{"id":2183,"date":"2014-09-01T15:37:47","date_gmt":"2014-09-01T19:37:47","guid":{"rendered":"http:\/\/blog.carlrobitaille.org\/2014\/09\/01\/videotitle-3\/"},"modified":"2018-11-12T15:06:42","modified_gmt":"2018-11-12T20:06:42","slug":"a-sunflower-at-infinity","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=2183","title":{"rendered":"A sunflower at infinity"},"content":{"rendered":"

Google+ reshared post<\/b><\/p>\n

A sunflower at infinity<\/b><\/p>\n

This picture by +<\/span>Roice Nelson<\/a><\/span> shows the ‘view at infinity’ of a honeycomb in hyperbolic space.<\/p>\n

A honeycomb<\/b> is a way of chopping space into polyhedra.\u00a0 For example, we can chop ordinary 3d space into cubes.\u00a0 This is called the {4,3,4} honeycomb<\/b>.\u00a0 Why?<\/p>\n

\u2022 a square has 4 sides so its symbol is {4}<\/p>\n

\u2022 a cube has 3 squares meeting at each corner so its symbol is {4,3}<\/p>\n

\u2022 the cubical honeycomb has 4 cubes meeting at each edge so its symbol is {4,3,4}<\/p>\n

The picture here is a view of the {3,3,7} honeycomb<\/b>.\u00a0 This is defined in the same sort of way, but it doesn’t fit into ordinary Euclidean space.\u00a0 It fits into a curved space called hyperbolic space!<\/i>\u00a0\u00a0 The honeycomb extends forever, and it forms this pattern where it meets the ‘plane at infinity’ of hyperbolic space.<\/p>\n

For links to related pictures, visit my +<\/span>American Mathematical Society<\/a><\/span> blog Visual Insight<\/i>:<\/p>\n

http:\/\/blogs.ams.org\/visualinsight\/2014\/09\/01\/intersection-of-337-honeycomb-and-the-plane-at-infinity\/<\/a><\/p>\n

#geometry<\/a> \u00a0<\/p><\/blockquote>\n

\"\"<\/p>\n

Import\u00e9 de Google+<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Google+ reshared post A sunflower at infinity This picture by +Roice Nelson shows the ‘view at infinity’ of a honeycomb in hyperbolic space. A honeycomb is a way of chopping space into polyhedra.\u00a0 For example, we can chop ordinary 3d … Continue reading →<\/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":[1],"tags":[],"class_list":["post-2183","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/2183","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=2183"}],"version-history":[{"count":2,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/2183\/revisions"}],"predecessor-version":[{"id":2265,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/2183\/revisions\/2265"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2183"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2183"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}