{"id":1834,"date":"2020-11-07T13:28:37","date_gmt":"2020-11-07T18:28:37","guid":{"rendered":"http:\/\/josmfs.net\/?p=1834"},"modified":"2021-01-05T18:46:22","modified_gmt":"2021-01-05T23:46:22","slug":"curve-making-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2020\/11\/07\/curve-making-puzzle\/","title":{"rendered":"Curve Making Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1832\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/11\/Curve-Making-Puzzle-Fig.jpg\" alt=\"\" width=\"200\" height=\"220\" \/>Here is a problem from <em>Five Hundred Mathematical Challenges<\/em> that I indeed found quite challenging.<\/p>\n<p><strong>\u201cProblem 235. <\/strong>Two fixed points <em>A<\/em> and <em>B<\/em> and a moving point <em>M <\/em>are taken on the circumference of a circle. On the extension of the line segment <em>AM <\/em>a point <em>N <\/em>is taken, outside the circle, so that lengths MN = MB<em>. <\/em>Find the locus of <em>N.<\/em>\u201d<\/p>\n<p>Since one of the first hurdles I faced with this problem was trying to figure out what type of shape was being generated, I thought I would omit my usual drawings illustrating the problem statement.\u00a0 There turned out to be a lot of cases to consider, but the result was most satisfying.\u00a0 I also included the case when <em>N<\/em> is inside the circle.\u00a0 Again Visio was my main tool to handle all the examples with the concomitant requirement to prove whatever Visio suggested.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/11\/Curve-Making-Puzzle-200928.pdf\">Curve Making Puzzle<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is a problem from Five Hundred Mathematical Challenges that I indeed found quite challenging. \u201cProblem 235. Two fixed points A and B and a moving point M are taken on the circumference of a circle. On the extension of the line segment AM a point N is taken, outside the circle, so that lengths [&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":[177,13],"class_list":["post-1834","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-500-math-challenges","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1834","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=1834"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1834\/revisions"}],"predecessor-version":[{"id":1928,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1834\/revisions\/1928"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1834"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1834"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}