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\u4e1a\u4f59\u6570\u5b66\u4e4b\u738b\u2014\u8d39\u9a6c<\/b><\/p>\n
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1637\u5e74\u5de6\u53f3\uff0c\u5728\u7814\u7a76\u300a\u7b97\u672f\u300b\u7b2c\u4e8c\u5377\u7684\u65f6\u5019\uff0c\u8d39\u9a6c\u88ab\u6bd5\u8fbe\u54e5\u62c9\u65af\u65b9\u7a0b(\u6211\u56fd\u4fd7\u79f0\u7684\u52fe\u80a1\u65b9\u7a0b:x^2 y^2\uff1dz^2)\u6709\u65e0\u7a77\u591a\u4e2a\u6574\u6570\u89e3\u8fd9\u4e2a\u73b0\u8c61\u6240\u5438\u5f15\uff0c\u4f46\u96c4\u5fc3\u52c3\u52c3\u7684\u8d39\u9a6c\u51b3\u5fc3\u641e\u70b9\u6bd4\u53e4\u5e0c\u814a\u4eba\u9ad8\u660e\u7684\u4e1c\u897f\u51fa\u6765\uff0c\u4e8e\u662f\u4ed6\u628a\u65b9\u7a0b\u7684\u5e42\u63d0\u9ad8\u52303\uff0c\u4e00\u756a\u82e6\u82e6\u601d\u7d22\u4e4b\u540e\uff0c\u8d39\u9a6c\u5e76\u6ca1\u6709\u5f97\u5230\u6574\u6570\u89e3\uff0c\u800c\u4ed6\u8fd8\u4e0d\u6ee1\u8db3\u4e8e\u6b64\uff0c\u7ee7\u7eed\u601d\u8003\u5982\u679c\u5e42\u6b21\u66f4\u9ad8\u662f\u5426\u4e5f\u65e0\u89e3\u5462\uff1f\u8d39\u9a6c\u628a\u4ed6\u601d\u8003\u7684\u7ed3\u679c\u5199\u5728\u4e86\u8fd9\u672c\u4e66\u9760\u8fd1\u7b2c\u516b\u4e2a\u95ee\u9898\u7684\u7a7a\u767d\u5904:<\/p>\n
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\u5bf9\u6570\u5b66\u5b66\u4e60\u8d8a\u6765\u8d8a\u6709\u4fe1\u5fc3\u7684\u70ed\u5c14\u66fc\u9010\u6e10\u628a\u6ce8\u610f\u529b\u8f6c\u79fb\u5230\u4e86\u6570\u8bba\u4e0a\uff0c\u7cbe\u529b\u5341\u5206\u65fa\u76db\u7684\u5979\u8fd8\u627e\u5230\u4e86\u9ad8\u65af(1777-1855)\u8fdb\u884c\u8ba8\u8bba\u3002\u5bf9\u4e8e\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u89e3\u51b3\uff0c\u70ed\u5c14\u66fc\u63d0\u51fa\u4e86\u65b0\u7684\u7b56\u7565:\u4e00\u6b21\u5c31\u9a8c\u8bc1\u4e00\u7c7b\u6570\u7684\u60c5\u5f62\uff0c\u4e5f\u5c31\u90a3\u4e9b\u4f7f\u5f97(2p\uff0b1)\u4e5f\u4e3a\u7d20\u6570\u7684\u7d20\u6570p\u3002\u5979\u5411\u9ad8\u65af\u5c55\u793a\u4e86\u81ea\u5df1\u7684\u201c\u5927\u6982\u201d\u8ba1\u7b97\uff0c\u4f46\u5e76\u6ca1\u6709\u8bc1\u660e\uff0c\u4f46\u8fd9\u79cd\u60f3\u6cd5\u5374\u6781\u5927\u5730\u6fc0\u53d1\u4e86\u6570\u5b66\u5bb6\u95e8\u7684\u7075\u611f\uff0c\u6570\u5b66\u754c\u5bf9\u8d39\u9a6c\u5927\u5b9a\u7406\u53c8\u91cd\u65b0\u71c3\u8d77\u4e86\u6fc0\u60c5\u3002<\/p>\n
<\/p>\n
