{"id":791,"date":"2019-03-24T20:01:14","date_gmt":"2019-03-25T00:01:14","guid":{"rendered":"http:\/\/josmfs.net\/?p=791"},"modified":"2024-04-14T11:22:17","modified_gmt":"2024-04-14T15:22:17","slug":"regiomontanus-1471-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/03\/24\/regiomontanus-1471-problem\/","title":{"rendered":"Regiomontanus 1471 Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3868\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Regiomontanus-1471-Prob-Fig2.jpg\" alt=\"\" width=\"301\" height=\"137\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Regiomontanus-1471-Prob-Fig2.jpg 601w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Regiomontanus-1471-Prob-Fig2-300x137.jpg 300w\" sizes=\"auto, (max-width: 301px) 100vw, 301px\" \/>This is an old problem I had seen before. Here is David Wells\u2019s rendition:<\/p>\n<p>\u201cJohannes M\u00fcller, named Regiomontanus after the Latin translation of K\u00f6rnigsberg, his city of birth, later made famous by Euler, proposed this problem in 1471. \u2026 it is usually put in this form \u2026: <strong>From what distance will a statue on a plinth appear largest to the eye [of a mouse!]?<\/strong> If we approach too close, the statue appears foreshortened, but from a distance it is simply small.\u201d<\/p>\n<p>I have added height numbers in feet for concreteness (as well as the mouse qualification, since the angles are measured from ground level). So the problem is to find the distance x such that the angle is maximal.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Regiomontanus-Prob-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/03\/Regiomontanus-1471-Problem-190324.pdf\">Regiomontanus 1471 Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is an old problem I had seen before. Here is David Wells\u2019s rendition: \u201cJohannes M\u00fcller, named Regiomontanus after the Latin translation of K\u00f6rnigsberg, his city of birth, later made famous by Euler, proposed this problem in 1471. \u2026 it is usually put in this form \u2026: From what distance will a statue on 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":[32,115,13],"class_list":["post-791","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-calculus","tag-david-wells","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/791","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=791"}],"version-history":[{"count":6,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/791\/revisions"}],"predecessor-version":[{"id":3870,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/791\/revisions\/3870"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=791"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=791"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}