{"id":28100,"date":"2017-05-24T00:11:01","date_gmt":"2017-05-23T16:11:01","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=28100"},"modified":"2018-07-29T09:13:41","modified_gmt":"2018-07-29T01:13:41","slug":"%e3%80%90%e5%a4%a7%e5%ae%87%e5%ae%99%e5%b0%8f%e6%95%85%e4%ba%8b%e3%80%9122-%e4%b8%8d%e5%81%87%e5%a4%96%e6%b1%82","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=28100","title":{"rendered":"\u3010\u5927\u5b87\u5b99\u5c0f\u6545\u4e8b\u301122 \u4e0d\u5047\u5916\u6c42"},"content":{"rendered":"<figure id=\"attachment_28101\" aria-describedby=\"caption-attachment-28101\" style=\"width: 300px\" class=\"wp-caption alignleft\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-28101\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/05\/22-1.jpg\" alt=\"\" width=\"300\" height=\"365\" \/><figcaption id=\"caption-attachment-28101\" class=\"wp-caption-text\">\u300a\u5e73\u9762\u570b\u5ea6\u300b\u7b2c\u4e00\u7248\u5c01\u9762(\u5716\u50cf\u4f86\u6e90\uff1a\u7dad\u57fa\u767e\u79d1)<\/figcaption><\/figure>\n<p><strong>\u64b0\u6587\uff5c<\/strong>\u8449\u674e\u83ef<\/p>\n<p>\u516c\u51431884\u5e74\uff0c\u4e00\u4f4d\u82f1\u570b\u6559\u5e2b\u4ee5\u300c\u65b9\u584a\u300d\u70ba\u7b46\u540d\uff0c\u5beb\u4e86\u4e00\u672c\u5bd3\u610f\u6df1\u9060\u7684\u6578\u5b78\u79d1\u5e7b\u5c0f\u8aaa\uff0c\u66f8\u540d\u53eb\u300a\u5e73\u9762\u570b\u5ea6\u300b(Flatland)\u3002\u5728\u90a3\u500b\u865b\u69cb\u7684\u4e8c\u7dad\u4e16\u754c\u88e1\uff0c\u842c\u4e8b\u842c\u7269\u90fd\u6c92\u6709\u539a\u5ea6\u6216\u9ad8\u5ea6\uff0c\u5305\u62ec\u751f\u7269\u5728\u5167\u3002\u6709\u8da3\u7684\u662f\uff0c\u90a3\u4e9b\u751f\u7269\u4e0d\u4f46\u6709\u667a\u6167\uff0c\u9084\u6709\u6027\u5225\u4e4b\u5206\uff0c\u7537\u6027\u662f\u5404\u7a2e\u591a\u908a\u5f62\uff0c\u5973\u6027\u5247\u4e00\u5f8b\u662f\u76f4\u7dda\uff0c\u9019\u6a23\u7684\u5b89\u6392\u60f3\u5fc5\u8b93\u4f5b\u6d1b\u4f0a\u5fb7\u7684\u9580\u5f92\u5931\u671b\u4e86\u3002<\/p>\n<p>\u9019\u500b\u6545\u4e8b\u81f3\u5c11\u6709\u5169\u500b\u7e8c\u96c6\uff0c\u66f8\u540d\u5206\u5225\u662f\u300a\u7403\u9762\u570b\u5ea6\u300b(Sphereland, 1965)\u8207\u300a\u66f4\u5e73\u7684\u570b\u5ea6\u300b(Flatterland, 2001)\uff0c\u4e0d\u904e\u4f5c\u8005\u7576\u7136\u53e6\u6709\u5176\u4eba\u3002<\/p>\n<p>\u6211\u81ea\u5df1\u5728\u770b\u9019\u500b\u6545\u4e8b\u7684\u6642\u5019\uff0c\u4e0d\u7981\u60f3\u5230\u4e00\u500b\u8010\u4eba\u5c0b\u5473\u7684\u554f\u984c\uff1a\u90a3\u4e9b\u4e8c\u7dad\u667a\u6167\u751f\u7269\u80fd\u5426\u767c\u5c55\u51fa(\u6b50\u6c0f)\u5e73\u9762\u5e7e\u4f55\u5b78\uff1f\u9019\u500b\u554f\u984c\u548c\u300a\u5e73\u9762\u570b\u5ea6\u300b\u4e26\u6c92\u6709\u76f4\u63a5\u95dc\u4fc2\uff0c\u5373\u4f7f\u4f60\u5c0d\u90a3\u672c\u66f8\u5b8c\u5168\u964c