1825\u5e74\uff0c\u72c4\u5229\u514b\u96f7(1805-1859)\u548c\u52d2\u8ba9\u5fb7(1752-1833)\u5728\u70ed\u5c14\u66fc\u5de5\u4f5c\u7684\u57fa\u7840\u4e0a\uff0c\u5f97\u5230\u4e86n\u4e3a5\u65f6\u7684\u8bc1\u660e\u300214\u4e4b\u540e\uff0c\u6cd5\u56fd\u6570\u5b66\u5bb6\u62c9\u6885(1795-1870)\u5728\u4e00\u756a\u6539\u8fdb\u4e4b\u540e\uff0c\u53c8\u8bc1\u660e\u4e86n\u4e3a7\u7684\u60c5\u5f62\u3002\u5f53\u7136\uff0c\u8fd9\u4e9b\u5de5\u4f5c\u90fd\u662f\u5728\u70ed\u5c14\u66fc\u7684\u57fa\u7840\u4e0a\u5b8c\u6210\u7684\u3002\u5728\u90a3\u4e2a\u5973\u6027\u5e76\u4e0d\u53d7\u79d1\u5b66\u754c\u5f85\u89c1\u7684\u5e74\u4ee3\uff0c\u70ed\u5c14\u66fc\u51ed\u501f\u987d\u5f3a\u7684\u6bc5\u529b\u548c\u60ca\u4eba\u7684\u624d\u534e\u8ba9\u6211\u4eec\u770b\u5230\u4e86\u5973\u6027\u4e5f\u53ef\u4ee5\u5728\u79d1\u5b66\u63a2\u7d22\u4e0a\u5360\u6709\u4e00\u5e2d\u4e4b\u5730\uff0c\u5341\u5206\u4ee4\u4eba\u8d5e\u53f9\u548c\u5c0a\u656c\uff01<\/p>\n
\u4e0d\u4e45\u540e\uff0c\u6cd5\u56fd\u79d1\u5b66\u9662\u4ee5\u91d1\u8d28\u5956\u7ae0\u548c3000\u6cd5\u90ce\u60ac\u8d4f\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u8bc1\u660e\u3002\u62c9\u6885\u548c\u67ef\u897f(1789-1857)\u5728\u6b64\u671f\u95f4\u660e\u4e89\u6697\u6597\uff0c\u76f8\u7ee7\u53d1\u8868\u4e86\u81ea\u5df1\u7684\u8bc1\u660e\uff0c\u7136\u800c\u5747\u542b\u7cca\u4e0d\u6e05\uff0c\u4f46\u4f17\u4eba\u53c8\u96be\u4ee5\u8bf4\u51fa\u6709\u4ec0\u4e48\u95ee\u9898\u3002\u4f17\u4eba\u8fd8\u610f\u72b9\u672a\u5c3d\u4e4b\u540e\u7684\u4e00\u4e2a\u6708\u540e\uff0c\u5218\u7ef4\u5c14(1809-1882)\u7a81\u7136\u5ba3\u8bfb\u4e86\u5fb7\u56fd\u6570\u5b66\u5bb6\u5e93\u9ed8\u5c14(1810-1893)\u7684\u6765\u4fe1\uff0c\u53ef\u8c13\u4e00\u77f3\u6fc0\u8d77\u5343\u5c42\u6d6a\u3002<\/p>\n
\u200b<\/p>\n
\u62ff\u7834\u4ed1\u653f\u5e9c\u7684\u5165\u4fb5\u7ed9\u5e74\u5e7c\u7684\u5e93\u9ed8\u5c14\u9020\u6210\u4e86\u6781\u5927\u7684\u5fc3\u7406\u521b\u4f24\uff0c\u5927\u5b66\u6bd5\u4e1a\u540e\u7684\u4ed6\u51b3\u5fc3\u7814\u7a76\u519b\u4e8b\u79d1\u5b66\uff0c\u4e0d\u518d\u8ba9\u81ea\u5df1\u7684\u7956\u56fd\u518d\u906d\u53d7\u78e8\u96be\u3002\u4f46\u540c\u65f6\uff0c\u5e93\u9ed8\u5c14\u4e5f\u79ef\u6781\u5730\u7814\u7a76\u81ea\u5df1\u70ed\u7231\u7684\u6570\u5b66\u3002<\/p>\n
