{"id":3116,"date":"2023-03-18T10:11:31","date_gmt":"2023-03-18T14:11:31","guid":{"rendered":"https:\/\/josmfs.net\/?p=3116"},"modified":"2024-10-04T16:14:09","modified_gmt":"2024-10-04T20:14:09","slug":"max-angle-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/03\/18\/max-angle-puzzle\/","title":{"rendered":"Max Angle Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3113\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Fig2.jpg\" alt=\"\" width=\"250\" height=\"153\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Fig2.jpg 501w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Fig2-300x183.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/>Here is a familiar <a href=\"https:\/\/mathigon.org\/puzzles#2021\">puzzle<\/a> from the <em>Mathigon<\/em> Puzzle Calendars for 2021.<\/p>\n<p>\u201cGiven a line and two points A and B, which point P on the line forms the largest angle APB?\u201d<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Puzzle-230316.pdf\">Max Angle Puzzle<\/a><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3115 alignright\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Rugby-Ex.jpg\" alt=\"\" width=\"254\" height=\"143\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Rugby-Ex.jpg 336w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Rugby-Ex-300x169.jpg 300w\" sizes=\"auto, (max-width: 254px) 100vw, 254px\" \/>An excellent application of the solution to this puzzle can be found at <a href=\"https:\/\/www.youtube.com\/watch?v=rHdYv62F5fs\">Numberphile<\/a>, where Ben Sparks explains an optimal rugby goal-kicking strategy.<\/p>\n<p><strong>(Update 3\/23\/2023)\u00a0 Solution Construction<\/strong><\/p>\n<p><!--more--><\/p>\n<p>Oscar Rojas has provided a construction of the solution to the problem:<\/p>\n<p>&#8220;An interesting fact about the solution to this problem, is that such point P (where the circle is tangent to the line) can be found by a straightedge and compass construction.&#8221;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-3121\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Rojas-comment.jpg\" alt=\"\" width=\"1010\" height=\"557\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Rojas-comment.jpg 1010w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Rojas-comment-300x165.jpg 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Rojas-comment-768x424.jpg 768w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/03\/Max-Angle-Rojas-comment-624x344.jpg 624w\" sizes=\"auto, (max-width: 1010px) 100vw, 1010px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is a familiar puzzle from the Mathigon Puzzle Calendars for 2021. \u201cGiven a line and two points A and B, which point P on the line forms the largest angle APB?\u201d See the Max Angle Puzzle An excellent application of the solution to this puzzle can be found at Numberphile, where Ben Sparks explains [&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":[250,268,13],"class_list":["post-3116","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-mathigon","tag-numberphile","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3116","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=3116"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3116\/revisions"}],"predecessor-version":[{"id":3122,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3116\/revisions\/3122"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}