{"id":2828,"date":"2022-08-13T09:10:12","date_gmt":"2022-08-13T13:10:12","guid":{"rendered":"https:\/\/josmfs.net\/?p=2828"},"modified":"2024-04-06T12:51:11","modified_gmt":"2024-04-06T16:51:11","slug":"two-squares-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/08\/13\/two-squares-problem\/","title":{"rendered":"Two Squares Problem"},"content":{"rendered":"

\"\"Via Alex Bellos I found another Russian math magazine with fun problems.\u00a0 It is called Kvantik<\/em> and Tanya Khovanova<\/a> has a description (2015):<\/p>\n

\u201cKvant<\/a><\/em> [Quantum<\/em>] was a very popular science magazine in Soviet Russia. It was targeted to high-school children and I was a subscriber. Recently I discovered that a new magazine appeared in Russia. It is called Kvantik<\/a><\/em>, which means Little Kvant. It is a science magazine for middle-school children. The previous years\u2019 archives are available online in Russian. I looked at 2012, the first publication year, and loved it.\u201d<\/p>\n

Unfortunately, the magazine is in Russian and the later issues are only partially given online.\u00a0 To get the full magazine you need to subscribe.\u00a0 I used Google Translate and the mathematical context to render the English.\u00a0\u00a0 Here is an interesting geometric problem that I would have thought to be quite challenging for middle schoolers.<\/p>\n

\u201cThe vertices of the two squares are joined by two segments, as in the figure. It is given that these segments are equal. Find the angle between them.<\/p>\n

Egor Bakaev\u201d<\/p>\n

Answer<\/a>.<\/p>\n

See the Two Squares Problem<\/a> for a solution.<\/p>\n

(Update 8\/22\/2022, 9\/1\/2022)\u00a0 Simpler Solution, Simplest Solution!
<\/strong><\/p>\n

(Update 8\/22\/2022) <\/strong>Oscar Rojas, a retired IBM systems engineer from Costa Rica, has provided a simpler solution to the problem:<\/p>\n

\u201cFor the Two-squares-problem my initial approach was to compute the sides and base of the isosceles triangle formed by the two congruent\u00a0segments, and then apply the Cosine-Law… But a partial result arises with some information that allowed me to take a non-trigonometric shortcut.\u201d<\/p>\n

\"\"<\/p>\n\n\n

<\/p>\n\n\n\n

(Update 9\/1\/2022)<\/strong> Update from Oscar Rojas: \u201cI commented this problem with my friend Ajit Athle from India. He sent this wonderful no-words-needed solution.\u201d<\/p>\n\n\n

\"\"<\/p>\n

Wow!\u00a0 This is fantastic!<\/p>","protected":false},"excerpt":{"rendered":"

Via Alex Bellos I found another Russian math magazine with fun problems.\u00a0 It is called Kvantik and Tanya Khovanova has a description (2015): \u201cKvant [Quantum] was a very popular science magazine in Soviet Russia. It was targeted to high-school children and I was a subscriber. Recently I discovered that a new magazine appeared in Russia. […]<\/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":[248,13],"class_list":["post-2828","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-kvantik-magazine","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2828","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=2828"}],"version-history":[{"count":6,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2828\/revisions"}],"predecessor-version":[{"id":3605,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2828\/revisions\/3605"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2828"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2828"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2828"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}