{"id":2692,"date":"2010-04-14T18:29:28","date_gmt":"2010-04-14T10:29:28","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=2692"},"modified":"2017-03-31T23:21:24","modified_gmt":"2017-03-31T15:21:24","slug":"%e3%80%90%e5%9b%9e%e9%9f%b3%e8%b0%b7%e3%80%91%e6%80%9d%e8%80%83%e3%80%8c%e6%95%b8%e5%ad%b8%e8%88%87%e6%96%87%e6%98%8e-%e6%a6%82%e8%bf%b0%e8%88%87%e9%87%8d%e8%a8%aa%e3%80%8d","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=2692","title":{"rendered":"\u3010\u56de\u97f3\u8c37\u3011\u601d\u8003\u300c\u6578\u5b78\u8207\u6587\u660e\u2014\u6982\u8ff0\u8207\u91cd\u8a2a\u300d"},"content":{"rendered":"<p><strong><span style=\"color: #800000;\">\u25a0 \u4eba\u985e\u4e08\u91cf\u5929\u7a7a\u7684\u5927\u5922\u5982\u4f55\u8207\u6578\u5b78\u548c\u6587\u660e\u6709\u95dc\uff1f\u9805\u6b66\u7fa9\u6559\u6388\u4eca\u5e74\u4e09\u6708\u5728\u53f0\u5927\u7684\u6f14\u8b1b\u300c\u6578\u5b78\u8207\u6587\u660e\u2014\u6982\u8ff0\u8207\u91cd\u8a2a\u300d\u5f15\u8d77\u4e86\u9019\u7bc7\u8ff4\u97ff\u3002<\/span><\/strong><\/p>\n<p><strong>?\u64b0\u6587<\/strong> \u2223 \u65bd\u535a\u4ec1\uff08\u53f0\u5927\u96fb\u6a5f\u7cfb\u4e8c\u5e74\u7d1a\uff09<\/p>\n<figure id=\"attachment_2695\" aria-describedby=\"caption-attachment-2695\" style=\"width: 340px\" class=\"wp-caption alignright\"><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-2695    \" title=\"Close-packed_spheres(wiki.en)\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2010\/04\/607px-Close-packed_spheres1.jpg\" alt=\"Close-packed_spheres(wiki.en)\" width=\"340\" height=\"336\" \/><figcaption id=\"caption-attachment-2695\" class=\"wp-caption-text\">\u5716\u4e00\uff1a\u523b\u535c\u52d2\uff08Kepler\uff09\u65bc1611\u5e74\u63d0\u51fa\u5982\u679c\u8981\u5728\u4e09\u7dad\u7a7a\u9593\u4e2d\u5806\u7a4d\u5927\u5c0f\u76f8\u540c\u7684\u7403\u9ad4\uff0c\u6700\u7bc0\u7701\u7a7a\u9593\u65b9\u6cd5\u662f\u5e02\u5834\u5c0f\u8ca9\u5806\u758a\u6a58\u5b50\u6216\u756a\u8304\u7684\u65b9\u5f0f\u3002<\/figcaption><\/figure>\n<p>\u3000\u3000\u9805\u6b66\u7fa9\u6559\u63881959\u5e74\u7562\u696d\u65bc\u53f0\u5927\u6578\u5b78\u7cfb\uff0c\u65e9\u5e74\u81f4\u529b\u65bc\u5e7e\u4f55\u5b78\u7814\u7a76\u30021990\u5e74\u5f8c\u53cd\u749e\u6b78\u771f\uff0c\u6539\u70ba\u7814\u7a76\u53e4\u5178\u5e7e\u4f55\u3001\u51fa\u7248\u4e86\u5e7e\u672c\u57fa\u790e\u6578\u5b78\u6559\u6750\uff0c\u4e5f\u7559\u610f\u6578\u5b78\u3001\u5929\u6587\u5b78\u767c\u5c55\u53f2\u3002\u9019\u6bb5\u6642\u671f\uff0c\u4ed6\u66fe\u63d0\u51fa\u4e86\u8457\u540d\u7684\u523b\u535c\u52d2\u731c\u60f3\uff08Kepler\u2019s Conjecture\uff09\u7684\u8b49\u660e[\u8a3b1]\uff0c\u8f5f\u52d5\u6578\u5b78\u754c\u3002?