{"id":2326,"date":"2010-02-10T13:43:44","date_gmt":"2010-02-10T12:43:44","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=2326"},"modified":"2011-02-14T18:44:58","modified_gmt":"2011-02-14T17:44:58","slug":"a-little-mathematics-for-valentines-day","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=2326","title":{"rendered":"A little mathematics for Valentine’s day"},"content":{"rendered":"

This is not a serious post but then mathematics doesn’t have to be serious all the time does it?\u00a0 Ever wondered what the equation of a 3D heart looks like?\u00a0 An old post of mine<\/a> will help you find the answer using Mathematica.\u00a0 Click on the image for more details (and a demonstration that you can run using the free Mathematica player<\/a>).<\/p>\n

\"math<\/a><\/p>\n

I don’t save all of my love for Mathematica though. I’ve got some for MATLAB<\/a> too:<\/p>\n

%code to plot a heart shape in MATLAB\r\n%set up mesh\r\nn=100;\r\nx=linspace(-3,3,n);\r\ny=linspace(-3,3,n);\r\nz=linspace(-3,3,n);\r\n[X,Y,Z]=ndgrid(x,y,z);\r\n%Compute function at every point in mesh\r\nF=320 * ((-X.^2 .* Z.^3 -9.*Y.^2.*Z.^3\/80) + (X.^2 + 9.* Y.^2\/4 + Z.^2-1).^3);\r\n%generate plot\r\nisosurface(F,0)\r\nview([-67.5 2]);\r\n<\/pre>\n
Did you know that the equation for a heart (or a cardioid<\/a> if you want to get technical) is very similar to the equation for a flower?\u00a0 The polar equation<\/a> you need is\u00a0 \"\" and you get a rotated cardioid for n=1.\u00a0 Change n to 6 and you get a flower.\u00a0 Let’s use the free maths package, SAGE<\/a>, this time.<\/p>\n
First, define the function:<\/p>\n
def eqn(x,n):\r\n    return(1-sin(n*x))\r\n<\/pre>\n
then plot it for n=1<\/p>\n
polar_plot(eqn(x,1), (x,-pi, pi),aspect_ratio=1,axes=False)\r\n<\/pre>\n
\"SAGE
\nand for n=7<\/p>\n
polar_plot(eqn(x,7), (x,-pi, pi),aspect_ratio=1,axes=False)\r\n<\/pre>\n
\"SAGE<\/p>\n
Back to Mathematica and the Wolfram Demonstrations project.  We have a Valentine’s version of the traditional Tangram puzzle<\/a>.<\/p>\n
\"Broken<\/a><\/p>\n
Feel free to let me know of any other Valentine’s math that you discover, puzzles<\/a>, fractals<\/a> or equations<\/a>, it’s all good :)<\/p>\n
Update Feb 14th 2011<\/strong><\/p>\n
Mariano Beguerisse D\u00edaz sent me some MATLAB code that uses a variation on the standard mandelbrot and I turned it into the movie below.\u00a0 His original code is in the comments section<\/p>\n
<\/object><\/p>\n","protected":false},"excerpt":{"rendered":"
This is not a serious post but then mathematics doesn’t have to be serious all the time does it?\u00a0 Ever wondered what the equation of a 3D heart looks like?\u00a0 An old post of mine will help you find the answer using Mathematica.\u00a0 Click on the image for more details (and a demonstration that you […]<\/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],"tags":[],"class_list":["post-2326","post","type-post","status-publish","format-standard","hentry","category-general-math"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3swhs-Bw","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/2326","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=2326"}],"version-history":[{"count":9,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/2326\/revisions"}],"predecessor-version":[{"id":3213,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/2326\/revisions\/3213"}],"wp:attachment":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}