\u5e93\u9ed8\u5c14\u867d\u8fdc\u5728\u5fb7\u56fd\uff0c\u4f46\u5bf9\u6cd5\u56fd\u79d1\u5b66\u9662\u6700\u8fd1\u6709\u5173\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u4e89\u8bba\u6253\u542c\u5f97\u4e00\u6e05\u4e8c\u695a\uff0c\u4e5f\u4ed4\u7ec6\u8bfb\u4e86\u62c9\u6885\u548c\u67ef\u897f\u7684\u8bc1\u660e\u3002\u505a\u4e3a\u5f53\u65f6\u6700\u5353\u8d8a\u7684\u6570\u8bba\u5b66\u5bb6\uff0c\u4ed6\u9a6c\u4e0a\u5c31\u770b\u51fa\u4e86\u95ee\u9898\u6240\u5728\u3002\u62c9\u6885\u548c\u67ef\u897f\u4e8c\u4eba\u7684\u8bc1\u660e\u90fd\u4f9d\u8d56\u4e8e\u7b97\u672f\u57fa\u672c\u5b9a\u7406:\u81ea\u7136\u6570\u90fd\u53ef\u4ee5\u8868\u793a\u4e3a\u4e00\u4e9b\u7d20\u6570\u7684\u4e58\u79ef\uff0c\u5982\u679c\u4e0d\u8ba1\u6b21\u5e8f\uff0c\u8fd9\u6837\u7684\u5206\u89e3\u8fd8\u662f\u552f\u4e00\u7684\u3002\u5206\u89e3\u7684\u552f\u4e00\u6027\u6b63\u662f\u4e8c\u4eba\u8bc1\u660e\u7684\u5173\u952e\u3002\u7136\u800c\u8bc1\u660e\u5e76\u4e0d\u5b8c\u5168\u662f\u9650\u5236\u5728\u5b9e\u6570\u57df\u5185\u8fdb\u884c\u7684\uff0c\u56e0\u6b64\u552f\u4e00\u6027\u4fbf\u4e5f\u4e0d\u518d\u6210\u7acb\uff0c\u4f8b\u598212\uff1d(1 \u221a-11)(1-\u221a-11)\uff1d(2 \u221a-10)(2-\u221a-10)\u3002\u5e93\u9ed8\u5c14\u7684\u6765\u4fe1\u4e00\u4e0b\u5b50\u4f7f\u4f17\u4eba\u6cc4\u4e86\u6c14\uff0c\u5e0c\u671b\u518d\u6b21\u6210\u4e86\u7edd\u671b\u3002\u5e93\u9ed8\u5c14\u4e0d\u4ec5\u6253\u51fb\u4e86\u5f53\u65f6\u7684\u6570\u5b66\u5bb6\uff0c\u4e5f\u4f7f\u5f97\u540e\u6765\u8005\u671b\u800c\u5374\u6b65\uff0c\u4e4b\u540e\u957f\u8fbe\u4e24\u4e2a\u4e16\u7eaa\u4e4b\u5185\uff0c\u8d39\u9a6c\u5927\u5b9a\u7406\u88ab\u5c18\u5c01\u4e86\u8d77\u6765\u3002<\/p>\n
\u66d9\u5149:\u8c37\u5c71-\u5fd7\u6751\u731c\u60f3<\/b><\/p>\n
\u6218\u540e\u7684\u65e5\u672c\u6ee1\u76ee\u75ae\u75cd\uff0c\u4f46\u6709\u4e24\u4f4d\u5e74\u8f7b\u4eba\u5374\u4ecd\u6267\u7740\u5730\u6c89\u8ff7\u4e8e\u6570\u5b66\u4e4b\u4e2d\uff0c\u4ed6\u4eec\u5c31\u662f\u5fd7\u6751\u4e94\u90ce(1930-)\u548c\u8c37\u5c71\u4e30(1927-1958)\u30021954\u5e74\uff0c\u4e24\u4eba\u56e0\u5171\u540c\u63a2\u8ba8\u4e00\u7bc7\u8bba\u6587\u800c\u7ed3\u8bc6\uff0c\u8c01\u4e5f\u6ca1\u60f3\u5230\uff0c\u5f53\u65f6\u540d\u4e0d\u89c1\u7ecf\u4f20\u7684\u4e8c\u4eba\u5c06\u4f1a\u5728\u8d39\u9a6c\u5927\u5b9a\u7406\u4e0a\u7559\u4e0b\u6d53\u58a8\u91cd\u5f69\u7684\u4e00\u7b14\u3002<\/p>\n
\u200b<\/p>\n
\u6a21\u5f62\u5f0f\u662f\u6570\u5b66\u4e2d\u975e\u5e38\u590d\u6742\u800c\u6df1\u523b\u7684\u5185\u5bb9\uff0c\u7b80\u5355\u6765\u8bf4\uff0c\u5b83\u7814\u7a76\u7684\u662f\u5728\u7279\u5b9a\u7684\u53d8\u6362\u4e4b\u4e0b\u4fdd\u6301\u67d0\u4e9b\u6027\u8d28\u4e0d\u53d8\u7684\u89e3\u6790\u51fd\u6570\u30021955\u5e74\uff0c\u4e00\u573a\u56fd\u9645\u5b66\u672f\u7814\u8ba8\u4f1a\u5728\u4e1c\u4eac\u4e3e\