\u751f\uff0c\u4e5f\u8acb\u653e\u5fc3\u7e7c\u7e8c\u8b80\u4e0b\u53bb\u3002<\/p>\n<p>\u7b54\u6848\u662f\uff0c\u53ea\u8981\u4ed6\u5011\u8db3\u5920\u8070\u660e\uff0c\u4e00\u5b9a\u80fd\u767c\u5c55\u51fa\u5b8c\u6574\u7684\u5e73\u9762\u5e7e\u4f55\u5b78\u3002\u63db\u53e5\u8a71\u8aaa\uff0c\u90a3\u4e9b\u667a\u6167\u751f\u7269\u552f\u4e00\u7684\u9650\u5236\uff0c\u5c31\u662f\u4ed6\u5011\u81ea\u5df1\u7684\u667a\u5546\u3002\u539f\u56e0\u5f88\u7c21\u55ae\uff0c\u5e73\u9762\u5e7e\u4f55\u662f\u4e00\u9580\u81ea\u7d66\u81ea\u8db3\u3001\u4e0d\u5047\u5916\u6c42\u7684\u5b78\u554f\uff1b\u5728\u7814\u7a76\u9019\u9580\u5b78\u554f\u7684\u6642\u5019\uff0c\u5b8c\u5168\u4e0d\u5fc5\u7528\u5230\u5176\u4ed6\u7684\u7a7a\u9593\u6216\u7dad\u5ea6\u3002<\/p>\n<p>\u8209\u4f8b\u4f86\u8aaa\uff0c\u300c\u8f14\u52a9\u7dda\u300d\u662f\u5e73\u9762\u5e7e\u4f55\u7684\u5e38\u5ba2\uff0c\u800c\u8f14\u52a9\u7dda\u7576\u7136\u8981\u756b\u5728\u540c\u4e00\u500b\u5e73\u9762\u4e0a\u3002\u81f3\u65bc\u4f5c\u5716\u984c\uff0c\u5247\u662f\u5728\u5e73\u9762\u4e0a\u756b\u51fa\u76f4\u7dda\u6216\u5713\uff0c\u548c\u5176\u4ed6\u7dad\u5ea6\u6c92\u6709\u4efb\u4f55\u95dc\u4fc2\u2500\u2500\u5018\u82e5\u4f60\u786c\u8981\u8aaa\u5713\u898f\u662f\u7acb\u9ad4\u7684\uff0c\u90a3\u5c31\u662f\u62ac\u69d3\u4e86\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u7528\u73fe\u4ee3\u6578\u5b78\u8a9e\u8a00\u4f86\u8aaa\uff0c\u5e73\u9762\u5e7e\u4f55\u662f\u4e00\u7a2e\u300c\u5167\u860a\u5e7e\u4f55\u300d(intrinsic geometry)\u3002<\/p>\n<p><strong>\u25cf\u5e73\u8d77\u4e0d\u5e73\u5750<\/strong><\/p>\n<p>\u76f8\u8f03\u4e4b\u4e0b\uff0c\u7403\u9762\u5e7e\u4f55\u5b78\u5c31\u4e0d\u592a\u4e00\u6a23\u3002<\/p>\n<p>\u65e9\u5728\u53e4\u5e0c\u81d8\u6642\u4ee3\uff0c\u7403\u9762\u5e7e\u4f55\u548c\u5e73\u9762\u5e7e\u4f55\u7684\u91cd\u8981\u6027\u5c31\u4e0d\u76f8\u4e0a\u4e0b\u3002\u56e0\u70ba\u5730\u7403\u8868\u9762\u662f\u7403\u9762\uff0c\u800c\u5929\u7403\u4e5f\u662f\u7403\u9762\uff0c\u6240\u4ee5\u53e4\u5e0c\u81d8\u5b78\u8005\u5c0d\u9019\u9580\u5b78\u554f\u76f8\u7576\u91cd\u8996\uff0c\u7d2f\u7a4d\u4e86\u8a31\u591a\u91cd\u8981\u7684\u6210\u679c\u3002<\/p>\n<p>\u7403\u9762\u672c\u8eab\u662f\u4e8c\u7dad\u7a7a\u9593\uff0c\u4f46\u5fc5\u9808\u7531\u4e09\u7dad\u7a7a\u9593\u4f86\u5bb9\u7d0d\u3002\u56e0\u6b64\u4e4b\u6545\uff0c\u53e4\u5e0c\u81d8\u5b78\u8005\u96d6\u7136\u91cd\u8996\u7403\u9762\u5e7e\u4f55\uff0c\u5167\u5fc3\u6df1\u8655\u537b\u8a8d\u70ba\u5b83\u662f\u7acb\u9ad4\u5e7e\u4f55\u7684\u85e9\u5c6c\uff0c\u4e26\u975e\u4e00\u9580\u7368\u7acb\u7684\u5e7e\u4f55\u5b78\u3002\u5c31\u9019\u500b\u89c0\u9ede\u800c\u8a00\uff0c\u7403\u9762\u5e7e\u4f55\u5c31\u4e0d\u80fd\u548c\u5e73\u9762\u5e7e\u4f55\u7b49\u91cf\u9f4a\u89c0\u3002\u63db\u8a00\u4e4b\uff0c\u5728\u53e4\u5e0c\u81d8\u5b78\u8005\u773c\u4e2d\uff0c\u7403\u9762\u5e7e\u4f55\u4e0d\u80fd\u7b97\u662f\u300c\u5167\u860a\u5e7e\u4f55\u300d\uff0c\u800c\u662f\u548c\u5b83\u91dd\u92d2\u76f8\u5c0d\u7684\u300c\u5916\u6c42\u5e7e\u4f55\u300d(extrinsic