{"id":1010,"date":"2009-04-20T22:27:04","date_gmt":"2009-04-20T14:27:04","guid":{"rendered":"http:\/\/www.Sun-Q.cn\/zu-chongzhi-write-the-greek-alphabet.html"},"modified":"2009-04-20T22:28:48","modified_gmt":"2009-04-20T14:28:48","slug":"zu-chongzhi-write-the-greek-alphabet","status":"publish","type":"post","link":"https:\/\/daibei.info\/index.php\/2009\/04\/20\/zu-chongzhi-write-the-greek-alphabet\/","title":{"rendered":"\u7956\u51b2\u4e4b\u4f1a\u5199\u5e0c\u814a\u5b57\u6bcd\uff1f"},"content":{"rendered":"<p><img decoding=\"async\" src=\"http:\/\/www.google.cn\/logos\/chongzhi09.gif\" \/> 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href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%9C%89%E6%95%88%E6%95%B0%E5%AD%97&amp;variant=zh-cn\">\u6709\u6548\u6570\u5b57<\/a>\uff09\u3002\u81f3\u4e8e\u5bc6\u7387<img decoding=\"async\" alt=\"\\frac{355}{113}\" src=\"http:\/\/upload.wikimedia.org\/math\/2\/9\/c\/29cde9f6ad7ad117be486b19047272bd.png\" \/>\u5219\u662f\u4e00\u4e2a\u6613\u4e8e\u8bb0\u5fc6\uff08\u4e09\u4e2a\u8fde\u7eed\u5947\u6570\uff1a113355\uff09\uff0c\u4e14\u7cbe\u786e\u81f37\u4f4d\u6709\u6548\u6570\u5b57\u7684\u5206\u6570\u8fd1\u4f3c\u503c\u3002<\/p>\n<p><a name=\".E5.AF.A6.E9.A9.97.E6.99.82.E6.9C.9F\"><\/a><\/p>\n<h5>[<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%9C%93%E5%91%A8%E7%8E%87&amp;action=edit&amp;section=3\">\u7f16\u8f91<\/a>] \u5b9e\u9a8c\u65f6\u671f<\/h5>\n<p>\u4e2d\u56fd\u53e4\u7c4d\u4e91\uff1a\u201c\u5468\u4e09\u5f84\u4e00\u201d<sup><a href=\"http:\/\/zh.wikipedia.org\/#_note-1\">[2]<\/a><\/sup>\uff0c\u610f\u5373\u53d6 \u03c0=3\u3002\u897f\u5143<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%89%8D17%E4%B8%96%E7%B4%80&amp;variant=zh-cn\">\u524d17\u4e16\u7eaa<\/a>\u7684\u57c3\u53ca\u53e4\u7c4d\u300a<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E9%98%BF%E7%BE%8E%E6%96%AF%E7%B4%99%E8%8D%89%E6%9B%B8&amp;action=edit&amp;redlink=1\">\u963f\u7f8e\u65af\u7eb8\u8349\u4e66<\/a>\u300b\uff08<i>Ahmes<\/i>\uff0c\u53c8\u79f0\u201c\u963f\u6885\u65af\u8349\u7247\u6587\u4e66\u201d\uff1b\u4e3a\u82f1\u56fd\u4ebaAlexander Henry Rhind\uff08\u83b1\u8335\u5fb7\uff09\u4e8e1858\u5e74\u53d1\u73b0\uff0c\u56e0\u6b64\u8fd8\u79f0\u201c\u83b1\u8335\u5fb7\u7eb8\u8349\u4e66\u201d Rhind Papyrus\uff09\u662f\u4e16\u754c\u4e0a\u6700\u65e9\u7ed9\u51fa\u5706\u5468\u7387\u7684\u8d85\u8fc7<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%8D%81%E9%80%B2%E5%88%B6&amp;variant=zh-cn\">\u5341\u5206\u4f4d<\/a>\u7684\u8fd1\u4f3c\u503c\uff0c\u4e3a 256\/81 ( = 3 + 1\/9 + 1\/27 + 1\/81) \u6216 3.160\u3002<\/p>\n<p>\u81f3<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E9%98%BF%E5%9F%BA%E7%B1%B3%E5%BE%B7&amp;variant=zh-cn\">\u963f\u57fa\u7c73\u5fb7<\/a>\u4e4b\u524d\uff0c\u03c0\u503c\u4e4b\u6d4b\u5b9a\u501a\u9760\u5b9e\u7269\u6d4b\u91cf\u3002<\/p>\n<p><a