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class=\"wp-caption-text\">19\u4e16\u7d00\u7684\u60f3\u50cf\u756b\uff1a\u7562\u6c0f\u7387\u9818\u5f92\u773e\u8fce\u63a5\u65e5\u51fa(\u5716\u50cf\u4f86\u6e90\uff1a\u7dad\u57fa\u767e\u79d1)<\/figcaption><\/figure>\n<p>\u7121\u7368\u6709\u5076\uff0c\u91cb\u8fe6\u725f\u5c3c\u751f\u524d\u6240\u5ba3\u63da\u7684\u6559\u7fa9\uff0c\u4e5f\u548c\u4e00\u822c\u7684\u5b97\u6559\u5927\u7570\u5176\u8da3\u3002\u6700\u660e\u986f\u7684\u8b49\u64da\u5c31\u662f\u300c\u795e\u300d\u5728\u6b63\u7d71\u4f5b\u6559\u4e2d\u6839\u672c\u4e0d\u5b58\u5728\uff0c\u800c\u300c\u4f5b\u300d\u4e5f\u53ea\u662f\u609f\u9053\u8005\u7684\u5c0a\u7a31\u7f77\u4e86\u3002<\/p>\n<p>\u7136\u800c\uff0c\u96a8\u8457\u4f5b\u6559\u7684\u767c\u5c55\u8207\u8301\u58ef\uff0c\u91cb\u8fe6\u725f\u5c3c\u300c\u4f5b\u300d\u7684\u5730\u4f4d\u8d8a\u4f86\u8d8a\u9ad8\uff0c\u6700\u5f8c\u5c45\u7136\u548c\u6cd5\u529b\u7121\u908a\u7684\u963f\u5f4c\u9640\u4f5b\u53ca\u5f4c\u52d2\u4f5b\u5e73\u8d77\u5e73\u5750\u3002\u8207\u6b64\u540c\u6642\uff0c\u9019\u985e\u7d14\u5c6c\u865b\u69cb\u7684\u8af8\u5929\u795e\u4f5b\u5247\u8d8a\u4f86\u8d8a\u591a\uff0c\u800c\u9019\u6b63\u662f\u5927\u4e58\u4f5b\u6559\u6709\u5225\u65bc\u539f\u59cb\u4f5b\u6559\u4e4b\u8655\u3002<\/p>\n<p>\u8a71\u53c8\u8aaa\u56de\u4f86\uff0c\u96d6\u7136\u5927\u4e58\u4f5b\u6559\u662f\u5f8c\u4eba\u7684\u767c\u660e\uff0c\u8ddf\u91cb\u8fe6\u725f\u5c3c\u6c92\u6709\u76f4\u63a5\u95dc\u4fc2\uff0c\u7136\u800c\u5c31\u4e16\u754c\u6587\u5316\u53f2\u800c\u8a00\uff0c\u5927\u4e58\u4f5b\u6559\u7684\u6559\u7fa9\u8207\u7d93\u5178\u4ecd\u662f\u4eba\u985e\u6587\u5316\u7684\u7470\u5bf6\uff0c\u5728\u54f2\u5b78\u5c64\u6b21\u4e0a\u4e0d\u4f46\u8d85\u8d8a\u539f\u59cb\u4f5b\u6559\uff0c\u751a\u81f3\u51cc\u99d5\u65bc\u5357\u50b3\u4f5b\u6559(\u4ea6\u5373\u4fd7\u7a31\u7684\u5c0f\u4e58\u4f5b\u6559)\u4e4b\u4e0a\u3002<\/p>\n<p><strong>\u25cf\u7562\u6c0f\u5b78\u6d3e\u7684\u5b78\u8853\u907a\u7522<\/strong><\/p>\n<p>\u985e\u4f3c\u7684\u60c5\u6cc1\u4e5f\u66fe\u767c\u751f\u65bc\u53e4\u5e0c\u81d8\u3002\u7562\u6c0f\u5b78\u6d3e\u6240\u7559\u4e0b\u7684\u6587\u5316\u907a\u7522\uff0c\u7d93\u7531\u4e9e\u91cc\u65af\u591a\u5fb7\u7b49\u4eba\u7684\u6574\u7406\u722c\u68b3\uff0c\u5f9e\u4e2d\u51dd\u934a\u51fa\u5e7e\u9580