{"id":59,"date":"2008-02-14T01:11:24","date_gmt":"2008-02-14T00:11:24","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=59"},"modified":"2010-01-31T20:09:45","modified_gmt":"2010-01-31T19:09:45","slug":"the-valentines-equations","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=59","title":{"rendered":"The Valentine’s Equations"},"content":{"rendered":"

A couple of weeks ago I started thinking about Valentine’s day and, since I like equations that have interesting plots<\/a> so much, I wondered if I could find one that had a heart-shaped graph. A quick google search came up Wolfram Research’s Heart Surface<\/a> page.<\/p>\n

The main page described a couple of heart shaped algebraic surfaces<\/a> which looked nice but there were a few more on the Mathematica notebook that the page linked to. This notebook was rather old and included plots from old versions of Mathematica so on the train ride home I wrapped these equations in some Manipulate functions and sent the resulting demo to Wolfram. The result was published today on the Wolfram Demonstrations site<\/a>.<\/p>\n

\"heart<\/p>\n

Essentially all this demo does is use Mathematica’s ContourPlot3D function to plot the curves formed from the following equations and allow you to play with the results a bit.<\/p>\n

Nordstrand
\n\" \light -\frac{8}{45} x^2 z^3-y^2 z^3+\left(\frac{32 x^2}{9}+2<\/p>\n

Kuska<\/p>\n

\" \light -\frac{1}{10} x^2 z^3-y^2 z^3+\left(2 x^2+y^2+z^2-1\right)^3=0\"<\/p>\n

Taubin<\/p>\n

\" \light -x^2 z^3-\frac{9 y^2 z^3}{80}+\left(x^2+\frac{9<\/p>\n

Trott<\/p>\n

\" \light 320 \left(-x^2 z^3-\frac{9 y^2 z^3}{80}+\left(x^2+\frac{9<\/p>\n

Each equation is named after the person who first wrote it down (to my knowledge at least). It’s a simple demo but I hope you like it.<\/p>\n

Happy Valentine’s day.<\/p>\n","protected":false},"excerpt":{"rendered":"

A couple of weeks ago I started thinking about Valentine’s day and, since I like equations that have interesting plots so much, I wondered if I could find one that had a heart-shaped graph. A quick google search came up Wolfram Research’s Heart Surface page. The main page described a couple of heart shaped algebraic […]<\/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-59","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-X","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/59","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=59"}],"version-history":[{"count":2,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/59\/revisions"}],"predecessor-version":[{"id":2261,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/59\/revisions\/2261"}],"wp:attachment":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=59"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=59"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=59"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}