{"id":3686,"date":"2009-09-22T03:00:23","date_gmt":"2009-09-22T08:00:23","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/swansont\/?p=3686"},"modified":"2009-09-22T03:00:23","modified_gmt":"2009-09-22T08:00:23","slug":"touch-my-monkey","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/swansont\/archives\/3686","title":{"rendered":"Touch My Monkey"},"content":{"rendered":"<p><a href=\"http:\/\/plus.maths.org\/issue52\/features\/gomboc\/index.html?nl=0\">The story of the G\u00f6mb\u00f6c<\/a><\/p>\n<blockquote><p>To give it its full mathematical description, a G\u00f6mb\u00f6c is a three-dimensional, convex and homogeneous object with exactly one stable point of equilibrium and one unstable point of equilibrium. Requiring it to be homogeneous amounts to saying that you&#8217;re not allowed to cheat: the material from which the G\u00f6mb\u00f6c is made has to be uniform throughout, so you&#8217;re not allowed to use weights, as those found in roly-poly toys, or other irregularities to get the G\u00f6mb\u00f6c to self-right. Convexity means that the G\u00f6mb\u00f6c is not allowed to bulge inwards, in other words, the straight line connecting any two points on the G\u00f6mb\u00f6c has to lie entirely within the G\u00f6mb\u00f6c. It&#8217;s easy to create a non-convex shape with one stable and one unstable equilibrium point, hence the restriction to convexity.<\/p><\/blockquote>\n<p>I have this mental image of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Sprockets_(Saturday_Night_Live)\">Dieter<\/a> describing the G\u00f6mb\u00f6c.  I don&#8217;t know why.<\/p>\n<p><em>Your three-dimensional, convex homogeneity has grown tiresome.  Now is the time on Sprockets vhen ve dance!<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The story of the G\u00f6mb\u00f6c To give it its full mathematical description, a G\u00f6mb\u00f6c is a three-dimensional, convex and homogeneous object with exactly one stable point of equilibrium and one unstable point of equilibrium. Requiring it to be homogeneous amounts &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/swansont\/archives\/3686\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,35,39],"tags":[],"class_list":["post-3686","post","type-post","status-publish","format-standard","hentry","category-math","category-other-science","category-physics"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/posts\/3686","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/comments?post=3686"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/posts\/3686\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/media?parent=3686"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/categories?post=3686"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/tags?post=3686"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}