<\/p>\n<p>\u3000\u30003\u670826\u65e5\u9805\u6559\u6388\u61c9\u53f0\u5927\u79d1\u6559\u4e2d\u5fc3\u4e4b\u9080\uff0c\u4ee5\u300c\u6578\u5b78\u8207\u6587\u660e\u2014\u6982\u8ff0\u8207\u91cd\u8a2a\u300d\u70ba\u984c\u8d74\u53f0\u5927\u8209\u884c\u6f14\u8b1b\u3002\u6b64\u6b21\u6f14\u8aaa\u7684\u4e09\u5927\u4e3b\u8ef8\u5206\u5225\u662f\u7269\u7406\u5b78\u3001\u5e7e\u4f55\u5b78\u3001\u5929\u6587\u5b78\uff0c\u4ee5\u5927\u6b77\u53f2\u7684\u89d2\u5ea6\u91cd\u8a2a\u5176\u767c\u5c55\uff0c\u4e26\u8a8d\u70ba\u9019\u4e09\u500b\u5b78\u79d1\u7684\u767c\u5c55\u90fd\u66fe\u8aa4\u5165\u6b67\u9014\uff0c\u53c8\u8ff7\u9014\u77e5\u8fd4\u3002\u5c31\u5e7e\u4f55\u5b78\u4f86\u8aaa\uff0c\u7562\u9054\u54e5\u62c9\u65af\u5b78\u6d3e\uff08The Pythagorean School\uff09[\u8a3b2]\u76f8\u4fe1\u4efb\u4f55\u7684\u91cf\u90fd\u53ef\u4ee5\u8868\u793a\u6210\u7c21\u55ae\u7684\u6574\u6578\u6bd4\uff0c\u5728\u5e7e\u4f55\u5b78\u4e0a\u7684\u610f\u7fa9\u5373\u662f\u5ba3\u7a31\uff1a\u7d66\u5b9a\u5169\u500b\u7dda\u6bb5\uff0c\u6211\u5011\u90fd\u53ef\u4ee5\u627e\u5230\u4e00\u500b\u6700\u9577\u7684\u7b2c\u4e09\u500b\u7dda\u6bb5\uff08\u7a31\u70ba\u6700\u5927\u53ef\u516c\u5ea6\uff09\uff0c\u4f7f\u9019\u5169\u500b\u7dda\u6bb5\u90fd\u662f\u7b2c\u4e09\u500b\u7dda\u6bb5\u7684\u6574\u6578\u500d\u3002\u4ee52cm\u548c2.5cm\u70ba\u4f8b\uff0c\u6700\u5927\u53ef\u516c\u5ea6\u5373\u662f0.5cm\u3002\u7136\u800c\u7562\u6c0f\u5b78\u6d3e\u7684\u7f8e\u5922\u7834\u788e\u4e86\uff0c\u50b3\u8aaa\u4e00\u4f4d\u6210\u54e1Hippasus\u6d29\u6f0f\uff08\u53e6\u4e00\u8aaa\u662f\u767c\u73fe\uff09\u4e86\u4e0d\u53ef\u516c\u5ea6\u6027\u7684\u79d8\u5bc6[\u8a3b3]\uff0c\u4f7f\u5b78\u6d3e\u540d\u8072\u6383\u5730\uff0c\u9a5a\u6050\u4e0d\u5df2\u7684\u5176\u4ed6\u6210\u54e1\u5c07\u4ed6\u62cb\u9032\u4e86\u5927\u6d77\u3002\u4e00\u76f4\u5230\u4e86Eudoxus\uff08\u7d04410 - 355 BC\uff09\u624d\u89e3\u6c7a\u4e86\u5e7e\u4f55\u5b78\u9762\u81e8\u57ae\u53f0\u7684\u96e3\u984c\uff0c\u76f8\u95dc\u7684\u90e8\u4efd\u8a18\u8f09\u65bc\u6b50\u5e7e\u91cc\u5fb7\uff08Euclid\uff09\u300a\u5e7e\u4f55\u539f\u672c\u300b\uff08Euclid's Elements\uff09\u7b2c\u4e94\u7ae0\uff08Book