name=\".E5.B9.BE.E4.BD.95.E6.B3.95.E6.99.82.E6.9C.9F.E2.80.94.E2.80.94.E5.8F.8D.E8.A6.86.E5.89.B2.E5.9C.93\"><\/a><\/p>\n<h5>[<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%9C%93%E5%91%A8%E7%8E%87&amp;action=edit&amp;section=4\">\u7f16\u8f91<\/a>] \u51e0\u4f55\u6cd5\u65f6\u671f\u2014\u2014\u53cd\u590d\u5272\u5706<\/h5>\n<p><a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E9%98%BF%E5%9F%BA%E7%B1%B3%E5%BE%B7&amp;variant=zh-cn\">\u963f\u57fa\u7c73\u5fb7<\/a>\u7528\u6b6396\u8fb9\u5f62\u5272\u5706\u672f\u5f97\u51fa\u5706\u5468\u7387\u4ecb\u4e4e <img decoding=\"async\" alt=\"3\\frac{1}{7}\" src=\"http:\/\/upload.wikimedia.org\/math\/4\/0\/5\/4059b0f0121d2627ece7d2796d05ee7c.png\" \/>\u4e0e <img decoding=\"async\" alt=\"3\\frac{10}{71}\" src=\"http:\/\/upload.wikimedia.org\/math\/b\/8\/3\/b8375b353847ac7fa7922ee6794cca6a.png\" \/>\u4e4b\u95f4\u3002<\/p>\n<p>\u897f\u5143<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=263%E5%B9%B4&amp;variant=zh-cn\">263\u5e74<\/a>\uff0c\u4e2d\u56fd\u6570\u5b66\u5bb6<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%8A%89%E5%BE%BD&amp;variant=zh-cn\">\u5218\u5fbd<\/a>\u7528\u201c<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%89%B2%E5%9C%86%E6%9C%AF_(%E5%88%98%E5%BE%BD)&amp;variant=zh-cn\">\u5272\u5706\u672f<\/a>\u201d\u8ba1\u7b97\u5706\u5468\u7387\uff0c\u4ed6\u5148\u4ece\u5706\u5185\u63a5\u6b63\u516d\u8fb9\u5f62\uff0c\u9010\u6b21\u5206\u5272\u4e3a12\u300124\u300148\u300196\u3001192\u8fb9\u5f62\u3002\u4ed6\u8bf4\u201c\u5272\u4e4b\u5f25\u7ec6\uff0c\u6240\u5931\u5f25\u5c11\uff0c\u5272\u4e4b\u53c8\u5272\uff0c\u4ee5\u81f3\u4e8e\u4e0d\u53ef\u5272\uff0c\u5219\u4e0e\u5706\u5468\u5408\u4f53\u800c\u65e0\u6240\u5931\u77e3\u3002\u201d\uff08\u5206\u5272\u6108\u7cbe\u7ec6\uff0c\u8bef\u5dee\u6108\u5c11\u3002\u5206\u5272\u4e4b\u540e\u518d\u5206\u5272\uff0c\u76f4\u5230\u4e0d\u80fd\u518d\u5206\u5272\u4e3a\u6b62\uff0c\u5b83\u5c31\u4f1a\u4e0e\u5706\u5468\u5b8c\u5168\u91cd\u53e0\uff0c\u5c31\u4e0d\u4f1a\u6709\u8bef\u5dee\u4e86\uff09\uff0c\u5176\u4e2d\u6709\u6c42\u6781\u9650\u7684\u601d\u60f3\u3002\u5218\u5fbd\u7ed9\u51fa\u03c0=3.141024\u7684\u5706\u5468\u7387\u8fd1\u4f3c\u503c\uff0c\u5e76\u4ee5 <img decoding=\"async\" alt=\"{157 \\over 50}=3.14\" src=\"http:\/\/upload.wikimedia.org\/math\/d\/6\/3\/d63d2b3791af0cd6589c96817092eda6.png\" \/>\uff08\u5fbd\u7387\uff09\u4e3a\u5176\u5206\u6570\u8fd1\u4f3c\u503c\u3002<\/p>\n<p>\u897f\u5143<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=466%E5%B9%B4&amp;variant=zh-cn\">466\u5e74<\/a>\uff0c\u4e2d\u56fd\u6570\u5b66\u5bb6<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E7%A5%96%E6%B2%96%E4%B9%8B&amp;variant=zh-cn\">\u7956\u51b2\u4e4b<\/a>\u5c06\u5706\u5468\u7387\u7b97\u5230\u5c0f\u6570\u70b9\u540e7\u4f4d\u7684\u7cbe\u786e\u5ea6\uff0c\u8fd9\u4e00\u7eaa\u5f55\u5728\u4e16\u754c\u4e0a\u4fdd\u6301\u4e86\u4e00\u5343\u5e74\u4e4b\u4e45\u3002\u540c\u65f6\uff0c<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E7%A5%96%E6%B2%96%E4%B9%8B&amp;variant=zh-cn\">\u7956\u51b2\u4e4b<\/a>\u7ed9\u51fa\u4e86<img