geometry)\u3002<\/p>\n<p>\u70ba\u4e86\u907f\u514d\u8d8a\u8aaa\u8d8a\u62bd\u8c61\uff0c\u8d95\u7dca\u4f86\u8b1b\u500b\u5be6\u969b\u7684\u4f8b\u5b50\u3002<\/p>\n<p>\u6211\u5011\u66fe\u5728\uff1c<a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=26654\">\u5e73\u7684\u9084\u662f\u5713\u7684<\/a>\uff1e\u9019\u7bc7\u6587\u7ae0\u4e2d\uff0c\u8a0e\u8ad6\u904e\u53e4\u5e0c\u81d8\u4eba\u5982\u4f55\u77e5\u66c9\u5730\u7403\u7684\u5f62\u72c0\u3002\u4f46\u82e5\u4ed4\u7d30\u63a8\u6572\uff0c\u4ed6\u5011\u6240\u7528\u7684\u65b9\u6cd5\u90fd\u727d\u6d89\u5230\u5916\u5728\u7a7a\u9593\uff0c\u6c92\u6709\u4efb\u4f55\u4f8b\u5916\u3002<\/p>\n<p>\u5929\u6587\u6cd5(\u6839\u64da\u6708\u98df\u7684\u9670\u5f71\u6216\u6046\u661f\u7684\u4f4d\u7f6e)\u81ea\u7136\u4e0d\u5728\u8a71\u4e0b\uff0c\u81f3\u65bc\u53e6\u5916\u5e7e\u500b\u65b9\u6cd5\uff0c\u540c\u6a23\u5fc5\u9808\u5f15\u9032\u5916\u5728\u7a7a\u9593\u3002<\/p>\n<p><em>\u3000\u30001.\u822a\u884c\u5728\u5927\u6d77\u4e2d\u7684\u8239\u96bb\uff0c\u5982\u679c\u99db\u8fd1\u67d0\u5ea7\u5cf6\u5dbc\uff0c\u8239\u54e1\u4e00\u5b9a\u5148\u770b\u5230\u5cf6\u4e0a\u7684\u5c71\u5cf0\uff0c\u7136\u5f8c\u6574\u5ea7\u5c71\u624d\u6703\u6162\u6162\u300c\u6d6e\u73fe\u300d\u3002<\/em><\/p>\n<p>\u8aaa\u660e\uff1a\u65e2\u7136\u662f\u5c71\u5cf0\uff0c\u4e00\u5b9a\u9ad8\u65bc\u6d77\u5e73\u9762\uff0c\u56e0\u6b64\u4f4d\u65bc\u300c\u4e8c\u7dad\u5730\u7403\u300d\u4e4b\u5916\u3002<\/p>\n<p><em>\u3000\u30002.\u822a\u884c\u4e2d\uff0c\u8239\u9577\u5e38\u6703\u6d3e\u4e00\u540d\u6c34\u624b\u722c\u4e0a\u6845\u6746\uff0c\u5982\u679c\u9644\u8fd1\u51fa\u73fe\u8239\u96bb\u6216\u9678\u5730\uff0c\u4e00\u5b9a\u662f\u9019\u540d\u6c34\u624b\u6700\u5148\u767c\u73fe\u3002<\/em><\/p>\n<p>\u8aaa\u660e\uff1a\u5982\u679c\u6211\u5011\u5c07\u5e06\u8239\u8996\u70ba\u7dca\u8cbc\u5730\u8868\uff0c\u6845\u6746\u5c31\u4e00\u5b9a\u9ad8\u65bc\u6d77\u5e73\u9762\u3002<\/p>\n<p><em>\u3000\u30003.\u5982\u679c\u4f60\u7ad9\u5728\u6d77\u908a\u76ee\u9001\u8239\u96bb\u96e2\u53bb\uff0c\u6703\u89ba\u5f97\u90a3\u8258\u8239\u662f\u9010\u6f38\u6d88\u5931\u7684\uff1b\u7576\u8239\u8eab\u88ab\u5730\u5e73\u7dda\u541e\u6c92\u6642\uff0c\u8239\u6845\u548c\u8239\u5e06\u4ecd\u820a\u4f9d\u7a00\u53ef\u898b\u3002<\/em>(\u539f\u56e0\u540c\u4e0a)<\/p>\n<p><strong>\u25cf\u77e5\u6613\u884c\u96e3<\/strong><\/p>\n<p>\u7136\u800c\uff0c\u6709\u6c92\u6709\u4efb\u4f55\u300c\u4e0d\u5047\u5916\u6c42\u300d\u7684\u65b9\u6cd5\uff0c\u80fd\u5920\u78ba\u5b9a\u4e16\u754c\u4e0d\u662f\u5e73\u7684\u5462\uff1f\u6216\u8005\u63db\u500