V\uff09\u3002<\/p>\n<p>\u3000\u3000\u7136\u800c\u7562\u6c0f\u5b78\u6d3e\u7684\u932f\u8aa4\u7455\u4e0d\u63a9\u745c\uff0c\u9805\u6b66\u7fa9\u6559\u6388\u76f8\u7576\u80af\u5b9a\u7562\u6c0f\u5b78\u6d3e\u7684\u8ca2\u737b\u3002\u7562\u6c0f\u5b78\u6d3e\u5ba3\u7a31\u5b87\u5b99\u7684\u548c\u8ae7\u548c\u7cbe\u8981\u5728\u65bc\u6578\u3001\u6bd4\u503c\u548c\u5e7e\u4f55\u5f62\u9ad4\u7684\u59a5\u52a0\u914d\u5408\uff0c\u9805\u6559\u6388\u500b\u4eba\u8a8d\u70ba\u4ee5\u4eca\u65e5\u7684\u5f8c\u898b\u4e4b\u660e\uff0c\u5373\u662f\u9810\u53d6\u4e86\uff1a\u300c\u6578\u7406\u5206\u6790\u4e43\u662f\u8a8d\u77e5\u5927\u81ea\u7136\u7684\u4e0d\u4e8c\u6cd5\u9580\u3002\u300d\u4e5f\u53ef\u4ee5\u8aaa\uff0c\u76f8\u4fe1\u5927\u81ea\u7136\u73fe\u8c61\u5b58\u5728\u8457\u300c\u7c21\u55ae\u7684\u300d\u6578\u503c\u95dc\u806f\uff0c\u4e43\u662f\u7269\u7406\u5b78\u65e9\u671f\u767c\u5c55\u7684\u95dc\u9375\u3002\u9019\u9ede\u5c07\u5728\u7a0d\u5f8c\u95e1\u8ff0\u3002<!--more--><\/p>\n<p>\u3000\u3000\u5929\u6587\u5b78\u4e5f\u540c\u6a23\u8ff7\u9014\u77e5\u8fd4\uff0c\u6f14\u8b1b\u4e2d\u8209\u4e86\u6258\u52d2\u5bc6\uff08Ptolemy\uff09\u7684\u5730\u5fc3\u8aaa\uff08\u5730\u7403\u4e2d\u5fc3\u8aaa\uff09\u3002\u76f4\u5230\u6587\u85dd\u5fa9\u8208\u6642\u671f\uff0c\u54e5\u767d\u5c3c\u3001\u4f3d\u5229\u7565\u3001\u523b\u535c\u52d2\u7b49\u5929\u6587\u5b78\u5bb6\u624d\u6b63\u5f0f\u6253\u7834\u9019\u6a23\u6709\u9650\u7684\u5b87\u5b99\u89c0\u3002\u9805\u6559\u6388\u76f8\u7576\u63a8\u5d07\u523b\u535c\u52d2\uff08Johannes Kepler,1571-1630\uff09\uff0c\u7136\u800c\u5e73\u5fc3\u800c\u8ad6\uff0c\u523b\u535c\u52d2\u4e0d\u904e\u662f\u6191\u85c9\u8457\u53e6\u4e00\u500b\u5049\u5927\u7684\u5929\u6587\u5b78\u5bb6\u7b2c\u8c37\uff08Tycho Brahe, 1546-1601\uff09\u8a73\u76e1\u7684\u89c0\u5bdf\u8cc7\u6599\uff0c\u505a\u985e\u4f3c\u4eca\u65e5\u6211\u5011\u4ee5excel\u5c0b\u627e\u5be6\u9a57\u6578\u64da\u95dc\u4fc2\u7684\u5de5\u4f5c\u3002\u523b\u535c\u52d2\u82b1\u8cbb\u4e8616\u5e74\uff0c\u767c\u73fe\u884c\u661f\u516c\u8f49\u9031\u671f\u7684\u5e73\u65b9\u548c\u516c\u8f49\u534a\u5f91\u7684\u7acb\u65b9\u6210\u6b63\u6bd4\uff1b\u9019\u6a23\u7684\u95dc\u806f\u4e26\u4e0d\u76f4\u89c0\uff0c\u523b\u535c\u52d2\u7684\u5de5\u4f5c\u986f\u7136\u6709\u76f2\u8a66\u7684\u6210\u4efd\u3002<\/p>\n<figure id=\"attachment_2697\" aria-describedby=\"caption-attachment-2697\" style=\"width: 135px\" class=\"wp-caption alignleft\"><img decoding=\"async\" class=\"size-full wp-image-2697 \" title=\"Johannes_Kepler\uff08wiki.en\uff09\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2010\/04\/225px-Johannes_Kepler_16101.jpg\" alt=\"Johannes_Kepler\" width=\"135\" height=\"185\" \/><figcaption