{"id":1466,"date":"2020-02-22T14:22:58","date_gmt":"2020-02-22T19:22:58","guid":{"rendered":"http:\/\/josmfs.net\/?p=1466"},"modified":"2020-02-23T08:52:55","modified_gmt":"2020-02-23T13:52:55","slug":"railroad-tie-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2020\/02\/22\/railroad-tie-problem\/","title":{"rendered":"Railroad Tie Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1467\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/02\/Railroad-Tie-Problem-Fig.jpg\" alt=\"\" height=\"208\" width=\"200\">This is a surprisingly challenging puzzle from the <em>Mathematics 2020<\/em> calendar.<\/p>\n<p>\u201cThe sketch is of equally spaced railroad ties drawn in a one point perspective. Two of the ties are perceived to the eye to be 25 feet and 20 feet respectively. What is the perceived length x of the third tie?\u201d<\/p>\n<p>Even though the ties are equally-spaced and of equal length in reality, from the point of view of perspective they are successively closer together and diminishing in length. The trick is to figure out what that compression factor is. I had to review my post on the <a href=\"https:\/\/josmfs.net\/wordpress\/2019\/01\/02\/perspective-map\/\">Perspective Map<\/a> to get some clues.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/02\/Railroad-Tie-Problem-200212.pdf\">Railroad Tie Problem<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a surprisingly challenging puzzle from the Mathematics 2020 calendar. \u201cThe sketch is of equally spaced railroad ties drawn in a one point perspective. Two of the ties are perceived to the eye to be 25 feet and 20 feet respectively. What is the perceived length x of the third tie?\u201d Even though the [&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":[183,148],"class_list":["post-1466","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-math-calendar","tag-perspective"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1466","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=1466"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1466\/revisions"}],"predecessor-version":[{"id":1472,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1466\/revisions\/1472"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1466"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1466"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1466"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}