b\u65b9\u5f0f\u4f86\u8aaa\uff0c\u5982\u679c\u6211\u5011\u8eab\u908a\u771f\u6709\u4e8c\u7dad\u667a\u6167\u751f\u7269\uff0c\u4ed6\u5011\u6709\u6c92\u6709\u8fa6\u6cd5\u78ba\u5b9a\u5730\u7403\u4e26\u975e\u4e00\u500b\u5e73\u9762\uff1f<\/p>\n<p>\u7576\u7136\u6709\uff0c\u800c\u4e14\u65b9\u6cd5\u4e0d\u53ea\u4e00\u7a2e\uff0c\u4e0d\u904e\u7531\u65bc\u5730\u7403\u592a\u5927\u800c\u5f27\u5ea6\u592a\u5c0f\uff0c\u9019\u4e9b\u65b9\u6cd5\u4e00\u5f8b\u8aaa\u4f86\u5bb9\u6613\u505a\u4f86\u96e3\uff0c\u4f46\u81f3\u5c11\u7406\u8ad6\u4e0a\u662f\u53ef\u884c\u7684\u3002<\/p>\n<p>\u65b9\u6cd5\u4e00\uff1a\u5728\u5730\u7403\u8868\u9762\u756b\u4e00\u500b\u5713\uff0c\u7136\u5f8c\u6e2c\u91cf\u5b83\u7684\u300c\u5713\u5468\u7387\u300d\u3002<\/p>\n<p>\u5728\u5e73\u9762\u5e7e\u4f55\u4e2d\uff0c\u5713\u5468\u7684\u9577\u5ea6\u662f\u534a\u5f91\u76842\u03c0\u500d(\u5176\u5be6\u9019\u662f\u03c0\u7684\u5b9a\u7fa9)\u3002\u4f46\u662f\uff0c\u8acb\u60f3\u50cf\u4f60\u5728\u5317\u6975\u91d8\u4e0b\u4e00\u6839\u6728\u6a01\uff0c\u7136\u5f8c\u4ee5\u9019\u6839\u6728\u6a01\u70ba\u5713\u5fc3\uff0c\u7528\u4e00\u689d\u7e69\u5b50\u7576\u534a\u5f91\uff0c\u5728\u5730\u8868\u756b\u51fa\u4e00\u500b\u5713\u5f62\uff0c\u90a3\u9ebc\u4f60\u5c31\u6703\u767c\u73fe\uff0c\u5713\u5468\u548c\u534a\u5f91\u7684\u6bd4\u503c\u4e00\u5b9a\u5c0f\u65bc2\u03c0\uff0c\u56e0\u6b64\u300c\u5713\u5468\u7387\u300d\u5c0f\u65bc\u03c0\u3002<\/p>\n<p>\u5982\u679c\u4f60\u89ba\u5f97\u6709\u9ede\u96e3\u4ee5\u60f3\u50cf\uff0c\u6559\u4f60\u4e00\u500b\u8a23\u7ac5\uff1a\u628a\u90a3\u500b\u5713\u76e1\u91cf\u64f4\u5927\uff0c\u4f8b\u5982\u8b8a\u6210\u8d64\u9053\uff0c\u9019\u6642\u5713\u5468\u525b\u597d\u662f\u300c\u534a\u5f91\u300d\u7684\u56db\u500d\uff0c\u56e0\u6b64\u300c\u5713\u5468\u7387\u300d\u7b49\u65bc\u4e8c(\u679c\u7136\u5c0f\u65bc\u03c0)\u3002\u9019\u6a23\u662f\u4e0d\u662f\u6bd4\u8f03\u6e05\u695a\u4e86\uff1f<\/p>\n<p>\u65b9\u6cd5\u4e8c\uff1a\u5728\u5730\u7403\u8868\u9762\u756b\u4e00\u500b\u4e09\u89d2\u5f62\uff0c\u7136\u5f8c\u6e2c\u91cf\u5b83\u7684\u5167\u89d2\u548c\u3002<\/p>\n<p>\u5982\u679c\u9019\u500b\u65b9\u6cd5\u8b93\u4f60\u806f\u60f3\u5230\u9ad8\u65af\u7684\u4e8b\u8e5f\uff0c\u62b1\u6b49\uff0c\u90a3\u662f\u932f\u8aa4\u806f\u60f3\u3002<\/p>\n<p>\u9ad8\u65af\u7576\u5e74\u6240\u6e2c\u91cf\u7684\u5927\u4e09\u89d2\u5f62\uff0c\u4e09\u500b\u9802\u9ede\u4f4d\u65bc\u4e09\u5ea7\u5c71\u7684\u5c71\u9802\uff0c\u4e09\u500b\u908a\u5247\u662f\u98c4\u6d6e\u5728\u7a7a\u4e2d\u7684\u5149\u7dda(\u8acb\u53c3\u8003\uff1c<a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=28036\" target=\"_blank\" rel=\"noopener