decoding=\"async\" alt=\"{355 \\over 113}\" src=\"http:\/\/upload.wikimedia.org\/math\/1\/9\/1\/191717478267094d0f3761538c315160.png\" \/>\uff08\u5bc6\u7387\uff09\u8fd9\u4e2a\u5f88\u597d\u7684\u5206\u6570\u8fd1\u4f3c\u503c\uff0c\u5b83\u662f\u5206\u6bcd\u5c0f\u4e8e10,000\u7684\u7b80\u5355\u5206\u6570\u4e2d\u6700\u63a5\u8fd1\u03c0\u7684\u3002\u4e3a\u7eaa\u5ff5<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E7%A5%96%E6%B2%96%E4%B9%8B&amp;variant=zh-cn\">\u7956\u51b2\u4e4b<\/a>\u5bf9\u5706\u5468\u7387\u53d1\u5c55\u7684\u8d21\u732e\uff0c<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%97%A5%E6%9C%AC&amp;variant=zh-cn\">\u65e5\u672c<\/a>\u6570\u5b66\u5bb6<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E4%B8%89%E4%B8%8A%E7%BE%A9%E5%A4%AB&amp;variant=zh-cn\">\u4e09\u4e0a\u4e49\u592b<\/a>\u5c06\u8fd9\u4e00\u63a8\u7b97\u503c\u547d\u540d\u4e3a\u201c\u7956\u51b2\u4e4b\u5706\u5468\u7387\u201d\uff0c\u7b80\u79f0\u201c\u7956\u7387\u201d\u3002\u53ef\u60dc<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E7%A5%96%E6%B2%96%E4%B9%8B&amp;variant=zh-cn\">\u7956\u51b2\u4e4b<\/a>\u7684\u8457\u4f5c\u300a\u7f00\u672f\u300b\u5df2\u7ecf\u4ea1\u4f5a\uff0c\u540e\u4eba\u65e0\u4ece\u5f97\u77e5<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E7%A5%96%E6%B2%96%E4%B9%8B&amp;variant=zh-cn\">\u7956\u51b2\u4e4b<\/a>\u5982\u4f55\u4f30\u7b97\u5706\u5468\u7387\u7684\u503c\u3002<\/p>\n<p><a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E9%8C%A2%E5%A4%A7%E6%98%95&amp;variant=zh-cn\">\u94b1\u5927\u6615<\/a>\u7684\u300a\u5341\u9a7e\u658b\u517b\u65b0\u5f55\u300b\u5377\u7b2c\u5341\u4e03\u9996\u6761\u3008\u5706\u5f84\u5468\u7387\u3009\u5f15\u300a\u968b\u4e66\u5f8b\u5386\u5fd7\u300b\uff1a\u201c\u53e4\u4e4b\u4e5d\u6570\uff0c\u5706\u5468\u7387\u4e09\u5706\u5f84\u7387\u4e00\uff0c\u5176\u672f\u758f\u821b\uff0c\u81ea\u5218\u6b46\u3001\u5f20\u8861\u3001\u5218\u5fbd\u3001\u738b\u8543\u3001\u76ae\u5ef6\u5b97\u4e4b\u5f92\uff0c\u5404\u8bbe\u65b0\u7387\uff0c\u672a\u81fb\u6298\u8877\u3002\u5b8b\u672b\u5357\u5f90\u5dde\u4ece\u4e8b\u53f2\u7956\u51b2\u4e4b\u66f4\u5f00\u5bc6\u7387\uff0c\u4ee5\u5706\u5f84\u4e00\u4ebf\u4e3a\u4e00\u4e08\uff0c\u5706\u5468\u76c8\u6570\u4e09\uff08\u523b\u672c\u4f5c\u4e8c\uff0c\u8bef\uff09\u4e08\u4e00\u5c3a\u56db\u5bf8\u4e00\u5206\u4e94\u5398\u4e5d\u6beb\u4e8c\u79d2\u4e03\u5ffd\uff0c\u6712\u6570\u4e09\u4e08\u4e00\u5c3a\u56db\u5bf8\u4e00\u5206