{"id":67,"date":"2008-02-14T01:08:40","date_gmt":"2008-02-14T00:08:40","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=67"},"modified":"2010-02-01T12:05:30","modified_gmt":"2010-02-01T11:05:30","slug":"the-polar-equations-for-hearts-and-flowers","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=67","title":{"rendered":"The Polar Equations for Hearts and Flowers"},"content":{"rendered":"<p>For my final Valentine&#8217;s day post I thought I would share a minor discovery I made while playing around with the polar equation<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/walkingrandomly.com\/wp-content\/ql-cache\/quicklatex.com-3689da15a0eff6a7272241ff178efdd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#105;&#103;&#104;&#116;&#32;&#114;&#61;&#49;&#45;&#92;&#115;&#105;&#110;&#40;&#110;&#92;&#116;&#104;&#101;&#116;&#97;&#41;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"117\" style=\"vertical-align: -4px;\"\/><\/p>\n<p>When n=1 the graph of this equation is a rotated cardioid which is exactly what I expected after reading the Math World page on the <a href=\"http:\/\/mathworld.wolfram.com\/HeartCurve.html\">Heart Curve<\/a>.<\/p>\n<p style=\"text-align: center\"><img decoding=\"async\" src=\"\/images\/mathematica\/cardioid.gif\" \/><\/p>\n<p>While playing around with the parameters I discovered that if you increase the value of n (to 10 say) then the resulting plot looks like a flower.<\/p>\n<p style=\"text-align: center\"><img decoding=\"async\" src=\"\/images\/mathematica\/card_flower.gif\" \/><\/p>\n<p>Very apt considering the time of year I think.  If you would like to play with this equation yourself then feel free to try my very simple <a href=\"http:\/\/demonstrations.wolfram.com\/ThePolarEquationsOfHeartsAndFlowers\/\">Wolfram Demonstration which was published today<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>For my final Valentine&#8217;s day post I thought I would share a minor discovery I made while playing around with the polar equation When n=1 the graph of this equation is a rotated cardioid which is exactly what I expected after reading the Math World page on the Heart Curve. While playing around with the [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[6,8,18],"tags":[],"class_list":["post-67","post","type-post","status-publish","format-standard","hentry","category-general-math","category-mathematica","category-wolfram-demonstrations"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3swhs-15","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/67","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=67"}],"version-history":[{"count":1,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/67\/revisions"}],"predecessor-version":[{"id":2274,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/67\/revisions\/2274"}],"wp:attachment":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=67"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=67"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}