noreferrer\">\u6b50\u5e7e\u91cc\u5f97\u8207\u4e16\u754c\u5927\u6230<\/a>\uff1e)\u3002\u9019\u88e1\u6240\u8a0e\u8ad6\u7684\u4e09\u89d2\u5f62\u5247\u662f\u7dca\u8cbc\u5730\u9762\uff0c\u6240\u4ee5\u5b83\u7684\u64cd\u4f5c\u578b\u5b9a\u7fa9\u662f\uff1a\u91d8\u4e0b\u4e09\u6839\u6728\u6a01\uff0c\u7136\u5f8c\u7528\u7e69\u5b50\u5728\u6728\u6a01\u4e4b\u9593\u62c9\u51fa\u908a\u754c(\u56e0\u6b64\u7e69\u5b50\u5fc5\u9808\u62c9\u7dca\uff0c\u4e0d\u80fd\u6709\u4efb\u4f55\u9b06\u5f1b)\u3002<\/p>\n<p>\u9019\u4e9b\u7dca\u7e43\u4e14\u7dca\u8cbc\u5730\u9762\u7684\u7e69\u5b50\uff0c\u5b78\u540d\u53eb\u4f5c\u300c\u6e2c\u5730\u7dda\u300d\u6216\u300c(\u6700)\u77ed\u7a0b\u7dda\u300d\u3002\u96d6\u7136\u5b83\u5011\u5176\u5be6\u662f\u66f2\u7dda\uff0c\u4f46\u7531\u65bc\u5730\u7403\u8868\u9762\u4e26\u6c92\u6709\u771f\u6b63\u7684\u76f4\u7dda\uff0c\u56e0\u6b64\u53ef\u5c07\u9019\u4e9b\u66f2\u7dda\u8996\u70ba\u300c\u7403\u9762\u4e0a\u7684\u76f4\u7dda\u300d\u3002<\/p>\n<p>\u5730\u7403\u4e0a\u7684\u6bcf\u4e00\u689d\u7d93\u7dda\u90fd\u662f\u6e2c\u5730\u7dda\uff0c\u4f46\u7def\u7dda\u5247\u4e0d\u7136\u2500\u2500\u9664\u4e86\u8d64\u9053\u5176\u4ed6\u90fd\u4e0d\u662f\u3002\u5982\u679c\u4f60\u4e00\u6642\u96e3\u4ee5\u63a5\u53d7\uff0c\u518d\u6559\u4f60\u4e00\u500b\u8a23\u7ac5\uff1a\u8acb\u60f3\u60f3\uff0c\u5317\u6975\u9644\u8fd1\u7684\u7d93\u7def\u7dda\u770b\u8d77\u4f86\u50cf\u4e0d\u50cf\u8718\u86db\u7db2\uff1f\u800c\u5728\u9019\u500b\u8718\u86db\u7db2\u4e2d\uff0c\u662f\u4e0d\u662f\u53ea\u6709\u7d93\u7dda\u985e\u4f3c\u76f4\u7dda\uff1f<\/p>\n<p>\u9806\u5e36\u4e00\u63d0\uff0c\u5728\u5730\u7403\u8868\u9762\uff0c\u4f60\u4e0d\u53ef\u80fd\u756b\u51fa\u6bd4\u8d64\u9053\u66f4\u5927\u7684\u5713\u5f62\uff0c\u6240\u4ee5\u6211\u5011\u7a31\u5b83\u70ba\u300c\u5927\u5713\u300d\uff0c\u76f8\u8f03\u4e4b\u4e0b\u5176\u4ed6\u7def\u5708\u90fd\u662f\u300c\u5c0f\u5713\u300d\u3002\u5982\u679c\u628a\u8d64\u9053\u8f49\u4e5d\u5341\u5ea6\uff0c\u5b83\u5c31\u6703\u901a\u904e\u5357\u5317\u6975\uff0c\u4e5f\u5c31\u662f\u8ddf\u67d0\u4e9b\u7d93\u7dda\u91cd\u5408\uff0c\u9019\u5c31\u610f\u5473\u8457\u7d93\u7dda\u4e5f\u662f\u5927\u5713(\u7684\u4e00\u90e8\u5206)\u3002\u56e0\u6b64\u6211\u5011\u6b78\u7d0d\u51fa\u4e00\u500b\u7d50\u8ad6\uff1a\u7403\u9762\u4e0a\u7684\u6e2c\u5730\u7dda\u7686\u70ba\u6240\u8b02\u7684\u300c\u5927\u5713\u300d\u3002<\/p>\n<p>\u63a5\u4e0b\u4f86\uff0c\u8acb\u60f3\u50cf\u90a3\u4e09\u6839\u6728\u6a01\uff0c\u4e00\u500b\u91d8\u5728\u5317\u6975\uff0c\u5169\u500b\u91d8\u5728\u8d64\u9053(\u76f8\u9694\u591a\u5c11\u7d93\u5ea6\u90fd\u53ef\u4ee5)\u3002\u9019\u6a23\u7684\u4e00\u500b\u300c\u7b49\u8170\u4e09\u89d2\u5f62\u300d\uff0c\u4e09\u908a\u5206\u5225\u7531\u7d93\u7dda\u548c\u8d64\u9053\u7d44\u6210\uff0c\u6240\u4ee5\u5167\u89d2\u548c\u4e00\u5b9a\u5927\u65bc180\u5ea6\u2500\u2500\u56e0\u70ba\u7d93\u7dda\u548c\u8d64\u9053\u5782\u76f4\uff0c\u5176\u4e2d\u5169\u500b\u5167\u89d2\u52a0\u8d77\