{"id":31136,"date":"2021-12-18T17:48:52","date_gmt":"2021-12-18T09:48:52","guid":{"rendered":"https:\/\/swarma.org\/?p=31136"},"modified":"2021-12-18T17:48:52","modified_gmt":"2021-12-18T09:48:52","slug":"%e4%bb%8e%e5%93%a5%e5%b0%bc%e6%96%af%e5%a0%a1%e4%b8%83%e6%a1%a5%e9%97%ae%e9%a2%98%e8%b0%88%e8%b5%b7%e4%b8%a8%e9%99%88%e5%85%b3%e8%8d%a3","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=31136","title":{"rendered":"\u4ece\u54e5\u5c3c\u65af\u5821\u4e03\u6865\u95ee\u9898\u8c08\u8d77\u4e28\u9648\u5173\u8363"},"content":{"rendered":"
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1. \u54e5\u5c3c\u65af\u5821\u4e03\u6865\u95ee\u9898<\/strong><\/strong><\/p>\n<\/section>\n

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\u54e5\u5c3c\u65af\u5821<\/span>\uff08K\u00f6nigsberg\uff09<\/span>\u662f\u5ea7\u5c0f\u5de7\u73b2\u73d1\u7684\u53e4\u90fd\uff0c\u4f4d\u4e8e\u6b27\u6d32\u6ce2\u7f57\u7684\u6d77\u4e1c\u5357\u6cbf\u5cb8\u7684\u6851\u6bd4\u4e9a\u534a\u5c9b\u5357\u90e8\uff0c\u9762\u79ef\u7ea61.5\u4e07\u5e73\u65b9\u516c\u91cc\uff0c\u4eca\u5929\u4eba\u53e3\u4e0d\u523050\u4e07\u3002\u8be5\u57ce\u5821\u7531\u6761\u987f\u9a91\u58eb\u56e2<\/span>\uff08Teutonic Order\uff09<\/span>\u5317\u65b9\u5341\u5b57\u519b\u4e8e1255\u5e74\u5efa\u7acb\uff0c\u5148\u540e\u6210\u4e3a\u6761\u987f\u9a91\u58eb\u56e2\u56fd\u3001\u666e\u9c81\u58eb\u516c\u56fd<\/span>\uff08Kingdom of Prussia\uff09<\/span>\u548c\u4e1c\u666e\u9c81\u58eb\u56fd<\/span>\uff08East Prussia\uff09<\/span>\u7684\u9996\u5e9c\u3002<\/span>         <\/span><\/p>\n


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\u56fe1  \u54e5\u5c3c\u65af\u5821\u6559\u5802\uff081895\u5e74\uff0c\u590d\u539f\u56fe\uff09<\/span>
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1771\u5e74\uff0c\u6cd5\u56fd\u6570\u5b66\u5bb6\u8303\u5fb7\u8499<\/span>\uff08Alexandre-Theophile Vandermonde\uff0c1735\uff0d1796\uff09<\/span>\u7814\u7a76\u4e86\u56fd\u9645\u8c61\u68cb\u7684\u201c\u9a91\u58eb\u201d\u80fd\u5426\u8d70\u904d\u68cb\u76d8\u6bcf\u4e00\u4e2a\u65b9\u683c\u7684\u6e38\u620f\u95ee\u9898<\/span>\uff08Knight’s Tour Problem\uff09<\/span>\u3002\u8fc7\u4e86\u597d\u591a\u5e74\u4e4b\u540e\uff0c\u57fa\u4e8e\u5bf9\u4e0a\u9762\u4e24\u4e2a\u56fe\u8bba\u6e38\u620f\u7684\u5174\u8da3\uff0c\u7231\u5c14\u5170\u6570\u5b66\u5bb6\u54c8\u5bc6\u987f<\/span>\uff08Sir William R. Hamilton\uff0c1805\uff0d1865\uff09<\/span>\u8003\u8651\u4e86\u4e00\u7c7b\u548c\u6b27\u62c9\u56fe\u201c\u5bf9\u5076\u201d\u7684\u56fe\uff0c\u5c31\u662f\u4e0d\u7ba1\u4e00\u5e45\u89c4\u6a21\u6709\u9650\u7684\u56fe\u6709\u591a\u5c11\u4e2a\u8282\u70b9\u548c\u591a\u5c11\u6761\u8fde\u8fb9\uff0c\u4e5f\u4e0d\u7ba1\u4f60\u4ece\u54ea\u4e2a\u8282\u70b9\u8d77\u6b65\uff0c\u5982\u679c\u603b\u5b58\u5728\u4e00\u6761\u8def\u5f84\u8ba9\u4f60\u8d70\u904d\u6240\u6709\u7684\u8282\u70b9\uff0c\u4e0d\u91cd\u590d\u4e5f\u4e0d\u9057\u6f0f\uff0c\u6700\u540e\u8fd8\u80fd\u56de\u5230\u8d77\u70b9\uff0c\u8fd9\u7c7b\u56fe\u5c31\u79f0\u4e3a\u54c8\u5bc6\u987f\u56fe\u3002\u54c8\u5bc6\u987f\u56fe\u5bf9\u4f60\u8d70\u8fc7\u591a\u5c11\u6761\u8fb9\uff0c\u6709\u6ca1\u6709\u9057\u6f0f\u4e00\u4e9b\u8fb9\uff0c\u90fd\u662f\u6ca1\u6709\u9650\u5236\u7684\u3002\u56e0\u6b64\uff0c\u8d70\u904d\u4e00\u5e45\u54c8\u5bc6\u987f\u56fe\u91cc\u6240\u6709\u8282\u70b9\u7684\u8def\u5f84\u53ef\u80fd\u4e0d\u662f\u552f\u4e00\u7684\uff0c\u56e0\u4e3a\u4e5f\u8bb8\u4f1a\u5b58\u5728\u4e0d\u540c\u7684\u8def\u5f84\u90fd\u53ef\u4ee5\u628a\u6240\u6709\u7684\u8282\u70b9\u8fde\u5728\u4e00\u8d77\u5e76\u4e14\u9996\u5c3e\u76f8\u63a5\u3002<\/span><\/section>\n

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\u56fe5  [\u5de6] \u6b27\u62c9\uff081707\uff0d1783\uff09\uff1b[\u53f3] \u54c8\u5bc6\u987f\uff081805\uff0d1865\uff09<\/span>
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\u81ea\u4ece\u6b27\u62c9\u89e3\u51b3\u4e86\u6c11\u95f4\u559c\u95fb\u4e50\u9053\u7684\u4e03\u6865\u95ee\u9898\u4e4b\u540e\uff0c\u54e5\u5c3c\u65af\u5821\u4fbf\u8d70\u8fdb\u4e86\u5927\u4f17\u7684\u89c6\u91ce\u3002<\/span><\/section>\n