\u4e94\u5398\u4e5d\u6beb\u4e8c\u79d2\u516d\u5ffd\uff0c\u6b63\u6570\u5728\u76c8\u6712\u4e8c\u9650\u4e4b\u95f4\uff0c\u5bc6\u7387\u5706\u5f84\u4e00\u767e\u4e00\u5341\u4e09\uff0c\u5706\u5468\u4e09\u767e\u4e94\u5341\u4e94\uff0c\u7ea6\u7387\u5706\u5f84\u4e03\uff0c\u5468\u4e8c\u5341\u4e8c\u3002\u53c8\u8bbe\u5f00\u5dee\u5e42\u3001\u5f00\u5dee\u7acb\uff0c\u517c\u4ee5\u6b63\u5706\u53c2\u4e4b\uff0c\u6307\u8981\u7cbe\u5bc6\uff0c\u7b97\u6c0f\u4e4b\u6700\u8005\u4e5f\u3002\u201d<\/p>\n<p><a name=\".E5.88.86.E6.9E.90.E6.B3.95.E6.99.82.E6.9C.9F.E2.80.94.E2.80.94.E7.84.A1.E7.AA.AE.E7.B4.9A.E6.95.B8\"><\/a><\/p>\n<h5>[<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%9C%93%E5%91%A8%E7%8E%87&amp;action=edit&amp;section=5\">\u7f16\u8f91<\/a>] \u5206\u6790\u6cd5\u65f6\u671f\u2014\u2014\u65e0\u7a77\u7ea7\u6570<\/h5>\n<p>\u8fd9\u4e00\u65f6\u671f\u4eba\u4eec\u5f00\u59cb\u6446\u8131\u5229\u7528\u5272\u5706\u672f\u7684\u7e41\u590d\u8ba1\u7b97\uff0c\u5f00\u59cb\u5229\u7528<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%97%A0%E7%A9%B7%E7%BA%A7%E6%95%B0&amp;variant=zh-cn\">\u65e0\u7a77\u7ea7\u6570<\/a>\u6216\u65e0\u7a77\u8fde\u4e58\u79ef\u6c42\u03c0\u3002<\/p>\n<p>Ludolph van Ceulen\uff08\u7ea6<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=1600%E5%B9%B4&amp;variant=zh-cn\">1600\u5e74<\/a>\uff09\u8ba1\u7b97\u51fa\u03c0\u7684\u5c0f\u6570\u70b9\u540e\u999635\u4f4d\u3002\u4ed6\u5bf9\u6b64\u611f\u5230\u81ea\u8c6a\uff0c\u56e0\u800c\u547d\u4eba\u628a\u5b83\u523b\u5728\u81ea\u5df1\u7684\u5893\u7891\u4e0a\u3002<\/p>\n<p><a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%96%AF%E6%B4%9B%E7%B6%AD%E5%B0%BC%E4%BA%9E%E4%BA%BA&amp;variant=zh-cn\">\u65af\u6d1b\u6587\u5c3c\u4e9a<\/a>\u6570\u5b66\u5bb6Jurij Vega\u4e8e<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=1789%E5%B9%B4&amp;variant=zh-cn\">1789\u5e74<\/a>\u5f97\u51fa\u03c0\u7684\u5c0f\u6570\u70b9\u540e\u9996140\u4f4d\uff0c\u5176\u4e2d\u6709137\u4f4d\u662f\u6b63\u786e\u7684\u3002\u8fd9\u4e2a\u4e16\u754c\u7eaa\u5f55\u7ef4\u6301\u4e86\u4e94\u5341\u5e74\u3002\u4ed6\u5229\u7528\u4e86John Machin\u4e8e<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=1706%E5%B9%B4&amp;variant=zh-cn\">1706\u5e74<\/a>\u63d0\u51fa\u7684\u6570\u5f0f\u3002<\/p>\n<p>\u6240\u6709\u4ee5\u4e0a\u7684\u65b9\u6cd5\u90fd\u4e0d\u80fd\u5feb\u901f\u7b97\u51fa\u03c0\u3002\u7b2c\u4e00\u4e2a\u5feb\u901f\u7b97\u6cd5\u7531 Machin \u63d0\u51fa\uff1a<\/p>\n<dl>\n<dd><img decoding=\"async\" alt=\"\\frac{\\pi}{4} = 4 \\arctan\\frac{1}{5} - \\arctan\\frac{1}{239} \" src=\"http:\/\/upload.wikimedia.org\/math\/f\/1\/5\/f15dc3d39c473c4bd718e3a98145da0d.png\" \/><\/dd>\n<\/dl>\n<p>\u5176\u4e2darctan(<i>x<\/i>) \u53ef\u7531<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%B3%B0%E5%8B%92%E7%BA%A7%E6%95%B0&amp;variant=zh-cn\">\u6cf0\u52d2\u7ea7\u6570<\/a>\u7b97\u51fa\u3002\u7c7b\u4f3c\u65b9\u6cd5\u79f0\u4e3a\u201c<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E9%A1%9EMachin%E7%AE%97%E6%B3%95&amp;action=edit&amp;redlink=1\">\u7c7bMachin\u7b97\u6cd5<\/a>\u201d\u3002<\/p>\n<p><a name=\".E8.A8.88.E7.AE.97.E5.99.A8.E6.99.82.E4.BB.A3\"><\/a><\/p>\n<h5>[<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%9C%93%E5%91%A8%E7%8E%87&amp;action=edit&amp;section=6\">\u7f16\u8f91<\/a>] \u8ba1\u7b97\u5668\u65f6\u4ee3<\/h5>\n<p>\u4e0a\u4e07\u4f4d\u4ee5\u4e0a\u7684\u5c0f\u6570\u4f4d\u503c\u901a\u5e38\u5229\u7528<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=Gauss-Legendre%E7%AE%97%E6%B3%95&amp;action=edit&amp;redlink=1\">Gauss-Legendre\u7b97\u6cd5<\/a>\u6216<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=Borweins%E7%AE%97%E6%B3%95&amp;action=edit&amp;redlink=1\">Borweins\u7b97\u6cd5<\/a>\uff1b\u53e6\u5916\u4ee5\u5f80\u4ea6\u66fe\u4f7f\u7528\u4e8e<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=1976%E5%B9%B4&amp;variant=zh-cn\">1976\u5e74<\/a>\u53d1\u73b0\u7684 <a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=Salamin-Brent%E7%AE%97%E6%B3%95&amp;action=edit&amp;redlink=1\">Salamin-Brent\u7b97\u6cd5<\/a>\u3002<\/p>\n<p>\u7b2c\u4e00\u4e2a\u03c0\u548c 1\/\u03c0\u7684\u5c0f\u6570\u70b9\u540e\u9996\u4e00\u767e\u4e07\u4f4d\u5229\u7528\u4e86<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%8F%A4%E8%85%BE%E5%A0%A1%E8%AE%A1%E5%88%92&amp;variant=zh-cn\">\u53e4\u817e\u5821\u8ba1\u5212<\/a>\u3002\u6700\u65b0\u7eaa\u5f55\u662f<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=2002%E5%B9%B4&amp;variant=zh-cn\">2002\u5e74<\/a>\u4e5d\u6708\u5f97\u51fa\u7684 1,241,100,000,000 \u4e2a\u5c0f\u6570\u4f4d\uff0c\u7531\u62e5\u67091TB\u4e3b\u5185\u5b58\u768464-node<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%97%A5%E7%AB%8B&amp;variant=zh-cn\">\u65e5\u7acb<\/a><a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E8%B6%85%E7%B4%9A%E9%9B%BB%E8%85%A6&amp;variant=zh-cn\">\u8d85\u7ea7\u7535\u8111<\/a>\uff0c\u4ee5\u6bcf\u79d2200\u4ebf\u8fd0\u7b97\u901f\u5ea6\u5f97\u51fa\uff0c\u6bd4\u65e7\u7eaa\u5f55\u591a\u7b97\u51fa\u4e00\u500d\uff08206\u4ebf\u5c0f\u6570\u4f4d\uff09\u3002\u6b64\u7eaa\u5f55\u7531\u4ee5\u4e0b<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E9%A1%9EMachin%E6%BC%94%E7%AE%97%E6%B3%95&amp;action=edit&amp;redlink=1\">\u7c7bMachin\u7b97\u6cd5<\/a>\u5f97\u51fa\uff1a<\/p>\n<dl>\n<dd><img decoding=\"async\" alt=\" \\frac{\\pi}{4} = 12 \\arctan\\frac{1}{49} + 32 \\arctan\\frac{1}{57} - 5 \\arctan\\frac{1}{239} + 12 \\arctan\\frac{1}{110443}\" src=\"http:\/\/upload.wikimedia.org\/math\/5\/2\/4\/524a01f928a2eddfb2d141f7d0089dd6.png\" \/> (K. Takano, <a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=1982%E5%B9%B4&amp;variant=zh-cn\">1982\u5e74<\/a>) <\/dd>\n<\/dl>\n<dl>\n<dd><img