{"id":39,"date":"2013-05-23T17:53:57","date_gmt":"2013-05-23T17:53:57","guid":{"rendered":"http:\/\/homepages.se.edu\/cmoretti\/?page_id=39"},"modified":"2019-10-28T15:42:41","modified_gmt":"2019-10-28T15:42:41","slug":"mathematica-notebooks-geometry","status":"publish","type":"page","link":"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-geometry\/","title":{"rendered":"Dr. Moretti&#8217;s Mathematica Notebooks &#8211; Geometry"},"content":{"rendered":"<h1 style=\"text-align: center\">Mathematica Notebooks for Geometry<\/h1>\n<p><span style=\"text-decoration: underline\">Important Note:<\/span>\u00a0The links for the notebooks open a new window or tab with a Google Drive page &#8211; the current settings for our homepages won&#8217;t allow me to host mathematica notebooks locally.<\/p>\n<h2>Triangle Centers<\/h2>\n<p>This notebook lets you explore different notions of the center of a triangle &#8211; the centroid, circumcenter, and so on.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/trianglecenters.jpg\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter  wp-image-75\" alt=\"finding centers of a triangle\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/trianglecenters-1024x940.jpg\" width=\"512\" height=\"470\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/trianglecenters-1024x940.jpg 1024w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/trianglecenters-300x275.jpg 300w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/trianglecenters-768x705.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/trianglecenters.jpg 1416w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImS1NPN0dIM3AxNWs&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my geometry notebooks from Google Drive<\/a><\/p>\n<h2>Projective Graphing<\/h2>\n<p>This notebook lets you graph an affine curve and find the &#8220;points at infinity&#8221; that correspond to the projective completion (and their multiplicity).<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/projectivegraphing.jpg\"><img decoding=\"async\" class=\"aligncenter  wp-image-76\" alt=\"projective graphing\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/projectivegraphing-1024x997.jpg\" width=\"512\" height=\"498\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/projectivegraphing-1024x997.jpg 1024w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/projectivegraphing-300x292.jpg 300w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/projectivegraphing-768x748.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/projectivegraphing.jpg 1366w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImS1NPN0dIM3AxNWs&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my geometry notebooks from Google Drive<\/a><\/p>\n<h2>Circles Tangent to 3 Lines<\/h2>\n<p>This manipulation finds the circles which are tangent to 3 given lines. \u00a0Most of the time the equations of the circles will be fairly ugly even if the equations of the lines themselves are nice (the algebra underlying the problem involves solving a system of quadratic equations).<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/threecircles.jpg\"><img decoding=\"async\" class=\"aligncenter  wp-image-77\" alt=\"circles tangent to 3 lines\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/threecircles-1024x732.jpg\" width=\"512\" height=\"366\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImS1NPN0dIM3AxNWs&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my geometry notebooks from Google Drive<\/a><\/p>\n<h2>Conic Sections<\/h2>\n<p>This manipulation lets you experiment with the focus-directrix definition of a conic section. \u00a0You can move the focus, the points defining the directrix, and the eccentricity of the conic.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/conics.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-78\" alt=\"conic sections\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/conics-886x1024.jpg\" width=\"443\" height=\"512\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/conics-886x1024.jpg 886w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/conics-260x300.jpg 260w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/conics-768x887.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/conics.jpg 1260w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImS1NPN0dIM3AxNWs&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my geometry notebooks from Google Drive<\/a><\/p>\n<h2>Estimating Pi<\/h2>\n<p>This manipulation shows one of the original ways to estimate the constant\u00a0\u03c0 \u00a0&#8211; by thinking of it as the area of the unit circle and then estimating the area of the circle using inscribed and circumscribed polygons. \u00a0The inscribed polygon areas are always under the true are and the circumscribed polygon areas are always over &#8211; but as the number of sides of the polygon grows, both areas converge on the single value of \u03c0.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingpi.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-79\" alt=\"estimating pi\" src=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingpi-738x1024.jpg\" width=\"369\" height=\"512\" srcset=\"https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingpi-738x1024.jpg 738w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingpi-216x300.jpg 216w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingpi-768x1065.jpg 768w, https:\/\/www.se.edu\/cmoretti\/wp-content\/uploads\/sites\/81\/2013\/05\/estimatingpi.jpg 966w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/a><\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/drive.google.com\/folderview?id=0BxSwUt0i0mImS1NPN0dIM3AxNWs&amp;usp=sharing\" target=\"_blank\" rel=\"noopener noreferrer\">Download this or other of my geometry notebooks from Google Drive<\/a><\/p>\n<p><a title=\"Mathematica Notebook Library\" href=\"http:\/\/homepages.se.edu\/cmoretti\/main\/mathematicalibrarymain\/\">Back to my Mathematica Library<\/a><\/p>\n<p><a title=\"Dr. Christopher Moretti\u2019s Homepage\" href=\"http:\/\/homepages.se.edu\/cmoretti\/\">Back to my homepage<\/a><\/p>\n<p><a title=\"Southeastern main page\" href=\"http:\/\/www.se.edu\">Back to the Southeastern Main Page<\/a>\t\t<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mathematica Notebooks for Geometry Important Note:\u00a0The links for the notebooks open a new window or tab with a Google Drive page &#8211; the current settings for our homepages won&#8217;t allow [&hellip;]<\/p>\n","protected":false},"author":24,"featured_media":0,"parent":19,"menu_order":0,"comment_status":"open","ping_status":"open","template":"page-templates\/page-with-sidebar.php","meta":{"footnotes":""},"class_list":["post-39","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Dr. Moretti&#039;s Mathematica Notebooks - Geometry -<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.se.edu\/cmoretti\/main\/mathematicalibrarymain\/mathematica-notebooks-geometry\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Dr. Moretti&#039;s Mathematica Notebooks - Geometry -\" \/>\n<meta property=\"og:description\" content=\"Mathematica Notebooks for Geometry Important Note:\u00a0The links for the notebooks open a new window or tab with a Google Drive page &#8211; 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