\u892a\u76e1\u795e\u79d8\u8272\u5f69\u7684\u79d1\u5b78\uff0c\u5305\u62ec\u5e7e\u4f55\u5b78(\u6700\u6709\u540d\u7684\u5c31\u662f\u300c\u7562\u6c0f\u5b9a\u7406\u300d)\u3001\u7b97\u8853\u5b78(\u4e3b\u8981\u662f\u95dc\u65bc\u6574\u6578\u7684\u898f\u5f8b)\u3001\u5929\u6587\u5b78(\u6709\u53ef\u80fd\u662f\u300c\u5730\u5713\u8aaa\u300d\u7684\u767c\u6e90\u5730)\u4ee5\u53ca\u97f3\u5f8b\u5b78(\u300c\u548c\u8ae7\u97f3\u7a0b\u300d\u7684\u76f8\u95dc\u7406\u8ad6\u662f\u5176\u4ee3\u8868\u4f5c)\u3002<\/p>\n<p>\u7531\u65bc\u7562\u6c0f\u5b78\u6d3e\u5c0d\u6574\u6578\u6709\u8457\u76f2\u76ee\u7684\u4fe1\u4ef0\u8207\u5d07\u62dc\uff0c\u56e0\u6b64\u5728\u4e0a\u8ff0\u5e7e\u9580\u79d1\u5b78\u4e2d\uff0c\u8655\u8655\u53ef\u898b\u6574\u6578\u7684\u8eab\u5f71\u3002\u4f8b\u5982\u6839\u64da\u7562\u6c0f\u5b9a\u7406\uff0c\u4efb\u4f55\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u908a\u9577\u90fd\u6eff\u8db3a<sup>2<\/sup>+b<sup>2<\/sup>=c<sup>2<\/sup>\u9019\u500b\u95dc\u4fc2\uff0c\u4f46\u662f\u7562\u6c0f\u5b78\u6d3e\u7279\u5225\u9752\u775e(a, b, c)\u7686\u70ba\u6574\u6578\u7684\u60c5\u5f62\uff0c\u4f8b\u5982(3, 4, 5), (5, 12, 13)\u7b49\u3002\u751a\u81f3\u5728\u97f3\u5f8b\u5b78\u4e2d\uff0c\u4ed6\u5011\u4e5f\u7368\u5177\u6167\u773c\uff0c\u4f7f\u7528\u6574\u6578\u4f86\u5275\u9020\u6240\u6709\u7684\u97f3\u7a0b(\u5373\u5f8c\u4e16\u6240\u8b02\u7684\u300c\u7562\u6c0f\u97f3\u7a0b\u300d)\u3002\u66f4\u6709\u8da3\u7684\u662f\uff0c\u9019\u4e9b\u5b78\u8005\u751a\u81f3\u5c07\u9019\u5957\u548c\u8ae7\u7406\u8ad6\u7528\u65bc\u5929\u6587\u5b78\uff0c\u8a66\u5716\u89e3\u91cb\u5730\u5fc3\u5b87\u5b99\u7684\u7d50\u69cb\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u7562\u6c0f\u5b78\u6d3e\u7684\u975e\u7406\u6027\u90e8\u5206\u5247\u88ab\u53e6\u4e00\u6279\u4eba\u767c\u63da\u5149\u5927\u3002\u4f8b\u5982\u300c\u6574\u6578\u8db3\u4ee5\u89e3\u91cb\u842c\u4e8b\u842c\u7269\u300d\u9019\u500b\u4fe1\u4ef0\uff0c\u5c31\u767c\u5c55\u6210\u4e86\u6700\u65e9\u7684\u300c\u6578\u79d8\u5b78\u300d(Numerology)\u3002<\/p>\n<p>\u300c\u6578\u79d8\u5b78\u300d\u4e26\u4e0d\u80fd\u548c\u300c\u6578\u5b57\u8ff7\u4fe1\u300d\u756b\u4e0a\u7b49\u865f\uff0c\u5f8c\u8005\u53ea\u662f\u55ae\u7d14\u5730\u76f8\u4fe1\u67d0\u4e9b\u6578\u76ee\u95dc\u4e4e\u5409\u51f6\uff0c\u800c\u6578\u79