{"id":234592,"date":"2016-06-21T02:00:00","date_gmt":"2016-06-20T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=cf1845d7bdd113bbe878a4a25ca4f9c5"},"modified":"2016-06-21T02:00:00","modified_gmt":"2016-06-20T23:00:00","slug":"yet-another-encounter-with-the-golden-ratio-balancing-laminar-bodies-on-the-edge","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=234592","title":{"rendered":"Yet another encounter with the golden ratio: balancing laminar bodies on the edge"},"content":{"rendered":"<p>If one removes a regular even sided polygon from a larger self-similar polygon then the excised<br \/>\npolygon can be balanced on the edge provided the ratio of the sides of the larger to the smaller<br \/>\npolygon is the golden ratio. Such an excision can be carried out in two ways: (i) vertex excision,<br \/>\nwhere the vertices of the two polygons coincide; and (ii) mid-side excision, where the mid points of<br \/>\nthe edges of two polygons coincide. We also show why such an exercise with an odd sided polygon does<br \/>\nnot yield a golden ratio. We briefly discuss the case of the circle which is a limiting case of a<br \/>\nregular polygon with an infinitely large number of sides. The results when generalised to other<br \/>\ndimensions lead to an interesting pattern of equations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If one removes a regular even sided polygon from a larger self-similar polygon then the excised<br \/>\npolygon can be balanced on the edge provided the ratio of the sides of the larger to the smaller<br \/>\npolygon is the golden ratio. Such an excision can be carr&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-234592","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/234592","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=234592"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/234592\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=234592"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=234592"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=234592"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}