decoding=\"async\" alt=\" \\frac{\\pi}{4} = 44 \\arctan\\frac{1}{57} + 7 \\arctan\\frac{1}{239} - 12 \\arctan\\frac{1}{682} + 24 \\arctan\\frac{1}{12943}\" src=\"http:\/\/upload.wikimedia.org\/math\/2\/0\/e\/20eeb32761f5204b35a62f50d7d1b2f5.png\" \/> (F. C. W. St\u00f6rmer, <a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=1896%E5%B9%B4&amp;variant=zh-cn\">1896\u5e74<\/a>) <\/dd>\n<\/dl>\n<p>\u8fd9\u4e48\u591a\u7684\u5c0f\u6570\u4f4d\u6ca1\u4ec0\u4e48\u5b9e\u7528\u4ef7\u503c\uff0c\u53ea\u7528\u4ee5\u6d4b\u8bd5<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E8%B6%85%E7%B4%9A%E9%9B%BB%E8%85%A6&amp;variant=zh-cn\">\u8d85\u7ea7\u7535\u8111<\/a>\u3002<\/p>\n<p><a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=1996%E5%B9%B4&amp;variant=zh-cn\">1996\u5e74<\/a>\uff0cDavid H. Bailey\u3001Peter Borwein\u53ca<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E8%A5%BF%E8%92%99%E2%80%A2%E6%99%AE%E5%8B%9E%E5%A4%AB&amp;action=edit&amp;redlink=1\">\u897f\u8499\u2022\u666e\u52b3\u592b<\/a>\u53d1\u73b0\u4e86\u03c0\u7684\u5176\u4e2d\u4e00\u4e2a\u65e0\u7a77\u7ea7\u6570\uff1a<\/p>\n<dl>\n<dd><img decoding=\"async\" alt=\"\\pi = \\sum_{k = 0}^{\\infty} \\frac{1}{16^k}&#10;\\left( \\frac{4}{8k + 1} - \\frac{2}{8k + 4} - \\frac{1}{8k + 5} - \\frac{1}{8k + 6}\\right)\" src=\"http:\/\/upload.wikimedia.org\/math\/f\/9\/7\/f9733b62958be8751fbab97431c27af5.png\" \/><\/dd>\n<\/dl>\n<p>\u4ee5\u4e0a\u8ff0\u516c\u5f0f\u53ef\u4ee5\u8ba1\u7b97\u03c0\u7684\u7b2c<i>n<\/i>\u4e2a<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E4%BA%8C%E9%80%B2%E4%BD%8D&amp;variant=zh-cn\">\u4e8c\u8fdb\u5236<\/a>\u6216<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%8D%81%E5%85%AD%E9%80%B2%E4%BD%8D&amp;variant=zh-cn\">\u5341\u516d\u8fdb\u5236<\/a>\u5c0f\u6570\uff0c\u800c\u4e0d\u9700\u5148\u8ba1\u7b97\u9996<i>n<\/i>-1 \u4e2a\u5c0f\u6570\u4f4d\u3002\u6b64\u7c7b\u03c0\u7b97\u6cd5\u79f0\u4e3a<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=Bailey-Borwein-Plouffe%E7%AE%97%E6%B3%95&amp;action=edit&amp;redlink=1\">Bailey-Borwein-Plouffe\u7b97\u6cd5<\/a>\u3002\u8bf7\u53c2\u8003 <a href=\"http:\/\/www.nersc.gov\/~dhbailey\/\">Bailey&#8217;s website<\/a> \u4e0a\u76f8\u5173<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E7%A8%8B%E5%BC%8F&amp;variant=zh-cn\">\u7a0b\u5f0f<\/a>\u3002<\/p>\n<p><a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=Fabrice_Bellard&amp;action=edit&amp;redlink=1\">Fabrice Bellard<\/a>\u4e8e<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=1997%E5%B9%B4&amp;variant=zh-cn\">1997\u5e74<\/a>\u7ed9\u51fa\u4e86\u8ba1\u7b97\u673a\u6548\u7387\u4e0a\u9ad8\u51fa\u4e0a\u5f0f47%\u7684BBP\u7b97\u6cd5\uff1a<\/p>\n<dl>\n<dd><img