{"id":176,"date":"2016-01-10T00:43:02","date_gmt":"2016-01-10T05:43:02","guid":{"rendered":"https:\/\/trigonography.com\/?p=176"},"modified":"2022-06-25T02:06:56","modified_gmt":"2022-06-25T07:06:56","slug":"three-squares-puzzle","status":"publish","type":"post","link":"https:\/\/trigonography.com\/?p=176","title":{"rendered":"Three Squares Puzzle"},"content":{"rendered":"\n

A puzzle by way of\u00a0Numberphile<\/a>:<\/p>\n\n\n

\n
\"trigonograph-threesquarespuzzle@2x\"<\/a><\/figure>\n<\/div>\n\n\n
$$x + y + z \\;=\\; \\text{???}$$<\/div>\n\n\n\n

A 1996 Math Horizons<\/cite> article by Martin Gardner ( re-printed here (PDF)<\/a> ) posed this puzzle
and provided some references, including Charles Trigg(!)’s 1971 compilation of 54 solutions.<\/p>\n\n\n\n

The following trigonograph is likely one of Trigg’s; indeed, I see that the key observation
appears in the solution given by Gardner. (Even so, I think this approach is a bit more direct,
and the presentation, if I do say so myself, slightly “AHA!”<\/a>-ier).<\/p>\n\n\n\n

SPOILERS<\/b><\/div>\n\n\n
\n
\"trigonograph-threesquarespuzzlesoln@2x\"<\/a><\/figure>\n<\/div>\n\n\n
$$x + y + z \\;=\\; 90^\\circ$$<\/div>\n\n\n\n

Note.<\/b> If you had a decent guess at the answer, then there’s an “obvious” proof using a trig formula.
(What is it?) But … formulas without pictures … What’s the fun in that?<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

A puzzle by way of\u00a0Numberphile: $$x + y + z \\;=\\; \\text{???}$$ A 1996 Math Horizons article by Martin Gardner ( re-printed here (PDF) ) posed this puzzleand provided some references, including Charles Trigg(!)’s 1971 compilation of 54 solutions. The following trigonograph is likely one of Trigg’s; indeed, I see that the key observationappears in the solution […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-176","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/176","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=176"}],"version-history":[{"count":10,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/176\/revisions"}],"predecessor-version":[{"id":1210,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/176\/revisions\/1210"}],"wp:attachment":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=176"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=176"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}