{"id":1224,"date":"2019-08-26T15:07:39","date_gmt":"2019-08-26T19:07:39","guid":{"rendered":"http:\/\/josmfs.net\/?p=1224"},"modified":"2024-04-10T15:21:30","modified_gmt":"2024-04-10T19:21:30","slug":"mountain-houses-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/08\/26\/mountain-houses-problem\/","title":{"rendered":"Mountain Houses Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-1222\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/08\/Mountain-Houses-Problem-Fig2.jpg\" alt=\"\" width=\"202\" height=\"177\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/08\/Mountain-Houses-Problem-Fig2.jpg 301w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/08\/Mountain-Houses-Problem-Fig2-300x263.jpg 300w\" sizes=\"auto, (max-width: 202px) 100vw, 202px\" \/>It is always fascinating to look at problems from the past. This one, given by Thomas Whiting himself, is over 200 years old from Whiting\u2019s 1798 <em>Mathematical, Geometrical, and Philosophical Delights<\/em>:<\/p>\n<p>\u201c<strong>Question 2, by <em>T. W. from Davison\u2019s Repository<\/em>.<\/strong><br \/>\nThere are two houses, one at the top of a lofty mountain, and the other at the bottom; they are both in the latitude of 45\u00b0, and the inhabitants of the summit of the mountain, are carried by the earth\u2019s diurnal rotation, one mile an hour more than those at the foot.<\/p>\n<p>Required the height of the mountain, supposing the earth a sphere, whose radius is 3982 miles.\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Mountain-Houses-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/08\/Mountain-Houses-Problem-190805.pdf\">Mountain Houses Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is always fascinating to look at problems from the past. This one, given by Thomas Whiting himself, is over 200 years old from Whiting\u2019s 1798 Mathematical, Geometrical, and Philosophical Delights: \u201cQuestion 2, by T. W. from Davison\u2019s Repository. There are two houses, one at the top of a lofty mountain, and the other at [&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":[157,41],"class_list":["post-1224","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-thomas-whiting","tag-trigonometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1224","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=1224"}],"version-history":[{"count":5,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1224\/revisions"}],"predecessor-version":[{"id":3809,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1224\/revisions\/3809"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}