decoding=\"async\" alt=\"\\pi = \\frac{1}{2^6} \\sum_{n=0}^{\\infty} \\frac{{(-1)}^n}{2^{10n}} \\left( - \\frac{2^5}{4n+1} - \\frac{1}{4n+3} + \\frac{2^8}{10n+1} - \\frac{2^6}{10n+3} - \\frac{2^2}{10n+5} - \\frac{2^2}{10n+7} + \\frac{1}{10n+9} \\right)\" src=\"http:\/\/upload.wikimedia.org\/math\/2\/c\/3\/2c39b196c4eb238086f391bdc6acef7b.png\" \/><\/dd>\n<\/dl>\n<p>\u8bf7\u53c2\u8003 <a href=\"http:\/\/bellard.org\/pi\/\">Fabrice Bellard&#8217;s PI page<\/a> \u3002<\/p>\n<p>\u5176\u4ed6\u8ba1\u7b97\u5706\u5468\u7387\u7684\u516c\u5f0f\u5305\u62ec\uff1a<\/p>\n<dl>\n<dd><img decoding=\"async\" alt=\" \\frac{1}{\\pi} = \\frac{2\\sqrt{2}}{9801} \\sum^\\infty_{k=0} \\frac{(4k!)(1103+26390k)}{(k!)^4 396^{4k}} \" src=\"http:\/\/upload.wikimedia.org\/math\/7\/7\/e\/77e9fac37840591d2aea360317141f34.png\" \/> (\u62c9\u9a6c\u52aa\u91d1 Ramanujan) <\/dd>\n<\/dl>\n<dl>\n<dd><img decoding=\"async\" alt=\" \\frac{1}{\\pi} = 12 \\sum^\\infty_{k=0} \\frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 640320^{3k + 3\/2}} \" src=\"http:\/\/upload.wikimedia.org\/math\/d\/c\/8\/dc88cec756645fb4751542454081ac6d.png\" \/> (David Chudnovsky \u53ca Gregory Chudnovsky) <\/dd>\n<\/dl>\n<dl>\n<dd><img decoding=\"async\" alt=\"\\pi = \\frac {426880 \\sqrt {10005}} {\\sum_{k=0}^\\infty \\frac {(6n)!\\ (545140134n + 13591409)} { (n!)^3\\ (3n)!\\ (-640320)^3n}} \" src=\"http:\/\/upload.wikimedia.org\/math\/a\/4\/c\/a4c0af1aa84f3fa7230a1fc372acc7cf.png\" \/><a href=\"http:\/\/www.jason314.com\/\">[1]<\/a><\/dd>\n<\/dl>\n<p>\u7f16\u5199\u7535\u8111\u7a0b\u5f0f\u65f6\uff0c\u4e5f\u53ef\u4ee5\u5229\u7528<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%8F%8D%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0&amp;variant=zh-cn\">\u53cd\u4e09\u89d2\u51fd\u6570<\/a>\u76f4\u63a5\u5b9a\u4e49 \u03c0 \u503c\uff0c\u4f46\u662f\u7f16\u8bd1\u5668\u5fc5\u987b\u5177\u5907<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B8&amp;variant=zh-cn\">\u4e09\u89d2\u51fd\u6570<\/a>\u7684\u51fd\u5f0f\u5e93\uff1a      <br \/>\u5229\u7528<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%AD%A3%E5%BC%A6%E5%87%BD%E6%95%B0&amp;variant=zh-cn\">\u6b63\u5f26\u51fd\u6570<\/a><\/p>\n<dl>\n<dd><img decoding=\"async\" alt=\"\\sin\\left(\\pi \/ 2 \\right)=1\" src=\"http:\/\/upload.wikimedia.org\/math\/6\/4\/f\/64f14e66c0b441d309d6a3f675944628.png\" \/><\/dd>\n<dd><img decoding=\"async\" alt=\"\\pi=2*\\arcsin\\left(1 \\right)\" src=\"http:\/\/upload.wikimedia.org\/math\/6\/6\/6\/66620461dc653ec126f8f50f69e3c003.png\" \/><\/dd>\n<\/dl>\n<p>\u5229\u7528<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E4%BD%99%E5%BC%A6%E5%87%BD%E6%95%B0&amp;variant=zh-cn\">\u4f59\u5f26\u51fd\u6570<\/a><\/p>\n<dl>\n<dd><img