{"version":"1.0","type":"rich","title":"Rose Curve","description":"Roses specified by the sinusoid \r\nr=cos(k * theta) for various rational numbered values of the angular frequency k=n\/d. \r\nRoses specified by r=sin(k * theta ) are rotations of these roses by one-quarter period of the sinusoid in a counter-clockwise direction about the pole (origin). For proper mathematical analysis, k must be expressed in irreducible form.","author_name":"rupertxrussell","author_url":"https:\/\/turtletoy.net\/user\/rupertxrussell","provider_name":"Turtletoy","provider_url":"https:\/\/turtletoy.net\/","license":{"fullName":"The MIT License","shortName":"MIT","url":"https:\/\/opensource.org\/licenses\/MIT"},"thumbnail_url":"https:\/\/turtletoy.net\/thumbnail\/68dd165364.jpg","thumbnail_width":512,"thumbnail_height":512,"html":"<iframe src=\"https:\/\/turtletoy.net\/embed\/68dd165364\" width=\"1025px\" height=\"554px\" style=\"max-width: 100%; border: 0\" sandbox=\"allow-scripts allow-top-navigation allow-top-navigation-by-user-activation allow-forms allow-popups allow-same-origin\"><\/iframe>","width":1025,"height":554}