id=\"caption-attachment-2697\" class=\"wp-caption-text\">\u523b\u535c\u52d2<\/figcaption><\/figure>\n<p>\u3000\u3000\u6216\u8a31\u662f\u56e0\u70ba\u523b\u535c\u52d2\u7684\u4fe1\u4ef0\uff0c\u4f8b\u5982\u76f8\u4fe1\u5b87\u5b99\u662f\u4e0a\u5e1d\u7684\u5f62\u8c61\uff0c\u59cb\u7d42\u6df1\u4fe1\u661f\u9ad4\u4e4b\u9593\u6709\u7c21\u55ae\u7684\u5e7e\u4f55\u3001\u6578\u5b78\u95dc\u806f\uff0c\u56e0\u800c\u4e0d\u8a08\u6210\u672c\u767c\u89ba\u300c\u771f\u7406\u300d\u3002\u5373\u4f7f\u5230\u4e86\u725b\u9813\u4e5f\u4e0d\u4f8b\u5916\uff0c\u4ed6\u7684\u8457\u4f5c\u6709\u6975\u5927\u7684\u90e8\u4efd\u5145\u6eff\u795e\u5b78\uff0c\u7d42\u5176\u4e00\u751f\u529b\u5716\u4ee5\u56b4\u8b39\u7684\u6578\u5b78\u65b9\u6cd5\uff0c\u8b49\u660e\u81ea\u7136\u4e16\u754c\u4e2d\u7684\u79e9\u5e8f\u662f\u4e0a\u5e1d\u7684\u5091\u4f5c\u3001\u795e\u7684\u610f\u5fd7\u6d3b\u52d5\u78ba\u5be6\u5b58\u5728\u3002\u8457\u540d\u7d93\u6fdf\u5b78\u5bb6\u51f1\u56e0\u65af\uff08John Keynes\uff09\u66fe\u947d\u7814\u725b\u9813\u907a\u7559\u7684\u624b\u7a3f\uff0c\u5373\u8a8d\u70ba\u300c\u725b\u9813\u4e0d\u662f\u7406\u6027\u6642\u4ee3\u7684\u7b2c\u4e00\u4eba\uff1b\u4ed6\u662f\u6700\u5f8c\u4e00\u500b\u7149\u91d1\u8853\u58eb\uff08magician\uff09\u300d\u3002\u6240\u4ee5\u6211\u5011\u5343\u842c\u4e0d\u80fd\u8a8d\u70ba\u79d1\u5b78\u59cb\u7d42\u662f\u4e00\u7a2e\u7d14\u7cb9\u7684\u7406\u6027\u6d3b\u52d5\uff0c\u4e0d\u5982\u8aaa\u5b83\u6df1\u523b\u53cd\u61c9\u4e86\u79d1\u5b78\u5bb6\u7684\u610f\u8b58\u89c0\u3002<\/p>\n<p>\u3000\u3000\u6216\u8a31\u6211\u5011\u53ef\u4ee5\u8aaa\uff0c\u7531\u65bc\u79d1\u5b78\u9769\u547d\u65e9\u671f\u7684\u79d1\u5b78\u5bb6\u5011\uff0c\u5c0d\u65bc\u7cbe\u7c21\u95dc\u4fc2\u6709\u76f8\u7576\u7684\u4fe1\u4ef0\uff0c\u9019\u5b87\u5b99\u4e5f\u525b\u597d\u6709\u8fd1\u4f3c\u7c21\u55ae\u7684\uff08\u6574\u6578\u95dc\u4fc2\u7684\uff09\u6cd5\u5247\uff0c\u624d\u7372\u81f4\u7b2c\u4e00\u5834\u79d1\u5b78\u767c\u5c55\u53f2\u4e0a\u524d\u6240\u672a\u6709\u7684\u5927\u8c50\u6536\uff0c\u9918\u6ce2\u6240\u53ca\uff0c\u751a\u81f3\u958b\u555f\u4e86\u555f\u8499\u6642\u4ee3\uff0c\u5929\u771f\u5730\u4ee5\u70ba\u900f\u904e\u7d93\u9a57\u3001\u6b78\u7d0d\u7b49\u79d1\u5b78\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5b8c\u7f8e\u5730\u70ba\u5404\u7a2e\u4eba\u4e8b\u95dc\u806f\u627e\u51fa\u898f\u5f8b\u3001\u6cd5\u5247\u3002\u7136\u800c\u6211\u5011\u5fc5\u9808\u6307\u51fa\uff0c\u5929\u9ad4\u7684\u904b\u52d5\u6a5f\u5236\u5176\u5be6\u592a\u904e\u7c21\u55ae\uff0c\u4e0d\u904e\u662f\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\uff0c\u800c\u4e14\u56e0\u70ba\u7406\u8ad6\u4e0a\uff0c\u7403\u9ad4\u9593\u7684\u5f15\u529b\u53ef\u4ee5\u7b49\u6548\u5c07\u8cea\u91cf\u5168\u90e8\u96c6\u4e2d\u65bc\u7403\u5fc3\u800c\u5927\u70ba\u7c21\u8f15\u4e86\u554f\u984c\u7684\u8907\u96dc\u5ea6\uff0c\u52a0\u4e0a\u771f\u7a7a\u4e2d\u6c92\u6709\u963b\u529b\u3001\u5176\u4ed6\u661f\u7cfb\u5c0d\u65bc\u592a\u967d\u7cfb\u5f15\u529b\u5e72\u6d89\u4e0d\u8db3\u4ee5\u6df7\u6dc6\u8996\u807d\u3002<\/p>\n<figure