{"id":3300,"date":"2023-08-26T09:52:01","date_gmt":"2023-08-26T13:52:01","guid":{"rendered":"https:\/\/josmfs.net\/?p=3300"},"modified":"2024-04-05T13:07:39","modified_gmt":"2024-04-05T17:07:39","slug":"pythagorean-parabola-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/08\/26\/pythagorean-parabola-puzzle\/","title":{"rendered":"Pythagorean Parabola Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3298\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/08\/Pythagorean-Parablola-Fig2.jpg\" alt=\"\" width=\"200\" height=\"224\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/08\/Pythagorean-Parablola-Fig2.jpg 401w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/08\/Pythagorean-Parablola-Fig2-269x300.jpg 269w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>Since the changes in Twitter (now X), I have not been able to see the posts, not being a subscriber.\u00a0 But I noticed poking around that some twitter accounts were still viewable.\u00a0 However, like some demented aging octogenarian they had lost track of time, that is, instead of being sorted with the most recent post first, they showed a random scattering of posts from different times.\u00a0 So a current post could be right next to one several years ago.\u00a0 That is what I discovered with the now defunct MathsMonday site.\u00a0 I found a <a href=\"https:\/\/twitter.com\/MEIMaths\/status\/1391679408310784003\">post<\/a> from 10 May 2021 that I had not seen before, namely,<\/p>\n<p>\u201cThe points A and B are on the curve y = x<sup>2<\/sup> such that AOB is a right angle.\u00a0 What points A and B will give the smallest possible area for the triangle AOB?\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Pythagorean-Parablola-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/08\/Pythagorean-Parabola-230820.pdf\">Pythagorean Parabola Puzzle<\/a> for solution.<\/p>\n<p><strong>(Update 9\/1\/2023) Elegant Alternative Solution by Oscar Rojas<br \/>\n<\/strong><!--more--><\/p>\n<p>I found a solution using plain geometry and elemental algebra:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-large wp-image-3304\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/09\/Pythagorean-Parabola-Rojas-1024x503.png\" alt=\"\" width=\"625\" height=\"307\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/09\/Pythagorean-Parabola-Rojas-1024x503.png 1024w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/09\/Pythagorean-Parabola-Rojas-300x147.png 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/09\/Pythagorean-Parabola-Rojas-768x377.png 768w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/09\/Pythagorean-Parabola-Rojas-624x306.png 624w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/09\/Pythagorean-Parabola-Rojas.png 1210w\" sizes=\"auto, (max-width: 625px) 100vw, 625px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Since the changes in Twitter (now X), I have not been able to see the posts, not being a subscriber.\u00a0 But I noticed poking around that some twitter accounts were still viewable.\u00a0 However, like some demented aging octogenarian they had lost track of time, that is, instead of being sorted with the most recent post [&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":[40,32,213],"class_list":["post-3300","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-analytic-geometry","tag-calculus","tag-mathsmonday"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3300","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=3300"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3300\/revisions"}],"predecessor-version":[{"id":3526,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3300\/revisions\/3526"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3300"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3300"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3300"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}