that I&#8217;ve learned enough hyperbolic <em>analytic<\/em> geometry to try making some pictures, there appears to be a flaw in my formula.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Some years ago, using basic theorems of hyperbolic trigonometry, I worked out a conformal representation of the hyperbolic plane which preserves one line &ndash; analogous to the Mercator projection of the sphere, a conformal map which preserves one great circle. &hellip; <a href=\"https:\/\/bendwavy.org\/wp\/?p=2069\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-2069","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/2069","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2069"}],"version-history":[{"count":0,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/2069\/revisions"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2069"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2069"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2069"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}