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\u5176\u5b9e\uff0c\u54e5\u5c3c\u65af\u5821\u867d\u7136\u5386\u53f2\u4e0d\u957f\uff0c\u5730\u57df\u4e0d\u5927\uff0c\u4f46\u5730\u7075\u4eba\u6770\uff0c\u540d\u4eba\u5f88\u591a\u3002\u5728\u54e5\u5c3c\u65af\u5821\u51fa\u751f\u957f\u5927\u7684\u4f17\u591a\u4eba\u7269\u4e4b\u4e2d\uff0c\u6211\u4eec\u53ea\u7b80\u5355\u5730\u8bf4\u8bf4\u201c\u4e00\u3001\u4e8c\u3001\u4e09\u201d\uff0c\u5373\u4e00\u4f4d\u54f2\u5b66\u5bb6<\/span>\uff08\u5eb7\u5fb7\uff09<\/span>\u3001\u4e8c\u4f4d\u7269\u7406\u5b66\u5bb6<\/span>\uff08\u57fa\u5c14\u970d\u592b\u548c\u7d22\u672b\u83f2\uff09<\/span>\u548c\u4e09\u4f4d\u6570\u5b66\u5bb6<\/span>\uff08\u54e5\u5fb7\u5df4\u8d6b\u3001\u5e0c\u5c14\u4f2f\u7279\u548c\u95f5\u53ef\u592b\u65af\u57fa\uff09<\/span>\u3002\u5b9e\u9645\u4e0a\uff0c\u8981\u6bd4\u8f83\u5b8c\u6574\u5730\u4ecb\u7ecd\u4ed6\u4eec\u4e4b\u4e2d\u4efb\u4f55\u4e00\u4f4d\u7684\u751f\u5e73\u548c\u8d21\u732e\uff0c\u90fd\u5f97\u5199\u4e00\u672c\u5c0f\u4e66\u3002\u6b64\u5916\uff0c\u8fd8\u6709\u4e00\u4e9b\u8457\u540d\u4eba\u7269\u5c31\u4e0d\u5217\u4e3e\u4e86\uff0c\u5982\u5316\u5b66\u5bb6\u74e6\u62c9\u8d6b<\/span>\uff08Otto Wallach\uff0c1847\uff0d1931\uff09<\/span>\u662f 1910 \u5e74\u8bfa\u8d1d\u5c14\u5316\u5b66\u5956\u5f97\u4e3b\u3001\u6570\u5b66\u5bb6\u83ab\u6cfd<\/span>\uff08Jurgen K. Moser\uff0c1928\uff0d1999\uff09<\/span>\u662f\u6570\u5b66\u52a8\u529b\u7cfb\u7edfKAM\u7406\u8bba\u4e2d\u7684M\u3001\u6570\u5b66\u5bb6\u9ed1\u585e<\/span>\uff08Ludwig O. Hesse\uff0c1811\uff0d1874\uff09<\/span>\u4ee5\u4ed6\u547d\u540d\u7684\u77e9\u9635<\/span>\uff08Hessian Matrix\uff09<\/span>\u4e3a\u5927\u5bb6\u6240\u719f\u8bc6 \uff0c\u8fd8\u4e0d\u8ba1\u53ca\u6587\u5b66\u3001\u5386\u53f2\u3001\u653f\u6cbb\u3001\u5b97\u6559\u3001\u97f3\u4e50\u3001\u827a\u672f\u7b49\u9886\u57df\u7684\u540d\u5bb6\u3002<\/span><\/section>\n

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\u54e5\u5c3c\u65af\u5821\u6700\u8457\u540d\u7684\u5e02\u6c11\u5f53\u6570\u54f2\u5b66\u5bb6\u5eb7\u5fb7<\/span>\uff08Immanuel Kant\uff0c1724\u5e744\u670822\u65e5\uff0d1804\u5e742\u670812\u65e5\uff09<\/span>\u3002<\/span><\/section>\n

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\u5eb7\u5fb7\u662f17\uff0d18\u4e16\u7eaa\u6b27\u6d32\u6587\u827a\u590d\u5174\u4e4b\u540e\u7684\u53cd\u5c01\u5efa\u601d\u60f3\u89e3\u653e\u542f\u8499\u8fd0\u52a8\u540e\u671f\u4e00\u4f4d\u4e3b\u8981\u54f2\u5b66\u5bb6\u3002\u4ed6\u8c03\u548c\u4e86\u7b1b\u5361\u513f\u7684\u7406\u6027\u4e3b\u4e49\u4e0e\u57f9\u6839\u7684\u7ecf\u9a8c\u4e3b\u4e49\uff0c\u53d1\u5c55\u4e86\u81ea\u6210\u4e00\u6d3e\u7684\u601d\u60f3\u4f53\u7cfb\uff0c\u88ab\u8ba4\u4e3a\u662f\u7ee7\u82cf\u683c\u62c9\u5e95\u3001\u67cf\u62c9\u56fe\u548c\u4e9a\u91cc\u65af\u591a\u5fb7\u540e\u897f\u65b9\u6700\u5177\u5f71\u54cd\u529b\u7684\u601d\u60f3\u5bb6\u4e4b\u4e00\u3002<\/span><\/section>\n

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\u5eb7\u5fb7\u6709\u4e0d\u5c11\u8bba\u8457\uff0c\u5176\u4e2d\u6838\u5fc3\u7684\u4e09\u5927\u8457\u4f5c\u88ab\u5408\u79f0\u4e3a\u201c\u4e09\u5927\u6279\u5224\u201d\uff0c\u5373\u300a\u7eaf\u7cb9\u7406\u6027\u6279\u5224\u300b\u3001\u300a\u5b9e\u8df5\u7406\u6027\u6279\u5224\u300b\u548c\u300a\u5224\u65ad\u529b\u6279\u5224\u300b\u3002\u8fd9\u4e09\u90e8\u8457\u4f5c\u5206\u522b\u7cfb\u7edf\u5730\u9610\u8ff0\u4e86\u4ed6\u7684\u77e5\u8bc6\u5b66\u3001\u4f26\u7406\u5b66\u548c\u7f8e\u5b66\u601d\u60f3\u3002\u300a\u7eaf\u7cb9\u7406\u6027\u6279\u5224\u300b\u4e00\u4e66\u88ab\u8ba4\u4e3a\u662f\u897f\u65b9\u54f2\u5b66\u53f2\u4e0a\u5212\u65f6\u4ee3\u7684\u5de8\u8457\u3002\u6b64\u5916\uff0c\u4ed6\u5728\u5b97\u6559\u54f2\u5b66\u3001\u6cd5\u5f8b\u54f2\u5b66\u548c\u5386\u53f2\u54f2\u5b66\u7b49\u65b9\u9762\u90fd\u6709\u91cd\u8981\u8d21\u732e\u3002\u4e00\u822c\u8ba4\u4e3a\uff0c\u5eb7\u5fb7\u7684\u9053\u5fb7\u54f2\u5b66\u4e0e\u4e2d\u56fd\u5112\u5bb6\u601d\u60f3\u7c7b\u4f3c\uff0c\u5f3a\u8c03\u4e2a\u4eba\u9053\u5fb7\u81ea\u5f8b\u4ece\u800c\u6784\u5efa\u7406\u60f3\u793e\u4f1a\u3002\u5eb7\u5fb7\u7684\u9053\u5fb7\u539f\u5219\u5c31\u662f\u201c\u4e3a\u9053\u5fb7\u800c\u9053\u5fb7\uff0c\u4e3a\u4e49\u52a1\u800c\u4e49\u52a1\u201d\uff0c\u5305\u62ec\u201c\u4e0d\u8981\u9a97\u4eba\u201d\u3001\u201c\u4e0d\u8981\u81ea\u6740\u201d\u3001\u201c\u53d1\u5c55\u81ea\u5df1\u7684\u624d\u80fd\u201d\u548c\u201c\u5e2e\u52a9\u522b\u4eba\u201d\u7b49\u65b9\u9762\uff0c\u4ee5\u81f4\u54f2\u5b66\u5bb6\u5c3c\u91c7<\/span>\uff08Friedrich W. Nietzsche\uff0c1844-1900\uff09<\/span>\u79f0\u5eb7\u5fb7\u4e3a\u201c\u54e5\u5c3c\u65af\u5821\u7684\u4e2d\u56fd\u4eba\u201d\u3002<\/span><\/section>\n

