{"id":4989,"date":"2015-08-29T15:43:22","date_gmt":"2015-08-29T14:43:22","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/ajb\/?p=4989"},"modified":"2015-08-29T15:43:22","modified_gmt":"2015-08-29T14:43:22","slug":"on-a-variant-of-rhodonea-curves","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/ajb\/2015\/08\/29\/on-a-variant-of-rhodonea-curves\/","title":{"rendered":"On a variant of rhodonea curves"},"content":{"rendered":"<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Rose_%28mathematics%29\" title=\"wiki\" target=\"_blank\">Rhodonea curves<\/a> or rose curves are plots of a polar equation of the form<br \/>\n\\(r = \\cos(k \\theta)\\).<\/p>\n<p>If we specialise to equations with<\/p>\n<p>\\(k= \\frac{n}{d}\\)<\/p>\n<p>for n and d integers (&gt;0), then we have plots of the form below. In the table n runs across and d down<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/scontent-lhr3-1.xx.fbcdn.net\/hphotos-xtp1\/v\/t1.0-9\/11895952_743111285815473_2301743374238846187_n.jpg?oh=3eb7ecf29346da70831198a3e265be3c&amp;oe=56811D62\" alt=\"\" \/><\/p>\n<p>Now, just for fun I considered a slight variant of this given by<\/p>\n<p>\\(r =  \\cos( k \\theta) &#8211; k\\)<\/p>\n<p>The plots are  as follows<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/scontent-lhr3-1.xx.fbcdn.net\/hphotos-xpf1\/v\/t1.0-9\/11898635_743111269148808_3607869161005147967_n.jpg?oh=88ef5fa5cf579369574800acb8d31437&amp;oe=5679B9F7\" alt=\"\" \/><\/p>\n<p>For another variant I considered<\/p>\n<p>\\(r =  \\cos( k \\theta) &#8211; k^{-1}\\)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/scontent-lhr3-1.xx.fbcdn.net\/hphotos-xpf1\/v\/t1.0-9\/11933448_743111279148807_4808558024327278912_n.jpg?oh=c4f4ae40ba5614e1efb0962430120cd2&amp;oe=56839CC6\" alt=\"\" \/><\/p>\n<p>I am not sure there is anything mathematically deep here, I just like the images and classify this as some basic mathematical art.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rhodonea curves or rose curves are plots of a polar equation of the form \\(r = \\cos(k \\theta)\\). If we specialise to equations with \\(k= \\frac{n}{d}\\) for n and d integers (&gt;0), then we have plots of the form below. In the table n runs across and d down Now, just for fun I considered &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/ajb\/2015\/08\/29\/on-a-variant-of-rhodonea-curves\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">On a variant of rhodonea curves<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,9],"tags":[],"class_list":["post-4989","post","type-post","status-publish","format-standard","hentry","category-general-mathematics","category-mathematical-art"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/4989","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/comments?post=4989"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/4989\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/media?parent=4989"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/categories?post=4989"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/tags?post=4989"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}