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"content": "<p>In August of Japan, the method of cutting pizza and cake into equal areas as shown in the figure was popular on Twitter! It can be found at the following URLs:<br /><a href=\"https://twitter.com/mathlava/status/1163796284760662017\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">twitter.com/mathlava/status/11</span><span class=\"invisible\">63796284760662017</span></a><br /><a href=\"https://twitter.com/5Hanayome/status/1164875472917811201\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">twitter.com/5Hanayome/status/1</span><span class=\"invisible\">164875472917811201</span></a><br />(I was most inspired by <a href=\"https://twitter.com/potetoichiro\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">twitter.com/potetoichiro</span><span class=\"invisible\"></span></a> .)<br />cf. <a href=\"https://zh.wikipedia.org/wiki/%E6%8A%AB%E8%96%A9%E5%AE%9A%E7%90%86#N=4%E7%9A%84%E6%83%85%E5%86%B5\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">zh.wikipedia.org/wiki/%E6%8A%A</span><span class=\"invisible\">B%E8%96%A9%E5%AE%9A%E7%90%86#N=4%E7%9A%84%E6%83%85%E5%86%B5</span></a><br />and <a href=\"https://arxiv.org/abs/1512.03794\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">arxiv.org/abs/1512.03794</span><span class=\"invisible\"></span></a></p>",
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"id": "https://mathstodon.xyz/users/unknown/statuses/102121800221032823",
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"summary": "Recently I was taught the following two expressions formula,",
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"published": "2019-05-19T08:36:48Z",
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"content": "<p>From <a href=\"https://youtu.be/dO40DZk-qNU\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">youtu.be/dO40DZk-qNU</span><span class=\"invisible\"></span></a> , I found <a href=\"https://www.wolframalpha.com/input/?i=(1%2Fx-5%2F(x%2Ba)%2B10%2F(x%2B2a)-10%2F(x%2B3a)%2B5%2F(x%2B4a)-1%2F(x%2B5a))*x*(x%2Ba)*(x%2B2a)*(x%2B3a)*(x%2B4a)*(x%2B5a)%3D(5!)+*+a%5E5\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://www.</span><span class=\"ellipsis\">wolframalpha.com/input/?i=(1%2</span><span class=\"invisible\">Fx-5%2F(x%2Ba)%2B10%2F(x%2B2a)-10%2F(x%2B3a)%2B5%2F(x%2B4a)-1%2F(x%2B5a))*x*(x%2Ba)*(x%2B2a)*(x%2B3a)*(x%2B4a)*(x%2B5a)%3D(5!)+*+a%5E5</span></a> , Still I can't prove this proof yet.<br />It does not matter at all, <br /><a href=\"https://mathstodon.xyz/tags/ENWP\" class=\"mention hashtag\" rel=\"tag\">#<span>ENWP</span></a> "Tangential quadrilateral" <a href=\"https://en.wikipedia.org/wiki/Tangential_quadrilateral\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">en.wikipedia.org/wiki/Tangenti</span><span class=\"invisible\">al_quadrilateral</span></a> has an inscribed circle if only three sides (The fourth side must be \\(a+b-c\\) .) are decided (The shape is completely determined by the determination of another angle).<br />Thanks from <a href=\"https://twitter.com/takatasennsei\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">twitter.com/takatasennsei</span><span class=\"invisible\"></span></a> !</p>",
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"en": "<p>From <a href=\"https://youtu.be/dO40DZk-qNU\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">youtu.be/dO40DZk-qNU</span><span class=\"invisible\"></span></a> , I found <a href=\"https://www.wolframalpha.com/input/?i=(1%2Fx-5%2F(x%2Ba)%2B10%2F(x%2B2a)-10%2F(x%2B3a)%2B5%2F(x%2B4a)-1%2F(x%2B5a))*x*(x%2Ba)*(x%2B2a)*(x%2B3a)*(x%2B4a)*(x%2B5a)%3D(5!)+*+a%5E5\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://www.</span><span class=\"ellipsis\">wolframalpha.com/input/?i=(1%2</span><span class=\"invisible\">Fx-5%2F(x%2Ba)%2B10%2F(x%2B2a)-10%2F(x%2B3a)%2B5%2F(x%2B4a)-1%2F(x%2B5a))*x*(x%2Ba)*(x%2B2a)*(x%2B3a)*(x%2B4a)*(x%2B5a)%3D(5!)+*+a%5E5</span></a> , Still I can't prove this proof yet.<br />It does not matter at all, <br /><a href=\"https://mathstodon.xyz/tags/ENWP\" class=\"mention hashtag\" rel=\"tag\">#<span>ENWP</span></a> "Tangential quadrilateral" <a href=\"https://en.wikipedia.org/wiki/Tangential_quadrilateral\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">en.wikipedia.org/wiki/Tangenti</span><span class=\"invisible\">al_quadrilateral</span></a> has an inscribed circle if only three sides (The fourth side must be \\(a+b-c\\) .) are decided (The shape is completely determined by the determination of another angle).<br />Thanks from <a href=\"https://twitter.com/takatasennsei\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">twitter.com/takatasennsei</span><span class=\"invisible\"></span></a> !</p>"
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"content": "<p>Now I make PDF <a href=\"https://shinshu.us/itou.pdf\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">shinshu.us/itou.pdf</span><span class=\"invisible\"></span></a> , Thanks! We will plan to generalize Twitter "じゃがりきんapu長ピーポ黄金角形" <a href=\"https://twitter.com/wasanp_/status/1097612948007088128\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">twitter.com/wasanp_/status/109</span><span class=\"invisible\">7612948007088128</span></a> in the future. <a href=\"https://mathstodon.xyz/tags/%E4%BA%88%E5%AE%9A%E6%9C%AA%E5%AE%9A\" class=\"mention hashtag\" rel=\"tag\">#<span>予定未定</span></a></p>",