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\u5eb7\u5fb7\u56fa\u7136\u662f\u4e00\u540d\u54f2\u5b66\u5bb6\uff0c\u4f46\u4e5f\u5199\u8fc7\u597d\u51e0\u7bc7\u81ea\u7136\u79d1\u5b66\u8bba\u6587\u30021746\u5e74\u5eb7\u5fb7\u7684\u7236\u4eb2\u901d\u4e16\uff0c\u4e4b\u540e\u4ed6\u5f00\u59cb\u4e86\u957f\u8fbe\u4e5d\u5e74\u7684\u5bb6\u5ead\u6559\u5e08\u751f\u6daf\u3002\u671f\u95f4\uff0c\u4ed6\u53d1\u8868\u4e86\u4e24\u7bc7\u79d1\u5b66\u8bba\u6587\uff1a1754\u5e74\u7684\u201c\u5730\u7403\u5728\u7ed5\u8f74\u81ea\u8f6c\u65f6\u662f\u5426\u53d1\u751f\u53d8\u5316\u201d\u548c1755\u5e74\u7684\u201c\u4ece\u7269\u7406\u5b66\u4e0a\u63a8\u8bba\u5730\u7403\u662f\u5426\u5df2\u7ecf\u8870\u8001\u201d\u30021755\u5e74\uff0c\u5eb7\u5fb7\u5199\u4e86\u4e00\u7bc7\u5b66\u672f\u8bba\u6587\u201c\u8bba\u706b\u201d\uff0c\u4ee5\u6b64\u83b7\u5f97\u7855\u58eb\u5b66\u4f4d\u3002\u5728\u540c\u4e00\u5e74\uff0c\u4ed6\u53c8\u5199\u4e86\u201c\u5f62\u800c\u4e0a\u5b66\u8ba4\u8bc6\u7b2c\u4e00\u539f\u7406\u7684\u65b0\u8bf4\u660e\u201d\u4e00\u6587\uff0c\u4ece\u800c\u83b7\u5f97\u7687\u5bb6\u54e5\u5c3c\u65af\u5821\u5927\u5b66<\/span>\uff08Royal Albertus University of K\u00f6nigsberg\uff09<\/span>\u4efb\u6559\u7684\u673a\u4f1a\uff0c\u5728\u90a3\u91cc\u62c5\u4efb\u4e8615\u5e74\u7684\u7f16\u5916\u8bb2\u5e08\u3002<\/span><\/section>\n

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\u5eb7\u5fb7\u6027\u683c\u5185\u5411\uff0c\u6bd5\u751f\u90fd\u6ca1\u6709\u79bb\u5f00\u8fc7\u5bb6\u4e61\u54e5\u5c3c\u65af\u5821\u3002\u4ed6\u957f\u671f\u8eab\u4f53\u865a\u5f31\uff0c\u8fc7\u7740\u6781\u7b80\u751f\u6d3b\uff0c\u7ec8\u8eab\u672a\u5a36\u3002\u5eb7\u5fb7\u901d\u4e16\u540e\uff0c\u5893\u7891\u4e0a\u523b\u7740\u4ed6\u90a3\u672c\u540d\u8457\u300a\u5b9e\u8df5\u7406\u6027\u6279\u5224\u300b\u91cc\u7684\u4e00\u53e5\u8bdd\ufe30\u201c\u7fa4\u661f\u82cd\u7a79\u5728\u6211\u4e4b\u4e0a\uff0c\u9053\u5fb7\u6cd5\u5219\u5b58\u6211\u5fc3\u4e2d\u201d<\/span>\uff08Der bestirnte Himmel \u00fcber mir und das moralische Gesetz in mir\uff09<\/span>\uff0c\u4f5c\u4e3a\u4ed6\u4e00\u751f\u7684\u603b\u7ed3\u3002<\/span><\/section>\n

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\u57fa\u5c14\u970d\u592b<\/span>\uff08Gustav R. Kirchhoff\uff0c1824\u5e743\u670812\u65e5\uff0d1887\u5e7410\u670817\u65e5\uff09<\/span>\u57281847\u5e74\u4ece\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u7269\u7406\u7cfb\u6bd5\u4e1a\u3002\u5728\u5927\u5b66\u671f\u95f4\uff0c\u57fa\u5c14\u970d\u592b\u4e00\u76f4\u53c2\u52a0\u6570\u5b66\u7269\u7406\u5b66\u5bb6\u8bfa\u4f9d\u66fc<\/span>\uff08Franz E. Neumann\uff0c1789\uff0d1895\uff09<\/span>\u548c\u96c5\u53ef\u6bd4<\/span>\uff08Carl G. J. Jacobi\uff0c1804\uff0d1851\uff09<\/span>\u9886\u5bfc\u7684\u7814\u7a76\u8ba8\u8bba\u73ed\uff0c\u6df1\u53d7\u6570\u5b66\u718f\u9676\u3002\u8fd9\u4f4d\u96c5\u53ef\u6bd4\u4ee5\u4ed6\u7684\u77e9\u9635\u548c\u884c\u5217\u5f0f\u4e3a\u7406\u5de5\u79d1\u5e08\u751f\u6240\u719f\u8bc6\u3002\u4ed6\u51fa\u751f\u4e8e\u5f53\u5e74\u5c5e\u4e8e\u666e\u9c81\u58eb\u7684\u6ce2\u8328\u5766\uff0c1826\u5e74\u5230\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u4efb\u6559\uff0c\u5728\u90a3\u91cc\u5de5\u4f5c\u4e8616\u5e74\uff0c\u4e4b\u540e\u56e0\u5065\u5eb7\u95ee\u9898\u9000\u9690\u67cf\u6797\u3002<\/span><\/section>\n

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1845\u5e74\uff0c\u8fd8\u662f\u672c\u79d1\u751f\u768421\u5c81\u57fa\u5c14\u970d\u592b\u53d1\u8868\u7b2c\u4e00\u7bc7\u8bba\u6587\uff0c\u5c31\u5efa\u7acb\u4e86\u7535\u8def\u7f51\u7edc\u4e2d\u7535\u6d41\u3001\u7535\u538b\u3001\u7535\u963b\u5173\u7cfb\u7684\u4e24\u6761\u57fa\u672c\u5b9a\u5f8b\uff0c\u5373\u4ee5\u4ed6\u547d\u540d\u7684\u201c\u7535\u6d41\u5b9a\u5f8b\u201d\u548c\u201c\u7535\u538b\u5b9a\u5f8b\u201d\uff0c\u6210\u4e3a\u5206\u6790\u3001\u8ba1\u7b97\u548c\u8bbe\u8ba1\u5404\u79cd\u590d\u6742\u7535\u8def\u4e0d\u53ef\u6216\u7f3a\u7684\u57fa\u7840\u7406\u8bba\u548c\u5de5\u5177\u3002\u4ed6\u540e\u6765\u53c8\u7814\u7a76\u4e86\u7535\u8def\u4e2d\u7535\u7684\u6d41\u52a8\u548c\u5206\u5e03\uff0c\u9610\u660e\u4e86\u7535\u8def\u4e2d\u4e24\u70b9\u95f4\u7684\u7535\u52bf\u548c\u9759\u7535\u5b66\u7684\u7535\u52bf\u8fd9\u4e24\u4e2a\u7269\u7406\u91cf\u5728\u91cf\u7eb2\u548c\u5355\u4f4d\u4e0a\u662f\u4e00\u81f4\u7684\uff0c\u4ece\u800c\u4f7f\u57fa\u672c\u7535\u8def\u5b9a\u5f8b\u5177\u6709\u66f4\u4e00\u822c\u7684\u6db5\u4e49\u548c\u5e94\u7528\u3002\u57fa\u5c14\u970d\u592b\u56e0\u6b64\u5728\u7535\u5b50\u548c\u7535\u5668\u5de5\u7a0b\u9886\u57df\u6781\u8d1f\u76db\u540d\uff0c\u88ab\u79f0\u4e3a\u201c\u7535\u8def\u6c42\u89e3\u5927\u5e08\u201d\u3002<\/span><\/section>\n

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1850\u5e74\uff0c\u57fa\u5c14\u970d\u592b\u5728\u67cf\u6797\u5927\u5b66\u6267\u6559\u65f6\u53d1\u8868\u4e86\u8bba\u6587\u201c\u5f39\u6027\u5706\u677f\u7684\u5e73\u8861\u4e0e\u8fd0\u52a8\u201d\uff0c\u4ece\u4e09\u7ef4\u5f39\u6027\u529b\u5b66\u7684\u53d8\u5206\u5f00\u59cb\uff0c\u5f15\u8fdb\u4e86\u8457\u540d\u7684\u201c\u57fa\u5c14\u970d\u592b\u8584\u677f\u5047\u8bbe\u201d\u5e76\u7ed9\u51fa\u4e86\u8fb9\u754c\u6761\u4ef6\uff0c\u8fd8\u5bfc\u51fa\u4e86\u5706\u677f\u7684\u81ea\u7531\u632f\u52a8\u89e3\u548c\u4e00\u822c\u632f\u52a8\u8868\u8fbe\u5f0f\u3002<\/span><\/section>\n