u529e\uff0c\u4f1a\u4e0a\uff0c\u5fd7\u6751\u4e94\u90ce\u548c\u8c37\u5c71\u4e30\u63d0\u51fa\u4e86\u731c\u60f3:\u692d\u5706\u65b9\u7a0b\u7684E-\u5e8f\u5217\u5bf9\u5e94\u4e8e\u4e00\u4e2a\u7279\u5b9a\u7684\u6a21\u5f62\u5f0f\u7684M-\u5e8f\u5217\u5e76\u5b8c\u5168\u76f8\u7b49\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u6bcf\u4e00\u4e2a\u692d\u5706\u975e\u5e38\u90fd\u5bf9\u5e94\u4e00\u4e2a\u6a21\u5f62\u5f0f\u3002\u5982\u679c\u731c\u60f3\u6210\u7acb\uff0c\u90a3\u770b\u4f3c\u6beb\u65e0\u5173\u7cfb\u7684\u4e24\u4e2a\u4e1c\u897f\u90fd\u4ea7\u751f\u4e86\u6df1\u523b\u7684\u8054\u7cfb\u3002\u7136\u800c\u5f53\u65f6\u7684\u6570\u5b66\u754c\u5374\u4f3c\u4e4e\u6ca1\u6709\u610f\u8bc6\u5230\u5b83\u7684\u91cd\u8981\u6027\u3002<\/p>\n
\u800c\u987d\u5f3a\u7684\u4e8c\u4eba\u51b3\u610f\u7ee7\u7eed\u5c06\u7814\u7a76\u8fdb\u884c\u4e0b\u53bb\u30021957\u5e74\uff0c\u5fd7\u6751\u5e94\u9080\u524d\u5f80\u666e\u6797\u65af\u987f\u8fdb\u884c\u4e3a\u671f\u4e24\u5e74\u7684\u5ba2\u5ea7\u6559\u6388\u4e4b\u65c5\uff0c\u5e76\u6253\u7b97\u56de\u6765\u4e4b\u540e\u7ee7\u7eed\u4e0e\u8c37\u5c71\u5408\u4f5c\u7814\u7a76\u3002\u7136\u800c\u5669\u8017\u7a81\u81f3:\u8c37\u5c71\u57281958\u5e7411\u670817\u65e5\u81ea\u6740\u8eab\u4ea1\uff0c\u968f\u4ed6\u524d\u53bb\u7684\u8fd8\u6709\u4ed6\u7684\u672a\u5a5a\u59bb\u3002\u7531\u4e8e\u4e8b\u53d1\u7a81\u7136\uff0c\u6ca1\u6709\u4eba\u77e5\u9053\u671f\u95f4\u7684\u5177\u4f53\u771f\u5b9e\u539f\u56e0\uff0c\u7559\u4e0b\u7684\u53ea\u6709\u65e0\u5c3d\u7684\u9057\u61be\u548c\u60cb\u60dc\u3002<\/p>\n
\u76f4\u5230\u5f53\u65f6\u7684\u9886\u8896\u7ea7\u6570\u5b66\u5bb6\u97e6\u4f9d\u80af\u5b9a\u8fd9\u4e2a\u731c\u60f3\u4e4b\u540e\uff0c\u8c37\u5c71-\u5fd7\u6751\u731c\u60f3\u624d\u8fdb\u5165\u4e3b\u6d41\u6570\u5b66\u5bb6\u7684\u89c6\u91ce\u4e2d\u3002<\/p>\n
\u8f6c\u673a\u548c\u7a81\u7834\u51fa\u73b0\u57281984\u5e74\u3002\u4e00\u573a\u5728\u5fb7\u56fd\u4e3e\u529e\u7684\u7814\u8ba8\u4f1a\u4e0a\uff0cFrey\u63d0\u51fa\u8bba\u65ad:\u5982\u679c\u8c37\u5c71-\u5fd7\u6751\u731c\u60f3\u6210\u7acb\uff0c\u90a3\u4e48\u8d39\u9a6c\u5927\u5b9a\u7406\u5c31\u6210\u7acb\uff01\u4f46\u4ed6\u672c\u4eba\u7684\u8bc1\u660e\u5374\u5e76\u4e0d\u5b8c\u6574\u3002\u4e00\u77f3\u6fc0\u8d77\u5343\u5c42\u6d6a\uff0c\u5728\u573a\u7684\u542c\u4f17\u5168\u90fd\u53d1\u4e86\u75af\u4e00\u6837\u7684\u51b2\u5411\u6253\u5370\u5ba4\uff0c\u8feb\u4e0d\u53ca\u5f85\u5730\u8981\u83b7\u5f97\u4e00\u4efdFrey\u7684\u62a5\u544a\uff0c\u597d\u56de\u53bb\u4e4b\u540e\u4ed4\u7ec6\u63a2\u7a76\u4ee5\u4fbf\u80fd\u5f25\u8865\u4ed6\u7684\u4e0d\u8db3\u3002<\/p>\n