d8\u5b78\u5247\u6709\u4e00\u5957\u7e41\u8907\u7684\u7406\u8ad6\u8207\u516c\u5f0f\uff0c\u5f88\u5bb9\u6613\u4ee4\u4eba\u8085\u7136\u8d77\u656c\u3002\u4e8b\u5be6\u4e0a\uff0c\u6578\u79d8\u5b78\u548c\u5360\u661f\u5b78\u4e00\u6a23\uff0c\u90fd\u662f\u62ab\u8457\u79d1\u5b78\u5916\u8863\u7684\u7384\u5b78\uff0c\u4e5f\u5c31\u662f\u4fd7\u7a31\u7684\u507d\u79d1\u5b78\u3002(\u8acb\u60f3\u60f3\uff0c\u4e2d\u6587\u59d3\u540d\u5b78\u7684\u7b46\u5283\u8a08\u7b97\u516c\u5f0f\u7b97\u4e0d\u7b97\u300c\u6578\u79d8\u5b78\u300d\uff1f)<\/p>\n<p>\u5c31\u6b63\u507d\u89c0\u9ede\u800c\u8a00\uff0c\u300c\u6578\u79d8\u5b78\u300d\u8207\u300c\u6578\u8ad6\u300d\u7684\u95dc\u4fc2\u6b63\u5982\u300c\u5360\u661f\u5b78\u300d\u8207\u300c\u5929\u6587\u5b78\u300d\u7684\u95dc\u4fc2\u3002\u4e0d\u540c\u7684\u662f\uff0c\u524d\u8005\u5728\u53e4\u5e0c\u81d8\u6642\u4ee3\u4fbf\u5df2\u5206\u9053\u63da\u9463\uff0c\u5f8c\u8005\u76f4\u5230\u5341\u4e03\u4e16\u7d00\u9084\u7cfe\u7e8f\u4e0d\u6e05\uff0c\u4f8b\u5982\u9f0e\u9f0e\u5927\u540d\u7684\u514b\u535c\u52d2\u5c31\u517c\u6709\u300c\u5929\u6587\u5b78\u5bb6\u300d\u8207\u300c\u5360\u661f\u5b78\u5bb6\u300d\u7684\u96d9\u91cd\u8eab\u4efd\u3002<\/p>\n<figure id=\"attachment_27320\" aria-describedby=\"caption-attachment-27320\" style=\"width: 350px\" class=\"wp-caption alignright\"><img decoding=\"async\" class=\"wp-image-27320\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2017\/03\/11-2.jpg\" alt=\"\" width=\"350\" height=\"495\" \/><figcaption id=\"caption-attachment-27320\" class=\"wp-caption-text\">15\u4e16\u7d00\u7684\u60f3\u50cf\u756b\uff1a\u7562\u6c0f\u9032\u884c\u97f3\u7a0b\u7814\u7a76<br \/> (\u5716\u50cf\u4f86\u6e90\uff1aIMSLP\/Petrucci Music Library)<\/figcaption><\/figure>\n<p><strong>\u25cf\u503c\u5f97\u4e00\u63d0\u7684\u50b3\u8aaa<\/strong><\/p>\n<p>\u96d6\u7136\u672c\u6587\u4e00\u518d\u5f37\u8abf\uff0c\u95dc\u65bc\u7562\u6c0f\u7684\u751f\u5e73\uff0c\u53ef\u4fe1\u7684\u53f2\u6599\u5c11\u4e4b\u53c8\u5c11\u3002\u4f46\u6709\u4e9b\u50b3\u8aaa\u5373\u4fbf\u4e26\u975e\u53f2\u5be6\uff0c\u4e5f\u662f\u9817\u5177\u555f\u767c\u6027\u548c\u6559\u80b2\u610f\u7fa9\u7684\u300c\u79d1\u5b78\u6545\u4e8b\u300d\u3002\u6b63\u5982\u300a\u4f0a\u7d22\u5bd3\u8a00\u300b\u5373\u4fbf\u7d55\u975e\u771f\u4eba\u771f\u4e