{"id":911,"date":"2007-12-01T15:01:15","date_gmt":"2007-12-01T07:01:15","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=911"},"modified":"2013-07-12T18:34:23","modified_gmt":"2013-07-12T10:34:23","slug":"friday-math-movie-moebius-transformations-revealed","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-moebius-transformations-revealed-911","title":{"rendered":"Friday math movie: Moebius Transformations Revealed"},"content":{"rendered":"<p>This is cool.<\/p>\n<p>According to this <a href=\"https:\/\/en.wikipedia.org\/wiki\/M%C3%B6bius_transformation\">Wikipedia article<\/a>, a M&ouml;bius (or in anglicised form, 'Moebius') Transformation is the result of performing...<\/p>\n<blockquote>\n<p>a stereographic projection from a plane to a sphere, rotating and moving that sphere to a new arbitrary location and orientation, and performing a stereographic projection back to the plane.<\/p>\n<\/blockquote>\n<p>The mathematics involves matrices, determinants, transformational geometry (translation, rotation, dilation), complex numbers, group theory, conic sections (parabola, ellipse, etc) and iterations.<\/p>\n<p>Apart from all that, it is a nice visual piece with an appropriate soundtrack (a piano solo that I used to play, from Schumann's Kinderscenen, Op. 15, I) . The movie has been accessed almost a million times on YouTube. <\/p>\n<p>Enjoy.<\/p>\n<div class=\"videoBG\">\n<iframe title=\"YouTube video player\" width=\"480\" height=\"303\" src=\"https:\/\/www.youtube.com\/embed\/JX3VmDgiFnY\" frameborder=\"0\" allowfullscreen><\/iframe>\n<\/div>\n<p class=\"alt\">See the <a href=\"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-moebius-transformations-revealed-911#comments\" id=\"comms\">3 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This week's movie is a clever demonstration of the M&ouml;bius Transformation using computer animation.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[105],"tags":[127],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/911"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=911"}],"version-history":[{"count":0,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/911\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=911"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=911"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}