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1854\u5e74\uff0c\u57fa\u5c14\u970d\u592b\u7531\u8457\u540d\u5316\u5b66\u5bb6\u672c\u751f<\/span>\uff08Robert W. Bunsen\uff0c1811\uff0d1899\uff09<\/span>\u63a8\u8350\uff0c\u5230\u4e86\u6d77\u5fb7\u5821\u5927\u5b66\u4efb\u804c\u6559\u6388\u3002<\/span><\/section>\n

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1859\u5e74\uff0c\u57fa\u5c14\u970d\u592b\u4e0e\u672c\u751f\u5408\u4f5c\uff0c\u5236\u6210\u7b2c\u4e00\u53f0\u5149\u8c31\u4eea\u5e76\u521b\u7acb\u4e86\u5149\u8c31\u5316\u5b66\u5206\u6790\u6cd5\uff0c\u7531\u6b64\u53d1\u73b0\u4e86\u5143\u7d20\u92ab\u548c\u92a3\u3002\u968f\u540e\uff0c\u5176\u4ed6\u79d1\u5b66\u5bb6\u5229\u7528\u5149\u8c31\u5316\u5b66\u5206\u6790\u6cd5\uff0c\u8fd8\u53d1\u73b0\u4e86\u9248\u548c\u7898\u7b49\u51e0\u79cd\u65b0\u5143\u7d20\u3002\u57fa\u5c14\u970d\u592b\u8fdb\u800c\u5229\u7528\u5149\u8c31\u5316\u5b66\u5206\u6790\u6cd5\u53bb\u7814\u7a76\u4e86\u592a\u9633\u53ca\u4e00\u4e9b\u884c\u661f\u7684\u5316\u5b66\u5143\u7d20\u8c31\u3002<\/span><\/section>\n

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1860\u5e74\uff0c\u57fa\u5c14\u970d\u592b\u505a\u4e86\u706f\u7130\u70e7\u707c\u98df\u76d0\u7684\u5b9e\u9a8c\uff0c\u5f97\u51fa\u4e86\u201c\u70ed\u8f90\u5c04\u57fa\u5c14\u970d\u592b\u5b9a\u5f8b\u201d\uff1a\u4efb\u4f55\u7269\u4f53\u7535\u78c1\u8f90\u5c04\u7684\u53d1\u5c04\u91cf\u548c\u5438\u6536\u91cf\u7684\u6bd4\u503c\u4e0e\u7269\u4f53\u672c\u8eab\u7279\u6027\u65e0\u5173\uff0c\u662f\u6ce2\u957f\u548c\u6e29\u5ea6\u7684\u666e\u9002\u51fd\u6570\uff0c\u4e0e\u5438\u6536\u7cfb\u6570\u6210\u6b63\u6bd4\u3002\u4ed6\u7531\u6b64\u5224\u65ad\uff1a\u592a\u9633\u5149\u8c31\u7684\u6697\u7ebf\u662f\u767d\u5149\u88ab\u5927\u6c14\u4e2d\u67d0\u4e9b\u5143\u7d20\u5438\u6536\u7684\u7ed3\u679c\u3002\u8fd9\u7ed9\u592a\u9633\u548c\u6046\u661f\u6210\u5206\u7684\u5206\u6790\u63d0\u4f9b\u4e86\u4e00\u79cd\u6709\u6548\u7684\u65b9\u6cd5\uff0c\u8ba9\u5929\u4f53\u7269\u7406\u8fdb\u5165\u4e86\u5149\u8c31\u5206\u6790\u7684\u65b0\u9636\u6bb5\u3002\u63a5\u7740\uff0c\u4ed6\u53c8\u63d0\u51fa\u4e86\u7edd\u5bf9\u9ed1\u4f53\u7684\u65b0\u6982\u5ff5\u3002<\/span><\/section>\n

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1862\u5e74\uff0c\u57fa\u5c14\u970d\u592b\u56e0\u5728\u592a\u9633\u5149\u548c\u4eba\u9020\u5149\u5149\u8c31\u7814\u7a76\u4e2d\u7684\u91cd\u8981\u8d21\u732e\u800c\u8363\u83b7Rumford\u5956\u7ae0\u3002<\/span><\/section>\n

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1875\u5e74\uff0c\u57fa\u5c14\u970d\u592b\u56de\u5230\u4e86\u67cf\u6797\u5927\u5b66\u4efb\u804c\u7406\u8bba\u7269\u7406\u6559\u6388\u3002\u5176\u65f6\uff0c\u4ed6\u7ed9\u51fa\u4e86\u60e0\u66f4\u65af-\u83f2\u6d85\u8033<\/span>\uff08Huygens\u2013Fresnel\uff09<\/span>\u539f\u7406\u7684\u4e25\u683c\u6570\u5b66\u5f62\u5f0f\uff0c\u5e76\u53d1\u8868\u4e864\u5377\u300a\u6570\u5b66\u7269\u7406\u5b66\u8bb2\u4e49\u300b\u3002<\/span><\/section>\n

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1887\u5e7410\u670817\u65e5\uff0c\u57fa\u5c14\u970d\u592b\u75c5\u901d\u4e8e\u67cf\u6797\uff0c\u4eab\u5e7463\u5c81\u3002<\/span><\/section>\n

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\u7d22\u672b\u83f2<\/span>\uff08Arnold J. W. Sommerfeld\uff0c1868\u5e7412\u67085\u65e5\uff0d1951\u5e744\u670826\u65e5\uff09<\/span>1886\u5e74\u8fdb\u5165\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u4e3b\u4fee\u6570\u5b66\uff0c1891 \u5e7423\u5c81\u65f6\u83b7\u535a\u58eb\u5b66\u4f4d\u3002\u4ed6\u968f\u540e\u51fa\u4efb\u54e5\u5ef7\u6839\u5927\u5b66\u52a9\u6559 \u30021897\u5e74\uff0c\u4ed6\u8f6c\u5230Clausthal\u77ff\u4e1a\u5b66\u6821\u4efb\u6559\u6388\uff0c1900\u5e74\u518d\u8f6c\u5230Aachen\u6280\u672f\u5b66\u9662\u4efb\u6559\u6388\uff0c1906\u5e74\u8d77\u5230\u6155\u5c3c\u9ed1\u5927\u5b66\u4efb\u7406\u8bba\u7269\u7406\u5b66\u6559\u6388\u76f4\u81f3\u9000\u4f11\u30021951\u5e744\u670826\u65e5\u5728\u6155\u5c3c\u9ed1\u610f\u5916\u88ab\u6c7d\u8f66\u649e\u5012\u4e0d\u6cbb\u79bb\u4e16\uff0c\u65f6\u5e7483\u5c81\u3002<\/span><\/section>\n

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\u7d22\u672b\u83f2\u7684\u4e3b\u8981\u79d1\u5b66\u5efa\u6811\u5728\u539f\u5b50\u7ed3\u6784\u53ca\u539f\u5b50\u5149\u8c31\u7406\u8bba\u65b9\u9762\u3002\u4ed6\u63d0\u51fa\u7528\u692d\u5706\u8f68\u9053\u4ee3\u66ff\u73bb\u5c14<\/span>\uff08Niels H. D. Bohr\uff0c1885\uff0d1962\uff09<\/span>\u539f\u5b50\u6a21\u578b\u7684\u5706\u5f62\u8f68\u9053\uff0c\u4ece\u800c\u5efa\u7acb\u4e86\u201c\u73bb\u5c14\uff0d\u7d22\u672b\u83f2\u539f\u5b50\u6a21\u578b\u201d\u3002\u4ed6\u8fd8\u5f15\u5165\u539f\u5b50\u8f68\u9053\u7a7a\u95f4\u91cf\u5b50\u5316\u7b49\u6982\u5ff5\uff0c\u6210\u529f\u5730\u89e3\u91ca\u4e86\u6c22\u539f\u5b50\u5149\u8c31\u548c\u91cd\u5143\u7d20 X \u5c04\u7ebf\u8c31\u7684\u7cbe\u7ec6\u7ed3\u6784\u4ee5\u53ca\u6b63\u5e38Zeeman\u6548\u5e94\u3002\u6b64\u5916\uff0c\u4ed6\u5bf9\u9640\u87ba\u8fd0\u52a8\u3001\u7535\u78c1\u6ce2\u4f20\u64ad\u4ee5\u53ca\u91d1\u5c5e\u7535\u5b50\u7406\u8bba\u591a\u6709\u8d21\u732e\u3002<\/span><\/section>\n