id=\"attachment_2701\" aria-describedby=\"caption-attachment-2701\" style=\"width: 240px\" class=\"wp-caption alignright\"><img decoding=\"async\" class=\"size-full wp-image-2701 \" title=\"Neptunerings\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2010\/04\/Neptunerings1.jpg\" alt=\"Neptunerings\" width=\"240\" height=\"206\" \/><figcaption id=\"caption-attachment-2701\" class=\"wp-caption-text\">\u822a\u6d77\u5bb6\u4e8c\u865f\u62cd\u5230\u7684\u6d77\u738b\u661f\u74b0<\/figcaption><\/figure>\n<p>\u3000\u3000\u6709\u8da3\u7684\u662f\uff0c1846\u5e74\u82f1\u570b\u8207\u6cd5\u570b\u5169\u4f4d\u5929\u6587\u6578\u5b78\u5bb6\u52d2\u7dad\u8036\uff08Urbain Le Verrier\uff09\u8207\u4e9e\u6b77\u65af\u2027\u5e03\u74e6\uff08Alexis Bouvard\uff09\u5206\u5225\u7531\u5929\u738b\u661f\u7684\u651d\u52d5\u73fe\u8c61\u8a08\u7b97\u51fa\u6d77\u738b\u661f\u7684\u8ecc\u9053\u3002\u5728\u5929\u6587\u5b78\u53f2\u4e0a\uff0c\u662f\u4e00\u4ef6\u4e86\u4e0d\u5f97\u7684\u5927\u4e8b\uff0c\u540c\u6642\u4e5f\u662f\u5c11\u6578\u5929\u624d\u624d\u80fd\u5920\u6191\u8457\u7d19\u7b46\u8a08\u7b97\u5b8c\u6210\u7684\u8271\u96e3\u5275\u8209\u3002\u7576\u6642\u53c3\u8207\u5176\u4e2d\u7684\u5df4\u9ece\u5929\u6587\u53f0\u53f0\u9577Fran\u00e7ois Arago\u7a31\u300c\u5728\u7b46\u982d\u7684\u5c16\u7aef\u770b\u898b\u4e86\u9019\u9846\u884c\u661f\u300d\u4e26\u4e0d\u70ba\u904e\u3002\u7136\u800c\u7576\u4ee3\u4f5c\u8005Michael Hoskin\u5728\u8457\u540d\u7684\u300a\u528d\u6a4b\u63d2\u5716\u5929\u6587\u53f2\u300b\u610f\u5473\u6df1\u9577\u5730\u8a55\u8ad6\u9053\uff1a\u300c\u5c0d\u6d77\u738b\u661f\u7684\u767c\u73fe\u662f\u725b\u9813\u529b\u5b78\u6210\u529f\u7684\u5dd4\u5cf0\u3002\u300d\u56e0\u70ba\u7576\u6642\u7684\u5929\u6587\u5b78\u5bb6\u5c07\u767c\u73fe\u7684\u6d77\u738b\u661f\u8003\u616e\u9032\u53bb\u4e4b\u5f8c\uff0c\u91cd\u65b0\u8a08\u7b97\u6c34\u661f\u7684\u8fd1\u65e5\u9ede\uff0c\u537b\u767c\u73fe\u6bcf\u4e00\u4e16\u7d00\u6bd4\u7406\u8ad6\u7b97\u51fa\u7684\u591a\u4e8638\u5f27\u79d2\uff081\u5f27\u79d2 = 