decoding=\"async\" alt=\"\\cos\\left(\\pi \\right)=-1\" src=\"http:\/\/upload.wikimedia.org\/math\/c\/4\/d\/c4d2e738f486930f8f3b085587217ba1.png\" \/><\/dd>\n<dd><img decoding=\"async\" alt=\"\\pi=\\arccos\\left(-1 \\right)\" src=\"http:\/\/upload.wikimedia.org\/math\/c\/6\/7\/c67720de0e0f237606a36b4d9663da61.png\" \/><\/dd>\n<\/dl>\n<p>&#160;<\/p>\n<\/blockquote>\n<p>\u7ef4\u57fa\u767e\u79d1\u5173\u4e8e\u7956\u51b2\u4e4b\uff1a<\/p>\n<blockquote>\n<p><b>\u7956\u51b2\u4e4b<\/b>\uff08<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=429%E5%B9%B4&amp;variant=zh-cn\">429\u5e74<\/a>\uff0d<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=500%E5%B9%B4&amp;variant=zh-cn\">500\u5e74<\/a>)\uff0c<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E8%A1%A8%E5%AD%97&amp;variant=zh-cn\">\u5b57<\/a><b>\u6587\u8fdc<\/b>\uff0c<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%8D%97%E5%8C%97%E6%9C%9D&amp;variant=zh-cn\">\u5357\u5317\u671d<\/a>\u65f6\u671f<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%95%B0%E5%AD%A6%E5%AE%B6&amp;variant=zh-cn\">\u6570\u5b66\u5bb6<\/a>\u3001<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%A4%A9%E6%96%87%E5%AD%A6%E5%AE%B6&amp;variant=zh-cn\">\u5929\u6587\u5b66\u5bb6<\/a>\u3002<\/p>\n<p>\u7956\u51b2\u4e4b\u7956\u7c4d\u8303\u9633\u90e1\u9052\u53bf\uff08\u4eca<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%B2%B3%E5%8C%97&amp;variant=zh-cn\">\u6cb3\u5317<\/a><a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%B6%9E%E6%B0%B4&amp;variant=zh-cn\">\u6d9e\u6c34<\/a>\uff09\uff0c\u4e3a\u907f\u6218\u4e71\uff0c\u7956\u51b2\u4e4b\u7684\u7956\u7236\u7956\u660c\u7531\u6cb3\u5317\u8fc1\u81f3\u6c5f\u5357\u3002\u7956\u660c\u66fe\u4efb<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%8D%97%E6%9C%9D%E5%AE%8B&amp;variant=zh-cn\">\u5218\u5b8b<\/a>\u7684\u201c\u5927\u5320\u537f\u201d\uff0c\u638c\u7ba1\u571f\u6728\u5de5\u7a0b\uff1b\u7956\u51b2\u4e4b\u7684\u7236\u4eb2\u4e5f\u5728\u671d\u4e2d\u505a\u5b98\u3002<\/p>\n<p>\u7956\u51b2\u4e4b\u751f\u4e8e<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%BB%BA%E5%BA%B7&amp;variant=zh-cn\">\u5efa\u5eb7<\/a>\uff08\u4eca<a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E6%B1%9F%E8%8B%8F&amp;variant=zh-cn\">\u6c5f\u82cf<\/a><a href=\"http:\/\/zh.wikipedia.org\/w\/index.php?title=%E5%8D%97%E4%BA%AC&amp;variant=zh-cn\">\u5357\u4eac<\/a>\uff09\u3002\u7956\u5bb6\u5386\u4ee3\u90fd\u5bf9\u5929\u6587\u5386\u6cd5\u7d20\u6709\u7814\u7a76\uff0c\u7956\u51b2\u4e4b\u4ece\u5c0f\u5c31\u6709\u673a\u4f1a\u63a5\u89e6\u5929\u6587\u3001\u6570\u5b66\u77e5\u8bc6\u3002\u7956\u51b2\u4e4b\u9752\u5e74\u65f6\uff0c\u5c31\u5f97\u5230\u535a\u5b66\u591a\u624d\u7684\u540d\u58f0\uff0c<a 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