{"id":1978,"date":"2007-04-28T19:45:36","date_gmt":"2007-04-29T03:45:36","guid":{"rendered":"http:\/\/www.ogre.nu\/wp\/?p=1978"},"modified":"2007-04-29T01:15:46","modified_gmt":"2007-04-29T09:15:46","slug":"fun-with-eigenvectors","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=1978","title":{"rendered":"fun with eigenvectors"},"content":{"rendered":"<p>After installing <a href=\"?p=1971\">that matrix math library<\/a>, I spent a week&#8217;s evenings pushing several abstract graphs through my &#8220;topological coordinates&#8221; program and finding, to my lack of complete shock, that none of them had any neat three-dimensional embedding.<\/p>\n<p>Then I tried a torus, and was again far from amazed that it didn&#8217;t work well either: all the vertices being equivalent under the inherent symmetries, there&#8217;s nothing to distinguish the &#8220;inner&#8221; from the &#8220;outer&#8221;.<\/p>\n<p>I cut a seam of the torus to make a cylinder, and then I got a surprise: the free ends curl in like an apple.  If anything I&#8217;d expect the opposite: the vertices along the edges, being topologically outermost, &#8220;ought&#8221; to curl outward.<\/p>\n<p align=center><img decoding=\"async\" src=\"\/doodle\/cylinder144.png\"><\/p>\n<p>One of these days I&#8217;ll get around to fullerenes.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>After installing that matrix math library, I spent a week&#8217;s evenings pushing several abstract graphs through my &#8220;topological coordinates&#8221; program and finding, to my lack of complete shock, that none of them had any neat three-dimensional embedding. Then I tried &hellip; <a href=\"https:\/\/bendwavy.org\/wp\/?p=1978\">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-1978","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/1978","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=1978"}],"version-history":[{"count":0,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/1978\/revisions"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1978"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1978"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}