\u5dee\u4e0d\u591a\u4e24\u5e74\u4e4b\u540e\uff0c\u6765\u81ea\u52a0\u5dde\u4f2f\u514b\u5229\u7684\u91cc\u8d1d\u7279\u5df2\u7ecf\u5b8c\u6210\u4e86\u8bc1\u660e\uff0c\u4f46\u4ed6\u81ea\u5df1\u5374\u8fd8\u6ca1\u610f\u8bc6\u5230\u3002\u5728\u6885\u4fee\u5c14\u7684\u63d0\u9192\u4e4b\u4e0b\uff0c\u4ed6\u624d\u610f\u8bc6\u5230\u81ea\u5df1\u5df2\u7ecf\u5b8c\u6210\u4e86\u8bc1\u660e\uff01\u7136\u800c\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u8bc1\u660e\u4f3c\u4e4e\u8fd8\u9065\u9065\u65e0\u671f\uff0c\u56e0\u4e3a\u8c37\u5c71-\u5fd7\u6751\u731c\u60f3\u8fd8\u6a2a\u4e98\u5728\u6570\u5b66\u5bb6\u9762\u524d\u3002<\/p>\n
\u201c\u6211\u60f3\u6211\u5c31\u5728\u8fd9\u91cc\u7ed3\u675f\u201d\u2014\u6000\u5c14\u65af<\/b><\/p>\n
\u6000\u5c14\u65af1953\u5e74\u51fa\u751f\u4e8e\u82f1\u56fd\u5251\u6865\uff0c\u7236\u4eb2\u662f\u4e00\u540d\u5de5\u7a0b\u5b66\u6559\u6388\u300210\u5c81\u7684\u65f6\u5019\uff0c\u4ed6\u5076\u7136\u5728\u4e00\u672c\u4e66\u4e2d\u4e86\u89e3\u5230\u4e86\u8d39\u9a6c\u5927\u5b9a\u7406\u7684\u5965\u5999\uff0c\u5e76\u6084\u7136\u5728\u5fc3\u4e2d\u57cb\u4e0b\u4e86\u63a2\u7d22\u7684\u79cd\u5b50\u30021974\u5e74\u672c\u79d1\u6bd5\u4e1a\u4e8e\u725b\u6d25\u5927\u5b66\u540e\uff0c\u6765\u5230\u5251\u6865\u5927\u5b66\u5f00\u59cb\u4ed6\u7684\u7814\u7a76\u751f\u5b66\u4e60\uff0c\u5728\u5bfc\u5e08\u7684\u6307\u5bfc\u4e0b\u8fdb\u884c\u692d\u5706\u65b9\u7a0b\u548c\u66f2\u7ebf\u7814\u7a76\uff0c\u535a\u58eb\u6bd5\u4e1a\u540e\u6765\u5230\u666e\u6797\u65af\u987f\u5de5\u4f5c\u3002<\/p>\n
<\/p>\n
1986\u5e74\u542c\u95fb\u91cc\u8d1d\u7279\u8bc1\u660e\u4e86Frey\u7684\u731c\u60f3\u4ee5\u540e\uff0c\u6539\u53d8\u6000\u5c14\u65af\u4e00\u751f\u7684\u65f6\u523b\u5230\u6765\u4e86\uff0c\u5b9e\u73b0\u4ed6\u513f\u65f6\u68a6\u60f3\u7684\u673a\u4f1a\u6765\u4e86\uff0c\u4ed6\u5df2\u4e0b\u5b9a\u51b3\u5fc3\uff0c\u6240\u5fc5\u987b\u505a\u7684\u4e00\u5207\u5c31\u662f\u8981\u8bc1\u660e\u8c37\u5c71-\u5fd7\u6751\u731c\u60f3\u3002\u4f46\u5305\u62ec\u4ed6\u5bfc\u5e08\u5728\u5185\u7684\u4f17\u591a\u6570\u5b66\u5bb6\u90fd\u76f8\u4fe1\u8fd9\u5c06\u65e0\u529f\u800c\u8fd4\uff0c\u4f46\u6000\u5c14\u65af\u5374\u575a\u6301\u53bb\u8ffd\u6c42\u81ea\u5df1\u7684\u68a6\u60f3\u3002<\/p>\n
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