{"id":28,"date":"2013-09-15T14:39:17","date_gmt":"2013-09-15T12:39:17","guid":{"rendered":"http:\/\/wp.berndt-schwerdtfeger.de\/?p=28"},"modified":"2021-10-15T00:24:50","modified_gmt":"2021-10-14T22:24:50","slug":"invariants-of-curves","status":"publish","type":"post","link":"https:\/\/berndt-schwerdtfeger.de\/?p=28","title":{"rendered":"Invariants of curves"},"content":{"rendered":"<p>Plane curves of 2. order (conic sections) treated by their invariants.<!--more--><\/p>\n<p>The article <a title=\"Invariants of curves of second order\" href=\"https:\/\/berndt-schwerdtfeger.de\/?page_id=75#c2\">Invariants of curves of second order<\/a> treats conic sections as algebraic curves by their invariants. <\/p>\n<p>Determining the invariants of curves of second order<br \/>\na<sub>11<\/sub>x<sup>2<\/sup> +2a<sub>12<\/sub>xy + a<sub>22<\/sub>y<sup>2<\/sup> + 2<sub>13<\/sub>x +2a<sub>23<\/sub>y + a<sub>33<\/sub> = 0<br \/>\nfrom the coefficients $a<sub>ik<\/sub>$ of the equation is a well known task.<br \/>\nWe derive formulas for the invariants following an elementary high school<br \/>\ncourse developed by Freudenthal and Heinrich 50 years ago.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Plane curves of 2. order (conic sections) treated by their invariants.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[3],"tags":[],"class_list":["post-28","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/posts\/28","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=28"}],"version-history":[{"count":4,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/posts\/28\/revisions"}],"predecessor-version":[{"id":149,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/posts\/28\/revisions\/149"}],"wp:attachment":[{"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=28"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=28"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}