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\u7d22\u672b\u83f2\u662f\u4e00\u4f4d\u51fa\u8272\u7684\u5bfc\u5e08\uff0c\u5148\u540e\u5e26\u51fa\u4e86\u4e03\u4e2a\u8bfa\u8d1d\u5c14\u5956\u5f97\u4e3b\uff0c\u5305\u62ec\u5fb7\u62dc<\/span>\uff08Peter Debye\uff0c 1884\uff0d1966\uff09<\/span>\u3001\u6ce1\u5229<\/span>\uff08Wolfgang Pauli\uff0c1900\uff0d1958\uff09<\/span>\u3001\u6d77\u68ee\u5821<\/span>\uff08Werner K. Heisenberg\uff0c1901\uff0d1976\uff09<\/span>\u3001\u8d1d\u7279<\/span>\uff08Hans Bethe\uff0c1906\uff0d2005\uff09<\/span>\u7b49\u56db\u4f4d\u535a\u58eb\u5b66\u751f\u548c\u9c8d\u6797<\/span>\uff08Linus Pauling\uff0c1901\uff0d1994\uff09<\/span>\u3001\u62c9\u6bd4<\/span>\uff08Isidor I. Rabi\uff0c1898\uff0d1988\uff09<\/span>\u3001\u52b3\u5384<\/span>\uff08Max von Laue\uff0c1879\uff0d1960\uff09<\/span>\u7b49\u4e09\u4f4d\u535a\u58eb\u540e\uff0c\u8fd8\u6709\u4e00\u6279\u5353\u6709\u5efa\u6811\u7684\u535a\u58eb\u751f\u3001\u535a\u58eb\u540e\u548c\u5408\u4f5c\u8005\uff0c\u4ee5\u53ca\u51e0\u4e2a\u540e\u6765\u83b7\u8bfa\u8d1d\u5c14\u5956\u7684\u5b66\u672f\u68af\u961f\u6210\u5458\u3002\u7231\u56e0\u65af\u5766\u66fe\u611f\u53f9\u5730\u5bf9\u7d22\u672b\u83f2\u8bf4\uff1a\u201c\u6211\u7279\u522b\u94a6\u4f69\u4f60\u7684\u662f\uff0c\u4f60\u80fd\u591f\u4ece\u5e73\u51e1\u4e2d\u5236\u9020\u51fa\u90a3\u4e48\u591a\u7684\u5e74\u8f7b\u5929\u624d\u3002\u201d<\/span><\/section>\n

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\u7d22\u672b\u83f2\u4e00\u751f\u5f97\u8fc7\u8bb8\u591a\u7684\u5956\u52b1\u548c\u8363\u8a89\uff0c\u662f\u591a\u4e2a\u56fd\u5bb6\u7684\u79d1\u5b66\u9662\u9662\u58eb\uff0c\u5e76\u5f97\u5230\u8fc7\u4e16\u754c\u4e0a\u591a\u6240\u5927\u5b66\u9881\u53d1\u7684\u8363\u8a89\u535a\u58eb\u5b66\u4f4d\u3002<\/span><\/section>\n

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\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u7d22\u672b\u83f2\u660e\u786e\u575a\u5b9a\u5730\u53cd\u5bf9\u7eb3\u7cb9\u7684\u53cd\u72b9\u592a\u8fd0\u52a8\u548c\u6240\u8c13\u7684\u201c\u5fb7\u610f\u5fd7\u7269\u7406\u5b66\u201d\uff0c\u56e0\u800c\u88ab\u653b\u51fb\u4e3a\u201c\u5b66\u672f\u754c\u4e2d\u72b9\u592a\u6587\u5316\u7684\u4ee3\u7406\u4eba\u201d\u3002\u4f46\u4ed6\u6beb\u65e0\u754f\u60e7\uff0c\u4ece\u672a\u9000\u8ba9\u8fc7\u3002<\/span><\/section>\n

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\u54e5\u5fb7\u5df4\u8d6b<\/span>\uff08Christian Goldbach\uff0c1690\u5e743\u670818\u65e5\uff0d1764\u5e7411\u670820\u65e5\uff09<\/span>\u4e8e1710\u5e74\u4ece\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u6bd5\u4e1a\u540e\u6e38\u5b66\u6b27\u6d32\u81f31724\u5e74\uff0c\u5230\u8fc7\u5fb7\u56fd\u591a\u4e2a\u5730\u65b9\u4ee5\u53ca\u82f1\u683c\u5170\u3001\u8377\u5170\u3001\u610f\u5927\u5229\u548c\u6cd5\u56fd\u3002\u7279\u522b\u662f\uff0c\u4ed6\u62dc\u8bbf\u8fc7\u83b1\u5e03\u5c3c\u5179<\/span>\uff08Gottfried W. Leibniz\uff0c1646-1716\uff09<\/span>\u3001\u6b27\u62c9\u548c\u8d1d\u52aa\u91cc<\/span>\uff08Nicholas I. Bernoulli\uff0c1687\uff0d1759\uff09<\/span>\u7b49\u5927\u6570\u5b66\u5bb6\u30021724\u5e74\u4ed6\u56de\u5230\u54e5\u5c3c\u65af\u5821\u4e4b\u540e\uff0c\u53c8\u4e0e\u6570\u5b66\u5bb6\u6bd4\u5c14\u82ac\u683c<\/span>\uff08Georg B. Bilfinger\uff0c1693\uff0d1750\uff09<\/span>\u548c\u8d6b\u5c14\u66fc<\/span>\uff08Jakob Hermann\uff0c1678\uff0d1733\uff09<\/span>\u7ed3\u4e3a\u597d\u53cb\uff0c\u591a\u6709\u5408\u4f5c\u3002<\/span><\/section>\n

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1725\u5e74\uff0c\u54e5\u5fb7\u5df4\u8d6b\u5230\u4e86\u5723\u5f7c\u5f97\u5821\u79d1\u5b66\u9662\u4efb\u804c\u6570\u5b66\u548c\u79d1\u5b66\u53f2\u6559\u6388\uff0c1728\u5e74\u6210\u4e3a\u4fc4\u7f57\u65af\u6c99\u7687\u4e8c\u4e16\u7684\u5bab\u5ead\u6559\u5e08\uff0c1742\u5e74\u540e\u8fd8\u66fe\u4efb\u804c\u4fc4\u7f57\u65af\u5916\u4ea4\u90e8\u3002<\/span><\/section>\n

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\u54e5\u5fb7\u5df4\u8d6b\u5728\u6570\u5b66\u5206\u6790\u65b9\u9762\u6709\u51fa\u8272\u7684\u8d21\u732e\uff0c\u4f8b\u5982\u6709\u4e00\u6761\u54e5\u5fb7\u5df4\u8d6b\uff0d\u6b27\u62c9\u5b9a\u7406\u3002\u4f46\u4ed6\u4e3b\u8981\u8d21\u732e\u5728\u6570\u8bba\u65b9\u9762\uff0c\u4f8b\u5982\u5173\u4e8e\u8d39\u9a6c\u6570<\/span>\uff08Fermat numbers\uff09<\/span>\u6709\u4e00\u6761\u54e5\u5fb7\u5df4\u8d6b\u5b9a\u7406\u3002\u5f53\u7136\uff0c\u4ed6\u6700\u51fa\u540d\u7684\u662f\u57281742\u5e746\u67087\u65e5\u5199\u7ed9\u6b27\u62c9\u4fe1\u4e2d\u63d0\u51fa\u7684\u201c\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u201d\uff1a\u4efb\u4f55\u4e00\u4e2a\u5927\u4e8e2\u7684\u5076\u6570\u90fd\u53ef\u5199\u6210\u4e24\u4e2a\u8d28\u6570\u4e4b\u548c\uff0c\u4fd7\u79f0\u4e3a\u201c1+1\u201d\u95ee\u9898\u3002\u5f53\u4eca\u6700\u597d\u7684\u7ed3\u679c\u662f\u9648\u666f\u6da61966\u5e74\u8bc1\u660e\u7684\u201c1+2\u201d\uff0c\u4f46\u5c1a\u4e0d\u662f\u95ee\u9898\u7684\u7ec8\u7ed3\u3002<\/span><\/section>\n

