{"id":4401,"date":"2025-05-24T09:39:04","date_gmt":"2025-05-24T13:39:04","guid":{"rendered":"https:\/\/josmfs.net\/?p=4401"},"modified":"2025-05-24T09:39:04","modified_gmt":"2025-05-24T13:39:04","slug":"wittenbauers-parallelogram","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2025\/05\/24\/wittenbauers-parallelogram\/","title":{"rendered":"Wittenbauer\u2019s Parallelogram"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-4399\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/05\/Wittenbauers-Parallelogram-Fig2.jpg\" alt=\"\" width=\"201\" height=\"142\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/05\/Wittenbauers-Parallelogram-Fig2.jpg 404w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/05\/Wittenbauers-Parallelogram-Fig2-300x212.jpg 300w\" sizes=\"auto, (max-width: 201px) 100vw, 201px\" \/>This is a lovely <a href=\"https:\/\/www.futilitycloset.com\/2025\/05\/12\/wittenbauers-parallelogram\/\">result<\/a> from Futility Closet.<\/p>\n<p>\u201cDraw an arbitrary quadrilateral and divide each of its sides into three equal parts. Draw a line through adjacent points of trisection on either side of each vertex and you\u2019ll have a parallelogram.<\/p>\n<p>Discovered by Austrian engineer Ferdinand Wittenbauer.\u201d<\/p>\n<p>Find a proof.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/05\/Wittenbauers-Parallelogram-250513.pdf\">Wittenbauer\u2019s Parallelogram<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a lovely result from Futility Closet. \u201cDraw an arbitrary quadrilateral and divide each of its sides into three equal parts. Draw a line through adjacent points of trisection on either side of each vertex and you\u2019ll have a parallelogram. Discovered by Austrian engineer Ferdinand Wittenbauer.\u201d Find a proof. See Wittenbauer\u2019s Parallelogram for a [&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":[16,13],"class_list":["post-4401","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-futility-closet","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4401","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=4401"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4401\/revisions"}],"predecessor-version":[{"id":4402,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4401\/revisions\/4402"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4401"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}