{"id":2066,"date":"2021-03-20T09:08:26","date_gmt":"2021-03-20T13:08:26","guid":{"rendered":"https:\/\/josmfs.net\/?p=2066"},"modified":"2021-09-22T12:01:55","modified_gmt":"2021-09-22T16:01:55","slug":"equitable-slice-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/03\/20\/equitable-slice-problem\/","title":{"rendered":"Equitable Slice Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2064\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/03\/Equitable-Slice-Fig2.jpg\" alt=\"\" width=\"249\" height=\"174\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/03\/Equitable-Slice-Fig2.jpg 500w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/03\/Equitable-Slice-Fig2-300x210.jpg 300w\" sizes=\"auto, (max-width: 249px) 100vw, 249px\" \/>This is another Brainteaser from the <em>Quantum<\/em> math magazine .<\/p>\n<p>\u201cHow can a polygonal line BDEFG be drawn in a triangle ABC so that the five triangles obtained have the same area?\u201d<\/p>\n<p>I found this problem rather challenging, especially when I first tried to solve it analytically (using hyperbolas).\u00a0 Eventually I arrived at a procedure that would accomplish the result. (revised)<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/09\/Equitable-Slice-Problem-210922rev.pdf\">Equitable Slice Problem<\/a>\u00a0 (revised)<\/p>\n<p><strong>(Update 9\/22\/2021) <\/strong>\u00a0I goofed.\u00a0 I erroneously and foolishly thought <em>Quantum<\/em> had not solved the problem.\u00a0 Upon a closer reading I see what they were getting at and revised the posting.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is another Brainteaser from the Quantum math magazine . \u201cHow can a polygonal line BDEFG be drawn in a triangle ABC so that the five triangles obtained have the same area?\u201d I found this problem rather challenging, especially when I first tried to solve it analytically (using hyperbolas).\u00a0 Eventually I arrived at a procedure [&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":[13,194],"class_list":["post-2066","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-plane-geometry","tag-quantum-magazine"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2066","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=2066"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2066\/revisions"}],"predecessor-version":[{"id":2389,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2066\/revisions\/2389"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2066"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2066"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2066"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}