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\u56fe9  \u54e5\u5fb7\u5df4\u8d6b\u7ed9\u6b27\u62c9\u7684\u4fe1\uff081742\u5e746\u67087\u65e5\uff09<\/span><\/section>\n

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\u5e0c\u5c14\u4f2f\u7279<\/span><\/strong><\/span><\/section>\n

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\u5e0c\u5c14\u4f2f\u7279<\/span>\uff08David Hilbert\uff0c1862\u5e741\u670823\u65e5\uff0d1943\u5e742\u670814\u65e5\uff09<\/span>\u88ab\u79f0\u4e3a\u201c\u6570\u5b66\u754c\u7684\u65e0\u5195\u4e4b\u738b\u201d\u3001\u201c\u6570\u5b66\u4e2d\u7684\u5e05\u624d\u201d\uff0c\u662f\u5386\u53f2\u4e0a\u6700\u5353\u8d8a\u7684\u6570\u5b66\u5bb6\u4e4b\u4e00\u3002<\/span><\/section>\n

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\u5e0c\u5c14\u4f2f\u72791880\u5e74\u8fdb\u5165\u54e5\u5c3c\u65af\u5821\u5927\u5b66\uff0c\u4f46\u4ed6\u6267\u610f\u8fdd\u80cc\u7236\u4eb2\u8ba9\u4ed6\u5b66\u4e60\u6cd5\u5f8b\u7684\u610f\u613f\uff0c\u9009\u62e9\u4e86\u6570\u5b66\uff0c\u4e8e1885\u5e7423\u5c81\u65f6\u83b7\u5f97\u535a\u58eb\u5b66\u4f4d\uff0c\u4e4b\u540e\u7559\u6821\u4efb\u8bb2\u5e08\u3001\u526f\u6559\u6388\uff0c1893\u5e74\u5347\u4e3a\u6b63\u6559\u6388\u30021895\u5e74\uff0c\u5e0c\u5c14\u4f2f\u7279\u63a5\u53d7\u514b\u83b1\u56e0<\/span>\uff08Christian F. Klein\uff0c1849\uff0d1925\uff09<\/span>\u9080\u8bf7\u5230\u4e86\u54e5\u5ef7\u6839<\/span>\uff08G\u00f6ttingen\uff09<\/span>\u5927\u5b66\u4efb\u6559\uff0c\u76f4\u81f31930\u5e74\u9000\u4f11\uff0c\u4e8e1943\u5e74\u901d\u4e16\uff0c\u4eab\u5e7481\u5c81\u3002<\/span><\/section>\n

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\u5e0c\u5c14\u4f2f\u7279\u66fe\u83b7\u4fc4\u7f57\u65af\u7f57\u5df4\u5207\u592b\u65af\u57fa\u5956\u548c\u745e\u5178\u79d1\u5b66\u9662Mittag-Leffler\u5956\uff0c1942\u5e74\u5f53\u9009\u4e3a\u67cf\u6797\u79d1\u5b66\u9662\u8363\u8a89\u9662\u58eb\u3002<\/span><\/section>\n

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\u5e0c\u5c14\u4f2f\u7279\u5728\u4e0d\u53d8\u91cf\u7406\u8bba\u3001\u4ee3\u6570\u6570\u8bba\u3001\u79ef\u5206\u65b9\u7a0b\u3001\u53d8\u5206\u6cd5\u3001\u6cdb\u51fd\u5206\u6790\u3001\u6570\u5b66\u548c\u51e0\u4f55\u5b66\u57fa\u7840\u3001\u6570\u5b66\u7269\u7406\u7b49\u9886\u57df\u4e2d\u4f5c\u51fa\u4e86\u5341\u5206\u91cd\u8981\u7684\u8d21\u732e\u3002\u5176\u4e2d\u6700\u503c\u5f97\u63d0\u53ca\u7684\u662f\u4ed61900\u5e748\u67088\u65e5\u5728\u5df4\u9ece\u7b2c\u4e8c\u5c4a\u56fd\u9645\u6570\u5b66\u5bb6\u5927\u4f1a\u4e0a\u7684\u8457\u540d\u6f14\u8bb2\u3002\u4ed6\u6307\u51fa\u4e86\u65b0\u4e16\u7eaa\u6570\u5b66\u5bb6\u5e94\u5f53\u52aa\u529b\u89e3\u51b3\u768423\u4e2a\u6570\u5b66\u95ee\u9898\uff0c\u5176\u4e2d\u7b2c8\u4e2a\u95ee\u9898\u5305\u542b\u4e86\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u3002\u90a3\u6b21\u6f14\u8bb2\u88ab\u8ba4\u4e3a\u662f20\u4e16\u7eaa\u6570\u5b66\u6700\u91cd\u8981\u95ee\u9898\u7684\u9009\u96c6\u3002\u5bf9\u90a3\u4e9b\u95ee\u9898\u7684\u7814\u7a76\uff0c\u540e\u6765\u5927\u5927\u63a8\u52a8\u4e86\u6570\u5b66\u7684\u8fdb\u6b65\u5e76\u5bf9\u4eca\u5929\u6570\u5b66\u7684\u53d1\u5c55\u4f9d\u7136\u6709\u7740\u6df1\u523b\u5f71\u54cd\u30021950\u5e74\uff0c\u5f53\u7f8e\u56fd\u6570\u5b66\u4f1a\u9080\u8bf7\u5e0c\u5c14\u4f2f\u7279\u7684\u535a\u58eb\u5b66\u751f\u3001\u8457\u540d\u6570\u5b66\u5bb6\u5916\u5c14<\/span>\uff08Hermann K. H. Weyl\uff0c1885\uff0d1955\uff09<\/span>\u603b\u7ed320\u4e16\u7eaa\u4e0a\u534a\u9875\u7684\u6570\u5b66\u5386\u53f2\u65f6\uff0c\u5916\u5c14\u5199\u9053\uff1a\u5e0c\u5c14\u4f2f\u7279\u5728\u5df4\u9ece\u63d0\u51fa\u768423\u4e2a\u6570\u5b66\u95ee\u9898\u201c\u662f\u4e00\u5f20\u5bfc\u822a\u56fe\u201d\uff1b\u5728\u8fc7\u53bb\u4e94\u5341\u5e74\u95f4\uff0c\u201c\u6570\u5b66\u5bb6\u4eec\u7ecf\u5e38\u6309\u7167\u8fd9\u5f20\u5bfc\u822a\u56fe\u53bb\u8861\u91cf\u6211\u4eec\u7684\u8fdb\u6b65\u201d\u3002<\/span><\/section>\n

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\u5e0c\u5c14\u4f2f\u7279\u540c\u65f6\u4e5f\u5341\u5206\u5173\u6ce8\u7269\u7406\u5b66\uff0c\u66fe\u628a\u4ed6\u8ba4\u4e3a\u201c\u6570\u5b66\u8f83\u5dee\u201d\u7684\u7231\u56e0\u65af\u5766\u8bf7\u5230\u54e5\u5ef7\u6839\u5927\u5b66\uff0c\u4e00\u8d77\u8ba8\u8bba\u540e\u6765\u88ab\u79f0\u4e3a\u201c\u7231\u56e0\u65af\u5766\u65b9\u7a0b\u201d\u7684\u7269\u7406\u5b66\u542b\u4e49\u3002\u671f\u95f4\uff0c\u6570\u7406\u903b\u8f91\u5b66\u5bb6\u54e5\u5fb7\u5c14<\/span>\uff08Kurt F.G\u00f6del\uff0c1906\uff0d1978\uff09<\/span>\u4e3a\u7231\u56e0\u65af\u5766\u65b9\u7a0b\u627e\u5230\u4e00\u4e2a\u89e3\uff0c\u8ba9\u4ed6\u6ee1\u8f7d\u800c\u5f52\u3002<\/span><\/section>\n

