{"id":3270,"date":"2023-08-05T11:44:37","date_gmt":"2023-08-05T15:44:37","guid":{"rendered":"https:\/\/josmfs.net\/?p=3270"},"modified":"2024-04-05T13:22:37","modified_gmt":"2024-04-05T17:22:37","slug":"square-in-a-quarter-circle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/08\/05\/square-in-a-quarter-circle\/","title":{"rendered":"Square In A Quarter Circle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3269\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/08\/Square-in-Quarter-Cirlce-Fig2.jpg\" alt=\"\" width=\"200\" height=\"228\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/08\/Square-in-Quarter-Cirlce-Fig2.jpg 407w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/08\/Square-in-Quarter-Cirlce-Fig2-264x300.jpg 264w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>Another <a href=\"https:\/\/mindyourdecisions.com\/blog\/2021\/12\/07\/square-in-a-quarter-circle\/\">puzzle<\/a> by Presh Talwalkar.<\/p>\n<p>\u201cThanks to John H. for the suggestion!<\/p>\n<p>A square is inscribed in a quarter circle such that the outer vertices are on the arc of the quarter circle. If the quarter circle has a radius equal to 1, what is the area of the square?<\/p>\n<p>I am told this was given to 7th grade students (ages 12-13), and I think it is a very challenging problem for that age group. In fact I think it is a good problem for any geometry student.\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Square-in-Quarter-Circle-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/08\/Square-In-Quarter-Circle-220530.pdf\">Square in Quarter Circle<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Another puzzle by Presh Talwalkar. \u201cThanks to John H. for the suggestion! A square is inscribed in a quarter circle such that the outer vertices are on the arc of the quarter circle. If the quarter circle has a radius equal to 1, what is the area of the square? I am told this was [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[13,17],"class_list":["post-3270","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-plane-geometry","tag-presh-talwalkar"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3270","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=3270"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3270\/revisions"}],"predecessor-version":[{"id":3530,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3270\/revisions\/3530"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3270"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3270"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3270"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}