u4f86\u5df2\u7d93\u7b49\u65bc180\u5ea6\u3002<\/p>\n<p>\u7e3d\u800c\u8a00\u4e4b\uff0c\u6211\u5011\u5b8c\u5168\u4e0d\u5fc5\u501f\u7528\u5176\u4ed6\u7a7a\u9593\uff0c\u5c31\u80fd\u78ba\u5b9a\u5730\u7403\u8868\u9762\u7684\u300c\u5713\u5468\u7387\u300d\u5c0f\u65bc\u03c0\uff0c\u800c\u4e14\u4e09\u89d2\u5f62\u7684\u5167\u89d2\u548c\u5927\u65bc180\u5ea6\uff0c\u9019\u4e9b\u90fd\u662f\u5730\u7403\u4e26\u975e\u5e73\u9762\u7684\u9435\u8b49\u3002\u56e0\u6b64\uff0c\u4e8c\u7dad\u751f\u7269\u7d55\u5c0d\u80fd\u7528\u81ea\u7d66\u81ea\u8db3\u7684\u65b9\u5f0f\uff0c\u78ba\u5b9a\u9019\u500b\u4e16\u754c\u5230\u5e95\u662f\u4e0d\u662f\u5e73\u9762\u3002(\u82e5\u60f3\u78ba\u5b9a\u5b83\u662f\u7403\u9762\uff0c\u9084\u9700\u8981\u505a\u9032\u4e00\u6b65\u7684\u6e2c\u91cf\u8207\u8a08\u7b97\u3002)<\/p>\n<p><strong>\u25cf\u59cd\u59cd\u4f86\u9072<\/strong><\/p>\n<p>\u5916\u6c42\u5e7e\u4f55\u5b78\u7684\u50b3\u7d71\u5f9e\u53e4\u5e0c\u81d8\u4e00\u76f4\u5ef6\u7e8c\u5230\u5341\u516b\u4e16\u7d00\uff0c\u7576\u6642\u7684\u5e7e\u4f55\u5b78\u65e9\u5df2\u9032\u6b65\u5230\u8207\u5fae\u7a4d\u5206\u7d50\u5408\uff0c\u4ea6\u5373\u6240\u8b02\u7684\u300c\u5fae\u5206\u5e7e\u4f55\u300d\uff0c\u53ef\u662f\u4ecd\u820a\u6c92\u6709\u4eba\u6311\u6230\u9019\u500b\u53e4\u5178\u89c0\u9ede\u3002<\/p>\n<p>\u6211\u5011\u5728\uff1c<a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=27996\" target=\"_blank\" rel=\"noopener noreferrer\">\u8ab0\u662f\u53d7\u5bb3\u8005<\/a>\uff1e\u9019\u7bc7\u6587\u7ae0\u4e2d\u66fe\u7d93\u5f37\u8abf\uff0c\u82e5\u8981\u7814\u7a76\u8b8a\u4f86\u8b8a\u53bb\u7684\u901f\u5ea6\uff0c\u5fae\u5206\u662f\u4e0d\u53ef\u6216\u7f3a\u7684\u5de5\u5177\u3002\u540c\u7406\uff0c\u60f3\u8981\u7814\u7a76\u873f\u8712\u66f2\u6298\u7684\u5e7e\u4f55\u5f62\u9ad4\uff0c\u89e3\u6790\u5e7e\u4f55\u672c\u8eab\u529b\u6709\u672a\u902e\uff0c\u5fc5\u9808\u548c\u5fae\u7a4d\u5206\u806f\u624b\u624d\u884c\u3002<\/p>\n<p>\u65e9\u671f\u7684\u5fae\u5206\u5e7e\u4f55\u4e3b\u8981\u4ee5\u66f2\u7dda\u548c\u66f2\u9762\u70ba\u7814\u7a76\u5c0d\u8c61\u3002\u9019\u4e9b\u7406\u8ad6\u90fd\u662f\u6b50\u9678\u6578\u5b78\u5bb6\u767c\u5c55\u7684\uff0c\u63db\u8a00\u4e4b\u725b\u9813\u7684\u7956\u570b\u4ea4\u4e86\u767d\u5377\uff0c\u800c\u9019\u7576\u7136\u4e5f\u662f\u300c\u5fae\u7a4d\u5206\u5927\u6230\u300d\u7684\u8cbd\u798d\u3002<\/p>\n<p>\u7531\u65bc\u66f2\u7dda\u53ea\u6709\u4e00\u7dad\uff0c\u4e0d\u53ef\u80fd\u767c\u5c55\u51fa\u5167\u860a\u5e7e\u4f55(\u4f60\u82e5\u662f\u4e00\u7dad\u4e16\u754c\u7684\u751f\u7269\uff0c\u7d55\u5c0d\u7121\u6cd5\u5206\u8fa8\u4f60\u7684\u4e16\u754c\u662f\u76f4\u7dda\u9084\u662f\u62cb\u7269\u7dda)\uff0c\u6240\u4ee5\u6211\u5011\u8868\u904e\u5c31\u7b97\u3002\u81f3\u65bc\u66f2\u9762\u7406\u8ad6\uff0c\u5247\u7336\u5982\u5169\u4f4d\u5927\u6578\u5b78\u5bb6\u7684\u63a5\u529b\u8cfd\uff0c\u503c\u5f97\u597d\u597d\u8ac7\u4e00\u8ac7\u3002<\/p>\n<p>\u7b2c\u4e00\u68d2\u662f\u745e\u58eb\u7c4d\u7684\u6b50\u62c9(Leonhard