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\u5e0c\u5c14\u4f2f\u7279\u53bb\u4e16\u540e\uff0c\u5728\u54e5\u5ef7\u6839\u7684\u5893\u4e0a\u523b\u7740\u4ed6\u9000\u4f11\u611f\u8a00\u4e2d\u7684\u6700\u540e\u4e00\u53e5\u8bdd\uff1a\u201c\u6211\u4eec\u5fc5\u987b\u77e5\u9053\uff0c\u6211\u4eec\u5fc5\u5c06\u77e5\u9053\u201d<\/span>\uff08Wir m\u00fcssen wissen\uff0cWir werden wissen\uff09<\/span>\u3002<\/span><\/section>\n

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\u56fe10  \u7b14\u8005\u5728\u54e5\u5ef7\u6839\u5e0c\u5c14\u4f2f\u7279\u5893\u7891\u65c1<\/span><\/section>\n

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\u95f5\u53ef\u592b\u65af\u57fa<\/span><\/strong><\/span><\/section>\n

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\u95f5\u53ef\u592b\u65af\u57fa<\/span>\uff08Hermann Minkowski\uff0c1864\u5e746\u670822\u65e5\uff0d1909\u5e741\u670812\u65e5\uff09<\/span>\u4e3a\u7406\u5de5\u79d1\u7684\u5b66\u8005\u4eec\u6240\u719f\u8bc6\uff0c\u5f88\u53ef\u80fd\u662f\u7531\u4e8e\u6570\u5b66\u5206\u6790\u4e2d\u7684\u201c\u95f5\u53ef\u592b\u65af\u57fa\u4e0d\u7b49\u5f0f\u201d\u3002<\/span><\/section>\n

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\u95f5\u53ef\u592b\u65af\u57fa1864\u5e74\u51fa\u751f\u4e8e\u4fc4\u56fd\u7684Alexotas<\/span>\uff08\u4eca\u7acb\u9676\u5b9b\u7684Kaunas\uff09<\/span>\u3002\u7531\u4e8e\u5f53\u65f6\u4fc4\u56fd\u653f\u5e9c\u8feb\u5bb3\u72b9\u592a\u4eba\uff0c1872\u5e74\u7236\u4eb2\u5e26\u7740\u5168\u5bb6\u79fb\u5c45\u5230\u4e86\u54e5\u5c3c\u65af\u5821\u3002\u4ed6\u4eec\u5bb6\u4e0e\u5e0c\u5c14\u4f2f\u7279\u7684\u5bb6\u4ec5\u4e00\u6cb3\u4e4b\u9694\uff0c\u4e24\u4eba\u4ece\u5c0f\u76f8\u8bc6\u3002<\/span><\/section>\n

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1879\u5e74\u95f5\u53ef\u592b\u65af\u57fa\u5165\u8bfb\u4e8e\u67cf\u6797\u5927\u5b66\uff0c\u4e0d\u4e45\u8f6c\u56de\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u3002\u5927\u5b66\u671f\u95f4\uff0c\u4ed6\u6388\u8bfe\u4e8e\u4ea5\u59c6\u970d\u5179<\/span>\uff08Hermann L. F. von Helmholtz\uff0c1821-1894\uff09<\/span>\u3001\u514b\u7f57\u5185\u514b<\/span>\uff08Leopold Kronecker, 1823-1891\uff09<\/span>\u3001\u7ef4\u5c14\u65af\u7279\u62c9\u65af<\/span>\uff08Karl T. W. Weierstrass\uff0c1815-1897\uff09<\/span>\u3001\u57fa\u5c14\u970d\u592b\u7b49\u7269\u7406\u5b66\u5bb6\u548c\u6570\u5b66\u5bb6\u3002<\/span><\/section>\n

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1882\u5e74\uff0c\u5e74\u4ec518\u5c81\u7684\u95f5\u53ef\u592b\u65af\u57fa\u56e0\u4e3a\u5efa\u7acb\u4e86\u591a\u5143\u4e8c\u6b21\u578b\u7684\u5b8c\u6574\u7406\u8bba\u4e0e\u82f1\u56fd\u8457\u540d\u6570\u5b66\u5bb6\u53f2\u5bc6\u65af<\/span>\uff08Henry J. S. Smith\uff0c1826\uff0d1883\uff09<\/span>\u5171\u540c\u5206\u4eab\u4e86\u6cd5\u56fd\u79d1\u5b66\u9662\u7684\u4e00\u4e2a\u5927\u5956\uff0c\u540d\u566a\u4e00\u65f6\u30021885\u5e74\uff0c21\u5c81\u7684\u95f5\u53ef\u592b\u65af\u57fa\u5728\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u83b7\u5f97\u535a\u58eb\u5b66\u4f4d\u30021886\u5e74\uff0c\u4ed6\u6210\u4e3a\u6ce2\u6069\u5927\u5b66\u8bb2\u5e08\uff0c\u7136\u540e\u4e8e1891\u5e74\u5347\u4e3a\u526f\u6559\u6388\u30021894\u5e74\uff0c\u4ed6\u56de\u5230\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u4efb\u6559\u30021895\u5e74\uff0c\u5e0c\u5c14\u4f2f\u7279\u79bb\u5f00\u54e5\u5c3c\u65af\u5821\u524d\u5f80\u54e5\u5ef7\u6839\u5927\u5b66\uff0c\u7531\u95f5\u53ef\u592b\u65af\u57fa\u63a5\u66ff\u4ed6\u7684\u4f4d\u7f6e\u62c5\u4efb\u6570\u5b66\u6559\u6388\u3002\u6b21\u5e74\uff0c\u95f5\u53ef\u592b\u65af\u57fa\u53c8\u8f6c\u5230\u745e\u58eb\u82cf\u9ece\u4e16\u8054\u90a6\u7406\u5de5\u5b66\u9662<\/span>\uff08ETH Z\u00fcrich\uff09<\/span>\u4efb\u6559\u3002\u671f\u95f4\uff0c\u9752\u5e74\u7231\u56e0\u65af\u5766\u5728\u8be5\u6821\u5c31\u8bfb\uff0c\u6210\u4e3a\u95f5\u53ef\u592b\u65af\u57fa\u7684\u5b66\u751f\u30021902\u5e74\uff0c\u95f5\u53ef\u592b\u65af\u57fa\u63a5\u53d7\u514b\u83b1\u56e0\u7684\u9080\u8bf7\uff0c\u52a0\u76df\u54e5\u5ef7\u6839\u5927\u5b66\u62c5\u4efb\u6570\u5b66\u6559\u6388\u76f4\u81f3\u79bb\u4e16\u3002<\/span><\/section>\n

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\u95f5\u53ef\u592b\u65af\u57fa\u6700\u5177\u72ec\u521b\u6027\u7684\u6210\u679c\u662f\u4ed6\u57281890\u5e74\u5f00\u521b\u7684\u201c\u6570\u7684\u51e0\u4f55\u201d<\/span>\uff08Geometrie der Zahlen\uff09<\/span>\uff0c\u4e66\u7a3f\u57281896\u5e74\u57fa\u672c\u5b8c\u6210\uff0c\u4e8e1910\u5e74\u6b63\u5f0f\u51fa\u7248\u3002\u4ed6\u5173\u4e8e\u6570\u7684\u51e0\u4f55\u7406\u8bba\u7684\u7814\u7a76\u5bfc\u81f4\u4e86\u5bf9\u51f8\u4f53\u586b\u5145\u95ee\u9898\u7684\u7814\u7a76\uff0c\u5373\u7ed9\u5b9a\u5f62\u72b6\u7684\u56fe\u5f62\u53ef\u4ee5\u653e\u7f6e\u5230\u53e6\u4e00\u4e2a\u7ed9\u5b9a\u5f62\u72b6\u56fe\u5f62\u4e2d\u7684\u4e2a\u6570\u548c\u65b9\u6cd5\uff0c\u5176\u4e2d\u5f15\u51fa\u4e86\u5927\u5bb6\u719f\u77e5\u7684\u201c\u9594\u53ef\u592b\u65af\u57fa\u4e0d\u7b49\u5f0f\u201d\u3002<\/span><\/section>\n

