{"id":337,"date":"2019-01-02T19:33:03","date_gmt":"2019-01-03T00:33:03","guid":{"rendered":"http:\/\/josmfs.net\/wordpress\/?p=337"},"modified":"2021-06-12T15:52:10","modified_gmt":"2021-06-12T19:52:10","slug":"perspective-map","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/01\/02\/perspective-map\/","title":{"rendered":"Perspective Map"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2251\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Perspective-Map-Fig2.jpg\" alt=\"\" width=\"246\" height=\"241\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Perspective-Map-Fig2.jpg 504w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Perspective-Map-Fig2-300x294.jpg 300w\" sizes=\"auto, (max-width: 246px) 100vw, 246px\" \/>A number of recent puzzles have involved perspective views of objects. I had never really explored the idea of a perspective map in detail. So some of the properties associated with it always seemed a bit vague to me. I decided I would derive the mathematical equations for the perspective or projective map and see how its properties fell out from the equations. With this information in hand I then addressed some questions I had about the article \u201cD\u00fcrer: Disguise, Distance, Disagreements, and Diagonals!\u201d by Annalisa Crannell, Marc Frantz, and Fumiko Futamura concerning a controversy over Albrecht D\u00fcrer\u2019s woodcut <em>St. Jerome in His Study<\/em> (1514). And finally, I read somewhere that a parabola under a perspective map becomes an ellipse, so I was able to show that as well. See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/01\/Perspective-Map-190108.pdf\">Perspective Map<\/a>.<\/p>\n<p><strong>(Update 7\/1\/2019) <\/strong><!--more--><\/p>\n<p>For a more historical and less mathematical approach to the perspective map see my 1 July 2019 post on <a href=\"https:\/\/josmfs.net\/wordpress\/2019\/07\/01\/albertis-perspective-construction\/\">Alberti\u2019s Perspective Construction<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A number of recent puzzles have involved perspective views of objects. I had never really explored the idea of a perspective map in detail. So some of the properties associated with it always seemed a bit vague to me. I decided I would derive the mathematical equations for the perspective or projective map and see [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[40,32,41,31],"class_list":["post-337","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-analytic-geometry","tag-calculus","tag-trigonometry","tag-vectors"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/337","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=337"}],"version-history":[{"count":8,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/337\/revisions"}],"predecessor-version":[{"id":2252,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/337\/revisions\/2252"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=337"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=337"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}