{"id":25,"date":"2002-02-22T15:15:29","date_gmt":"2002-02-22T23:15:29","guid":{"rendered":"http:\/\/www.ogre.nu\/wp\/?p=25"},"modified":"2025-02-10T23:18:26","modified_gmt":"2025-02-11T07:18:26","slug":"hyperbolic-baby","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=25","title":{"rendered":"hyperbolic, baby!"},"content":{"rendered":"<p>Pretty things:  <a href=\"http:\/\/www.plunk.org\/~hatch\/HyperbolicTesselations\/\">hyperbolic planar tesselations<\/a> by Don Hatch.  Presented in the conformal <i>Poincar&eacute; disc<\/i> mapping, which is the most common; it&#8217;s analogous to stereographic projection of a sphere.  Another favorite mapping is the half-plane, which has no analogue that I can think of.<\/p>\n<p>But I&#8217;ve never seen a conformal &lsquo;Mercator&rsquo; mapping, preserving one line.  Instead of a circle, the infinite hyperbolic plane would become an infintely long but finitely wide strip; Escher&#8217;s <i>Circle Limit<\/i>, transformed through such a projection, would make a nifty frieze (or runner rug).<\/p>\n<p>Sadly I&#8217;ve yet to find enough information (clear enough for my lazy mind) on <i>doing stuff<\/i> in hyperbolic space.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pretty things: hyperbolic planar tesselations by Don Hatch. Presented in the conformal Poincar&eacute; disc mapping, which is the most common; it&#8217;s analogous to stereographic projection of a sphere. Another favorite mapping is the half-plane, which has no analogue that I &hellip; <a href=\"https:\/\/bendwavy.org\/wp\/?p=25\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16,12],"tags":[],"class_list":["post-25","post","type-post","status-publish","format-standard","hentry","category-eye-candy","category-mathematics"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/25","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\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=25"}],"version-history":[{"count":3,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/25\/revisions"}],"predecessor-version":[{"id":4685,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/25\/revisions\/4685"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}