8b\uff0c\u4e5f\u662f\u9817\u5177\u555f\u767c\u6027\u548c\u6559\u80b2\u610f\u7fa9\u7684\u300c\u9053\u5fb7\u6545\u4e8b\u300d\u3002<\/p>\n<p>\u95dc\u65bc\u300c\u7562\u6c0f\u97f3\u7a0b\u300d\u7684\u50b3\u8aaa\u5c31\u662f\u5f88\u597d\u7684\u4f8b\u5b50\u3002\u8a71\u8aaa\u7562\u6c0f\u67d0\u5929\u7d93\u904e\u4e00\u9593\u6253\u9435\u8216\uff0c\u807d\u5230\u6253\u9435\u8072\u7adf\u7136\u76f8\u7576\u6085\u8033\uff0c\u4fbf\u597d\u5947\u5fc3\u5927\u767c\uff0c\u7576\u5834\u505a\u8d77\u7814\u7a76\u3002\u7531\u65bc\u4ed6\u8070\u660e\u7d55\u9802\uff0c\u5f88\u5feb\u767c\u73fe\u4e86\u5176\u4e2d\u7684\u5967\u79d8\u3002\u539f\u4f86\u56db\u540d\u9435\u5320\u6240\u7528\u7684\u939a\u5b50\uff0c\u91cd\u91cf\u5206\u5225\u662f6, 8, 9, 12(\u65a4)\u2500\u2500\u7c21\u55ae\u6574\u6578\u6bd4\uff01\u65bc\u662f\u4ed6\u8d95\u7dca\u885d\u56de\u5bb6\uff0c\u6539\u7528\u7434\u5f26\u4f86\u505a\u5be6\u9a57\uff0c\u5f88\u5feb\u5c31\u6b78\u7d0d\u51fa\u985e\u4f3c\u7684\u898f\u5f8b\uff1a\u53ea\u8981\u5169\u689d\u7434\u5f26\u7684\u9577\u5ea6\u6210\u7c21\u55ae\u6574\u6578\u6bd4\uff0c\u4f8b\u59824:3, 3:2, 2:1\uff0c\u767c\u51fa\u7684\u8072\u97f3\u5c31\u6703\u548c\u8ae7\u6085\u8033\u3002\u7528\u73fe\u4ee3\u8853\u8a9e\u4f86\u8aaa\uff0c\u9019\u4e09\u7d44\u97f3\u7a0b\u5206\u5225\u662f\u5b8c\u5168\u56db\u5ea6(\u76f8\u5dee5\u500b\u534a\u97f3)\u3001\u5b8c\u5168\u4e94\u5ea6(\u76f8\u5dee7\u500b\u534a\u97f3)\u4ee5\u53ca\u5b8c\u5168\u516b\u5ea6(\u76f8\u5dee12\u500b\u534a\u97f3)\u3002<\/p>\n<p>\u53e6\u4e00\u500b\u50b3\u8aaa\u5247\u76f8\u7576\u60b2\u6158\uff0c\u597d\u5728\u771f\u7684\u53ea\u662f\u50b3\u8aaa\u800c\u5df2\u3002\u8a71\u8aaa\u7531\u65bc\u7562\u6c0f\u5805\u4fe1\u6574\u6578\u5a01\u529b\u7121\u7aae\uff0c\u56e0\u6b64\u7576\u67d0\u4f4d\u5f1f\u5b50\u5728\u300c\u7562\u6c0f\u5b9a\u7406\u300d\u4e2d\u767c\u73fe\u4e00\u500b\u6574\u6578\u7121\u6cd5\u63cf\u8ff0\u7684\u73fe\u8c61\uff0c\u7562\u6c0f\u7121\u6cd5\u63a5\u53d7\u9019\u500b\u90aa\u60e1\u7684\u4e8b\u5be6\uff0c\u7d22\u6027\u4e0b\u4ee4\u628a\u4ed6\u4e1f\u5230\u5927\u6d77\u6df9\u6b7b\u4e86\u3002<\/p>\n<p>\u90a3\u4f4d\u5012\u6963\u7684\u5f1f\u5b50\u5230\u5e95\u767c\u73fe\u4e86\u4ec0\u9ebc\uff0c\u7adf\u7136\u7121\u7aef\u60f9\u4f86\u6bba\u8eab\u4e4b\u798d\uff1f\u5728\u63ed\u66c9\u8b0e\u5e95\u4e4b\u524d\uff0c\u