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1905\u5e74\uff0c\u95f5\u53ef\u592b\u65af\u57fa\u5efa\u7acb\u4e86\u5b9e\u7cfb\u6570\u6b63\u5b9a\u4e8c\u6b21\u578b\u7684\u201c\u95f5\u53ef\u592b\u65af\u57fa\u7ea6\u5316\u7406\u8bba\u201d\u30021908\u5e74\uff0c\u5728Cologne\u7684\u4e00\u6b21\u8457\u540d\u5b66\u672f\u6f14\u8bb2\u4e2d\uff0c\u95f5\u53ef\u592b\u65af\u57fa\u63d0\u51fa\u4e86\u56db\u7ef4\u65f6\u7a7a\u7684\u6982\u5ff5\uff0c\u4e3a\u540e\u6765\u7231\u56e0\u65af\u5766\u7684\u5e7f\u4e49\u76f8\u5bf9\u8bba\u63d0\u4f9b\u4e86\u57fa\u672c\u6846\u67b6\uff0c\u88ab\u79f0\u4e3a\u201c\u95f5\u53ef\u592b\u65af\u57fa\u65f6\u7a7a\u201d\u7406\u8bba\u3002<\/span><\/section>\n

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1909\u5e741\u670811\u65e5\uff0c\u95f5\u53ef\u592b\u65af\u57fa\u56e0\u6025\u6027\u9611\u5c3e\u708e\u62a2\u6551\u65e0\u6548\u5728\u54e5\u5ef7\u6839\u901d\u4e16\uff0c\u65f6\u5e74\u4ec545\u5c81\u3002\u5e0c\u5c14\u4f2f\u7279\u968f\u5373\u6574\u7406\u4e86\u4ed6\u7684\u9057\u4f5c\uff0c\u4e8e1911\u5e74\u51fa\u7248\u4e86\u300a\u95f5\u53ef\u592b\u65af\u57fa\u5168\u96c6\u300b<\/span>\uff08Gesammelte Abhandlungen von Hermann Minkowski<\/em>\uff09<\/span>\u3002<\/span><\/section>\n

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\u56fe11  \u95f5\u53ef\u592b\u65af\u57fa\uff081864\uff0d1909\uff09<\/span><\/section>\n

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3. \u52a0\u91cc\u5b81\u683c\u52d2<\/strong><\/strong><\/p>\n<\/section>\n

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\u73b0\u5728\uff0c\u8ba9\u6211\u4eec\u56de\u5230\u54e5\u5c3c\u65af\u5821\u3002<\/span><\/section>\n

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\u7136\u800c\uff0c\u4eca\u5929\u666e\u9c81\u58eb\u4e0d\u590d\u5b58\u5728\uff0c\u54e5\u5c3c\u65af\u5821\u4e5f\u4e0d\u590d\u5b58\u5728\u3002<\/span><\/section>\n

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\u7b2c\u4e8c\u6b21\u4e16\u754c\u5927\u6218\u672b\uff0c\u54e5\u5c3c\u65af\u5821\u88ab\u8f70\u70b8\u5f97\u5929\u7ffb\u5730\u8986\u30021945\u5e744\u67089\u65e5\uff0c\u82cf\u8054\u519b\u961f\u5b8c\u5168\u5360\u9886\u4e86\u54e5\u5c3c\u65af\u5821\u3002\u540c\u5e748\u67082\u65e5\uff0c\u82cf\u3001\u7f8e\u3001\u82f1\u4e09\u56fd\u5728\u67cf\u6797\u8054\u5408\u53d1\u8868\u4e86\u300a\u6ce2\u8328\u5766\u516c\u544a\u300b\u3002\u6839\u636e\u516c\u544a\u7684\u51b3\u8bae\uff0c\u6218\u8d25\u7684\u5fb7\u56fd\u5c06\u4e1c\u666e\u9c81\u58eb\u5730\u533a\u5272\u8ba9\u7ed9\u6ce2\u5170\u548c\u82cf\u8054\u3002\u5176\u4e2d\uff0c\u884c\u653f\u4e0a\u54e5\u5c3c\u65af\u5821\u6210\u4e86\u82cf\u8054\u9886\u5730\u3002\u4f46\u5730\u7406\u4e0a\uff0c\u57ce\u5821\u4e0e\u82cf\u8054\u672c\u571f\u4e0d\u4f46\u4e92\u4e0d\u90bb\u63a5\uff0c\u800c\u4e14\u76f8\u53bb\u751a\u8fdc\uff0c\u4e2d\u95f4\u9694\u7740\u7acb\u9676\u5b9b\u548c\u767d\u4fc4\u7f57\u65af\uff0c\u56e0\u6b64\u88ab\u620f\u79f0\u4e3a\u201c\u98de\u5730\u201d\u30021946\u5e74\uff0c\u82cf\u8054\u653f\u5e9c\u628a\u54e5\u5c3c\u65af\u5821\u6539\u540d\u4e3a\u52a0\u91cc\u5b81\u683c\u52d2<\/span>\uff08Kaliningrad\uff09<\/span>\uff0c\u4ee5\u7eaa\u5ff5\u521a\u53bb\u4e16\u7684\u6700\u9ad8\u82cf\u7ef4\u57c3\u4e3b\u5e2d\u56e2\u4e3b\u5e2d\u52a0\u91cc\u5b81<\/span>\uff08Mikhail I. Kalinin\uff0c1875\uff0d1946\uff09<\/span>\u3002\u4e24\u5e74\u4e4b\u540e\uff0c\u82cf\u8054\u653f\u5e9c\u53c8\u628a\u54e5\u5c3c\u65af\u5821\u5927\u5b66\u6539\u540d\u4e3a\u201c\u52a0\u91cc\u5b81\u683c\u52d2\u56fd\u7acb\u5e08\u8303\u5b66\u9662\u201d\uff0c1967\u5e74\u518d\u66f4\u540d\u4e3a\u201c\u52a0\u91cc\u5b81\u683c\u52d2\u56fd\u7acb\u5927\u5b66\u201d\u3002<\/span><\/section>\n

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\u56fe12  \u52a0\u91cc\u5b81\u683c\u52d2\u5e02\u533a\u98ce\u666f<\/span><\/section>\n

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1944\u5e74\uff0c\u54e5\u5c3c\u65af\u5821\u7684\u4e03\u6761\u8001\u6865\u5728\u6218\u706b\u4e2d\u88ab\u5168\u90e8\u70b8\u6bc1\u3002\u540e\u6765\uff0c\u52a0\u91cc\u5b81\u5e02\u653f\u5e9c\u4fee\u590d\u4e86\u4e94\u9053\u6865<\/span>\uff08\u56fe3\u4e2d\u7684A-B\u548cA-C\u4e4b\u95f4\u5206\u522b\u53ea\u4fee\u590d\u4e86\u4e00\u9053\u6865\uff09<\/span>\uff0c\u4fdd\u5b58\u81f3\u4eca\u3002\u73b0\u5728\u8fd9\u4e9b\u8001\u6865\u4e3b\u8981\u4f9b\u65c5\u6e38\u89c2\u5149\u4f7f\u7528\u3002<\/span><\/section>\n

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\u56fe13  \u52a0\u91cc\u5b81\u683c\u52d2\u73b0\u5728\u53ea\u6709\u4e94\u6761\u6865\uff082014\u5e74\u7167\u7247\uff09<\/span><\/section>\n

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\u56fe14  \u52a0\u91cc\u5b81\u683c\u52d2\u4e94\u6865\u95ee\u9898<\/span><\/section>\n

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\u7f51\u7edc\u79d1\u5b66\u96c6\u667a\u8bfe\u5802\u7b2c\u4e09\u671f\u62a5\u540d\u4e2d<\/strong><\/span><\/p>\n

\u4ece\u6570\u5b66\u5efa\u6a21\u5230\u591a\u5b66\u79d1\u5e94\u7528
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\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/p>\n