{"id":105,"date":"2018-11-09T12:02:46","date_gmt":"2018-11-09T14:02:46","guid":{"rendered":"http:\/\/www.professores.uff.br\/vitorbalestro\/?page_id=105"},"modified":"2018-11-09T12:02:54","modified_gmt":"2018-11-09T14:02:54","slug":"discrete-cycloids-from-convex-symmetric-polygons","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/vitorbalestro\/publications\/discrete-cycloids-from-convex-symmetric-polygons\/","title":{"rendered":"Discrete cycloids from convex symmetric polygons"},"content":{"rendered":"<p id=\"h.p_QxIgHokcG3DU\" class=\"zfr3Q\">M. Craizer, R. Teixeira and V. Balestro, <strong>Discrete cycloids from convex symmetric polygons<\/strong>, Discrete and Computational Geometry 60(4), pp. 859-884, 2018. (<a class=\"dhtgD\" href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Farxiv.org%2Fabs%2F1702.00522&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNEF9oz2PJD6i2xlOX32-xEN09bFdQ\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv link<\/a>) (<a class=\"dhtgD\" href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%252Fs00454-017-9955-y&amp;sa=D&amp;sntz=1&amp;usg=AFQjCNExvulVYB32nNFTvvwxiQbHto1k1w\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a>)<\/p>\n<p id=\"h.p_oVZ7csaQG4fW\" class=\"zfr3Q\">Comments: A convex centrally symmetric polygon P in a plane naturally induces a discrete curvature concept for polygons whose sides are respectively parallel to P. Then, discrete evolutes are defined to be the polygon joining the centers of the &#8220;osculating&#8221; polygons, and discrete cycloids can be characterized as the eigenvectors of a certain linear transformation (which &#8220;plays the role&#8221; of a Sturm-Liouville operator). Interestingly, the discrete theory can be developed in a very analogous way to the continuous counterpart. This suggests that the discrete curvature considered is a very natural one.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>M. Craizer, R. Teixeira and V. Balestro, Discrete cycloids from convex symmetric polygons, Discrete and Computational Geometry 60(4), pp. 859-884, 2018. (arXiv link) (journal link) Comments: A convex centrally symmetric polygon P in a plane naturally induces a discrete curvature concept for polygons whose sides are respectively parallel to P. Then, discrete evolutes are defined [&hellip;]<\/p>\n","protected":false},"author":205,"featured_media":0,"parent":12,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[],"tags":[],"class_list":["post-105","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/105","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/users\/205"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/comments?post=105"}],"version-history":[{"count":1,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/105\/revisions"}],"predecessor-version":[{"id":107,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/105\/revisions\/107"}],"up":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/pages\/12"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/media?parent=105"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/categories?post=105"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/vitorbalestro\/wp-json\/wp\/v2\/tags?post=105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}