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"en": "<p>Now I make PDF <a href=\"https://shinshu.us/itou.pdf\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">shinshu.us/itou.pdf</span><span class=\"invisible\"></span></a> , Thanks! We will plan to generalize Twitter "じゃがりきんapu長ピーポ黄金角形" <a href=\"https://twitter.com/wasanp_/status/1097612948007088128\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">twitter.com/wasanp_/status/109</span><span class=\"invisible\">7612948007088128</span></a> in the future. <a href=\"https://mathstodon.xyz/tags/%E4%BA%88%E5%AE%9A%E6%9C%AA%E5%AE%9A\" class=\"mention hashtag\" rel=\"tag\">#<span>予定未定</span></a></p>"
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"content": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@jsiehler\" class=\"u-url mention\">@<span>jsiehler</span></a></span> I'm playing your <a href=\"https://mathstodon.xyz/tags/SlidingBlockPuzzles\" class=\"mention hashtag\" rel=\"tag\">#<span>SlidingBlockPuzzles</span></a> with so exciting! <a href=\"http://homepages.gac.edu/~jsiehler/games/Blocks-App/index.html\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">http://</span><span class=\"ellipsis\">homepages.gac.edu/~jsiehler/ga</span><span class=\"invisible\">mes/Blocks-App/index.html</span></a> (If I understand mechanism that one piece moving one time anyway is counted as 1-move, I may be able to reduce MOVES more!)</p>",
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"content": "<p>1: "Sums of three cubes" <a href=\"https://en.wikipedia.org/wiki/Sums_of_three_cubes\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">en.wikipedia.org/wiki/Sums_of_</span><span class=\"invisible\">three_cubes</span></a> has generalized parametric representation "A New Method in the Problem of Three Cubes" <a href=\"https://arxiv.org/abs/1802.06776\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">arxiv.org/abs/1802.06776</span><span class=\"invisible\"></span></a> (cf. ex. Old article in Japanese <a href=\"http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math04/math0403.htm\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">http://www.</span><span class=\"ellipsis\">asahi-net.or.jp/~KC2H-MSM/math</span><span class=\"invisible\">land/math04/math0403.htm</span></a> ).<br />2: DANIEL SCHER "A DOUBLE SPIRAL FROM DAVID HENDERSON" <a href=\"http://www.sineofthetimes.org/a-double-spiral-from-david-henderson/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">http://www.</span><span class=\"ellipsis\">sineofthetimes.org/a-double-sp</span><span class=\"invisible\">iral-from-david-henderson/</span></a><br />3: Paul Bourke "Danzer Aperiodic Tiling" <a href=\"http://paulbourke.net/geometry/tilingplane/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">http://</span><span class=\"ellipsis\">paulbourke.net/geometry/tiling</span><span class=\"invisible\">plane/</span></a> telling by GirihApp@Twitter <a href=\"https://twitter.com/GirihApp/status/1106615831742558208\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">twitter.com/GirihApp/status/11</span><span class=\"invisible\">06615831742558208</span></a> . I do similar one of the attached image</p>",
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"ja": "<p>1: "Sums of three cubes" <a href=\"https://en.wikipedia.org/wiki/Sums_of_three_cubes\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">en.wikipedia.org/wiki/Sums_of_</span><span class=\"invisible\">three_cubes</span></a> has generalized parametric representation "A New Method in the Problem of Three Cubes" <a href=\"https://arxiv.org/abs/1802.06776\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">arxiv.org/abs/1802.06776</span><span class=\"invisible\"></span></a> (cf. ex. Old article in Japanese <a href=\"http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math04/math0403.htm\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">http://www.</span><span class=\"ellipsis\">asahi-net.or.jp/~KC2H-MSM/math</span><span class=\"invisible\">land/math04/math0403.htm</span></a> ).<br />2: DANIEL SCHER "A DOUBLE SPIRAL FROM DAVID HENDERSON" <a href=\"http://www.sineofthetimes.org/a-double-spiral-from-david-henderson/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">http://www.</span><span class=\"ellipsis\">sineofthetimes.org/a-double-sp</span><span class=\"invisible\">iral-from-david-henderson/</span></a><br />3: Paul Bourke "Danzer Aperiodic Tiling" <a href=\"http://paulbourke.net/geometry/tilingplane/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">http://</span><span class=\"ellipsis\">paulbourke.net/geometry/tiling</span><span class=\"invisible\">plane/</span></a> telling by GirihApp@Twitter <a href=\"https://twitter.com/GirihApp/status/1106615831742558208\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">twitter.com/GirihApp/status/11</span><span class=\"invisible\">06615831742558208</span></a> . I do similar one of the attached image</p>"
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