6211\u5011\u8981\u5148\u505a\u9ede\u6e96\u5099\u5de5\u4f5c\u3002<\/p>\n<p>\u7562\u6c0f\u8a8d\u70ba\u6574\u6578\u80fd\u5920\u89e3\u91cb\u4e00\u5207\u3001\u4ee3\u8868\u4e00\u5207\uff0c\u9019\u500b\u300c\u4e00\u5207\u300d\u7576\u7136\u5305\u62ec\u6240\u6709\u7684\u5206\u6578\uff0c\u4f8b\u59822\/3\u96d6\u7136\u4e0d\u662f\u6574\u6578\uff0c\u537b\u662f\u5169\u500b\u6574\u6578\u76f8\u9664\u7684\u7d50\u679c\u3002\u7562\u6c0f(\u5b78\u6d3e)\u8a8d\u70ba\u4e00\u65e6\u5982\u6b64\u64f4\u5927\u89e3\u91cb\uff0c\u5c31\u80fd\u628a\u5929\u5730\u9593\u6240\u6709\u7684\u6578\u5305\u62ec\u5728\u5167\u3002\u63db\u6210\u5e7e\u4f55\u7684\u8aaa\u6cd5\uff0c\u5c31\u662f\u4efb\u4f55\u7dda\u6bb5\u7684\u9577\u5ea6\u90fd\u80fd\u7528\u6574\u6578\u6216\u5206\u6578\u4f86\u8868\u793a\u3002<\/p>\n<p>\u4e0d\u6599\uff0c\u90a3\u4f4d\u5f1f\u5b50\u5c45\u7136\u767c\u73fe\u5728\u300c\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\u300d\u7684\u4e09\u500b\u908a\u9577\u4e2d\uff0c\u81f3\u5c11\u6709\u4e00\u500b\u65e2\u4e0d\u662f\u6574\u6578\u4e5f\u4e0d\u662f\u5206\u6578\u3002\u6bd4\u65b9\u8aaa\uff0c\u5982\u679c\u5169\u8170\u7684\u9577\u5ea6\u662f1\uff0c\u90a3\u9ebc\u659c\u908a\u5c31\u662f\u221a2=1.41421\u2026\uff0c\u7576\u7136\u4e0d\u80fd\u8868\u793a\u70ba\u6574\u6578\u9664\u4ee5\u6574\u6578\u3002\u6240\u4ee5\u5c0d\u65bc\u73fe\u4ee3\u8b80\u8005\u4f86\u8aaa\uff0c\u9019\u6a23\u7684\u8b0e\u5e95\u6050\u6015\u6709\u9ede\u53cd\u9ad8\u6f6e\u3002<\/p>\n<p>\u56e0\u6b64\u4e4b\u6545\uff0c\u9019\u500b\u6545\u4e8b\u6700\u597d\u7a0d\u52a0\u6539\u5beb\uff0c\u6bd4\u65b9\u8aaa\u52a0\u4e0a\u4e00\u500b\u7d50\u5c3e\uff1a\u8655\u6b7b\u90a3\u4f4d\u5f1f\u5b50\u4e4b\u5f8c\uff0c\u7562\u6c0f\u51b7\u975c\u4e0b\u4f86\uff0c\u611f\u5230\u5f8c\u6094\u4e0d\u5df2\uff0c\u70ba\u4e86\u63d0\u9192\u81ea\u5df1\u5225\u518d\u5931\u53bb\u7406\u667a\uff0c\u9042\u5c07\u221a2\u547d\u540d\u70ba\u7121\u7406\u6578\u3002<\/p>\n<p>\u9019\u500b\u7d50\u5c3e\u7d14\u5c6c\u865b\u69cb\uff0c\u8acb\u5927\u5bb6\u5343\u842c\u5225\u76f8\u4fe1\uff01\u81f3\u65bc\u300c\u7121\u7406\u6578\u300d\u5230\u5e95\u662f\u600e\u9ebc\u4f86\u7684\uff0c\u90a3\u5c31\u662f\u53e6\u4e00\u500b\u6545\u4e8b\u4e86\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><a 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