Euler, 1707-1783)\uff0c\u7b2c\u4e8c\u68d2\u662f\u5fb7\u570b\u7684\u9ad8\u65af(Carl F. Gauss, 1777-1855)\uff0c\u76f8\u4fe1\u5927\u5bb6\u5c0d\u4ed6\u5011\u90fd\u4e0d\u964c\u751f\u3002<\/p>\n<figure id=\"attachment_28102\" aria-describedby=\"caption-attachment-28102\" style=\"width: 617px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-28102\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/05\/22-2.jpg\" alt=\"\" width=\"617\" height=\"300\" \/><figcaption id=\"caption-attachment-28102\" class=\"wp-caption-text\">\u745e\u58eb\u6cd5\u90ce\u4e0a\u7684\u6b50\u62c9\u50cf(\u5716\u50cf\u4f86\u6e90\uff1a\u7dad\u57fa\u767e\u79d1)<\/figcaption><\/figure>\n<p>\u6b50\u62c9\u7528\u300c\u5916\u6c42\u6cd5\u300d\u7814\u7a76\u66f2\u9762\uff0c\u82b1\u4e86\u5341\u591a\u5e74\u7684\u6642\u9593\uff0c\u65bc1760\u5e74\u5927\u529f\u544a\u6210(\u4e00\u8aaa63\u5e74)\uff0c\u4f46\u9072\u81f31767\u5e74\u624d\u6b63\u5f0f\u767c\u8868\u3002<\/p>\n<p>\u9ad8\u65af\u540c\u6a23\u662f\u4ee5\u300c\u5916\u6c42\u6cd5\u300d\u5207\u5165\u9019\u500b\u9818\u57df\uff0c\u4f46\u5728\u7814\u7a76\u904e\u7a0b\u4e2d\uff0c\u4ed6\u9010\u6f38\u6478\u7d22\u51fa\u300c\u5167\u5916\u517c\u4fee\u300d\u7684\u6cd5\u9580\uff0c\u7d42\u65bc\u767c\u73fe\u4e86\u5fae\u5206\u5e7e\u4f55\u4e2d\u7b2c\u4e00\u500b\u5167\u860a\u5b9a\u7406\uff0c\u6642\u9593\u662f\u516c\u51431827\u5e74\u3002<\/p>\n<p>\u9ad8\u65af\u8a8d\u70ba\u9019\u500b\u767c\u73fe\u7cbe\u91c7\u7d55\u502b\uff0c\u56e0\u6b64\u5728\u4ee5\u62c9\u4e01\u6587\u5beb\u6210\u7684\u8ad6\u6587\u4e2d\uff0c\u4ed6\u5fcd\u4e0d\u4f4f\u7528Egregium\u4f86\u5f62\u5bb9\u9019\u500b\u5b9a\u7406\u3002\u7531\u65bc\u9019\u500b\u6709\u8da3\u7684\u5178\u6545\uff0c\u5f8c\u4e16\u6578\u5b78\u5bb6\u7d22\u6027\u7a31\u4e4b\u70ba\u300c\u7d55\u5999\u5b9a\u7406\u300d(Theorema Egregium)\u3002<\/p>\n<p>\u7d55\u5999\u5b9a\u7406\u96d6\u7136\u6709\u9ede\u6df1\u5967\uff0c\u4f46\u5927\u53ef\u7528\u5982\u4e0b\u65b9\u5f0f\u7406\u89e3\uff1a\u6211\u5011\u5df2\u7d93\u77e5\u9053\u300c\u7403\u9762\u4e0a\u7684\u4e8c\u7dad\u751f\u7269\u6709\u8fa6\u6cd5\u78ba\u5b9a\u81ea\u5df1\u751f\u6d3b\u5728\u7403\u9762\u4e0a\u300d\uff0c\u7d55\u5999\u5b9a\u7406\u5247\u5c07\u9019\u500b\u7d50\u8ad6\u63a8\u5ee3\u6210\u300c\u4efb\u4f55\u66f2\u9762\u4e0a\u7684\u4e8c\u7dad\u751f\u7269\u90fd\u6709\u8fa6\u6cd5\u78ba\u5b9a\u81ea\u5df1\u751f\u6d3b\u5728\u66f2\u9762\u4e0a\uff0c\u800c\u4e14\u80fd\u7528\u4e0d\u5047\u5916\u6c42\u7684\u65b9\u6cd5\u6e2c\u91cf\u51fa\u5404\u8655\u7684\u5f4e\u66f2\u7a0b\u5ea6\uff0c\u4e5f\u5c31\u662f\u6240\u8b02\u7684\u66f2\u7387\u300d