{"id":3338,"date":"2023-10-07T10:16:25","date_gmt":"2023-10-07T14:16:25","guid":{"rendered":"https:\/\/josmfs.net\/?p=3338"},"modified":"2023-10-07T10:16:25","modified_gmt":"2023-10-07T14:16:25","slug":"elliptical-medians-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/10\/07\/elliptical-medians-problem\/","title":{"rendered":"Elliptical Medians Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3336\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/10\/Elliptical-Medians-Fig2.jpg\" alt=\"\" width=\"200\" height=\"112\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/10\/Elliptical-Medians-Fig2.jpg 406w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/10\/Elliptical-Medians-Fig2-300x168.jpg 300w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>This is a tantalizing problem from the 1977 <em>Crux Mathematicorum<\/em>.<\/p>\n<p><strong>\u201c278<\/strong>. <em>Proposed by W.A. McWorter, Jr., The Ohio State University.<\/em><\/p>\n<p>If each of the medians of a triangle is extended beyond the sides of the triangle to 4\/3 its length, show that the three new points formed and the vertices of the triangle all lie on an ellipse.\u201d<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/10\/Elliptical-Medians-Puzzle-210901.pdf\">Elliptical Medians Problem<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a tantalizing problem from the 1977 Crux Mathematicorum. \u201c278. Proposed by W.A. McWorter, Jr., The Ohio State University. If each of the medians of a triangle is extended beyond the sides of the triangle to 4\/3 its length, show that the three new points formed and the vertices of the triangle all lie [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[212,13],"class_list":["post-3338","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-crux-mathematicorum","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3338","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=3338"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3338\/revisions"}],"predecessor-version":[{"id":3339,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3338\/revisions\/3339"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3338"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3338"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3338"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}