\u3002<\/p>\n<p>\u9019\u500b\u5b9a\u7406\u70ba\u5fae\u5206\u5e7e\u4f55\u6307\u51fa\u4e00\u500b\u65b0\u65b9\u5411\uff0c\u53ef\u60dc\u7684\u662f\u9ad8\u65af\u4e26\u672a\u4e58\u52dd\u8ffd\u64ca\uff0c\u56e0\u6b64\u7d55\u5999\u5b9a\u7406\u5c31\u662f\u4ed6\u5728\u9019\u500b\u9818\u57df\u7684\u6700\u9ad8\u6210\u5c31\u4e86\u2500\u2500\u6216\u8a31\u9019\u5c31\u662f\u6240\u8b02\u7684\u300c\u4e00\u4ee3\u4eba\u53ea\u80fd\u505a\u4e00\u4ee3\u4eba\u7684\u4e8b\u300d\u3002<\/p>\n<p>\u5e78\u597d\u591a\u5e74\u5f8c\uff0c\u56b4\u683c\u8aaa\u4f86\u662f\u9ad8\u65af\u751f\u547d\u4e2d\u7684\u6700\u5f8c\u4e00\u5e74\uff0c\u4ed6\u7684\u611b\u5f92\u9ece\u66fc(Bernhard Riemann, 1826-1866)\u52c7\u6562\u5730\u63a5\u4e0b\u7b2c\u4e09\u68d2\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/line.me\/R\/ti\/p\/%40fcx6182w\" target=\"_blank\" rel=\"noopener noreferrer\"><img decoding=\"async\" class=\"alignnone\" src=\"https:\/\/scdn.line-apps.com\/n\/line_add_friends\/btn\/zh-Hant.png\" alt=\"\u52a0\u5165\u597d\u53cb\" width=\"212\" height=\"36\" border=\"0\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7d55\u5999\u5b9a\u7406\u96d6\u7136\u6709\u9ede\u6df1\u5967\uff0c\u4f46\u5927\u53ef\u7528\u5982\u4e0b\u65b9\u5f0f\u7406\u89e3\uff1a\u6211\u5011\u5df2\u7d93\u77e5\u9053\u300c\u7403\u9762\u4e0a\u7684\u4e8c\u7dad\u751f\u7269\u6709\u8fa6\u6cd5\u78ba\u5b9a\u81ea\u5df1\u751f\u6d3b\u5728\u7403\u9762\u4e0a\u300d\uff0c\u7d55\u5999\u5b9a\u7406\u5247\u5c07\u9019\u500b\u7d50\u8ad6\u63a8\u5ee3\u6210\u300c\u4efb\u4f55\u66f2\u9762\u4e0a\u7684\u4e8c\u7dad\u751f\u7269\u90fd\u6709\u8fa6\u6cd5\u78ba\u5b9a\u81ea\u5df1\u751f\u6d3b\u5728\u66f2\u9762\u4e0a\uff0c\u800c\u4e14\u80fd\u7528\u4e0d\u5047\u5916\u6c42\u7684\u65b9\u6cd5\u6e2c\u91cf\u51fa\u5404\u8655\u7684\u5f4e\u66f2\u7a0b\u5ea6\uff0c\u4e5f\u5c31\u662f\u6240\u8b02\u7684\u66f2\u7387\u300d\u3002<\/p>\n","protected":false},"author":20,"featured_media":28106,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3112,3293],"tags":[3407,3405,3406,3408,693],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/05\/22-0.jpg","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/28100"}],"collection":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=28100"}],"version-history":[{"count":5,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/28100\/revisions"}],"predecessor-version":[{"id":31742,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/28100\/revisions\/31742"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/28106"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=28100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=28100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=28100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}