1\/3600\u5ea6\uff09\u3002\u52d2\u7dad\u8036\u53c8\u7528\u4e86\u540c\u6a23\u7684\u65b9\u6cd5\uff0c\u8a8d\u70ba\u6c34\u661f\u8ecc\u9053\u5167\u9084\u6709\u53e6\u4e00\u9846\u884c\u661f\uff0c\u9019\u6b21\u4ed6\u537b\u932f\u4e86\u3002\u76f4\u52301915\u5e74\u611b\u56e0\u65af\u5766\u767c\u8868\u4e86\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u4e4b\u5f8c\uff0c\u95e1\u660e\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u53ea\u662f\u4e00\u500b\u8fd1\u4f3c\u7684\u95dc\u4fc2\uff0c\u624d\u5b8c\u6574\u89e3\u6c7a\u4e86\u6c34\u661f\u7684\u554f\u984c\u3002<\/p>\n<p>\u3000\u3000\u5728\u6b64\uff0c\u503c\u5f97\u5927\u5bb6\u601d\u8003\u7684\u662f\uff0c\u300c\u4e0d\u591a\u4e0d\u5c11\u7684\u300d\u8aa4\u5dee\u5141\u8a31\u4e86\u725b\u9813\u4ee5\u4f86\u7684\u4eba\u6191\u8457\u6709\u9650\u7684\u6e2c\u91cf\u5de5\u5177\u5370\u8b49\u7c21\u55ae\u7684\u6578\u5b78\u95dc\u4fc2\uff0c\u7269\u7406\u79d1\u5b78\u624d\u5f97\u4ee5\u767c\u5c55\u3002<\/p>\n<p>\u3000\u3000\u5176\u5be6\uff0c\u5728\u79d1\u5b78\u767c\u5c55\u53f2\u4e0a\u8ff7\u9014\u77e5\u8fd4\u7684\u6b77\u7a0b\u5c62\u898b\u4e0d\u9bae\uff0c\u751a\u81f3\u662f\u5fc5\u7d93\u7684\u7a0b\u5e8f\u3001\u5fc5\u7136\u7684\u4e8b\u5be6\u3002\u79d1\u5b78\u53f2\u5bb6\u5b54\u6069\uff08Thomas Kuhn\uff09\u5c0d\u65bc\u79d1\u5b78\u53f2\u7684\u7814\u7a76\u5c31\u6307\u51fa\uff0c\u79d1\u5b78\u7684\u6f14\u9032\u4e0d\u662f\u65b0\u77e5\u8b58\u7684\u7dda\u6027\u7d2f\u7a4d\uff08linear accumulation\uff09\uff0c\u800c\u662f\u4e00\u5834\u4e00\u5834\u9031\u671f\u6027\u7684\u9769\u547d\uff08periodic revolutions\uff09\uff1a\u4e00\u6279\u65b0\u7684\u79d1\u5b78\u5bb6\u6253\u7834\u820a\u6709\u7684\u300c\u6cd5\u5247\u300d\uff0c\u79d1\u5b78\u7684\u5178\u7bc4\uff08paradigm\uff09\u9762\u81e8\u5371\u6a5f\uff0c\u7576\u65b0\u7684\u3001\u7570\u5e38\u7684\u8b49\u64da\u9010\u6f38\u5efa\u7acb\u51fa\u4f86\u5f8c\uff0c\u820a\u6709\u7684\u6cd5\u5247\u9023\u540c\u65b0\u7684\u7814\u7a76\uff0c\u5f62\u6210\u4e00\u500b\u66f4\u5927\u800c\u517c\u5bb9\u7684\u9ad4\u7cfb\uff08framework\uff09\uff0c\u4ed6\u7684\u79d1\u5b78\u53f2\u7814\u7a76\u6307\u51fa\u79d1\u5b78\u7684\u767c\u5c55\u4e5f\u6709\u9769\u547d\u7684\u8272\u5f69\u3002<\/p>\n<figure id=\"attachment_2705\" aria-describedby=\"caption-attachment-2705\" style=\"width: 209px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-2705 \" title=\"Gaffurio_Pythagoras(wiki)\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2010\/04\/435px-Gaffurio_Pythagoras1.png\" alt=\"Gaffurio_Pythagoras\" width=\"209\" height=\"287\" \/><figcaption id=\"caption-attachment-2705\" class=\"wp-caption-text\">\u7562\u9054\u54e5\u62c9\u65af\u7684\u97f3\u5f8b\u5be6\u9a57\uff08Pythagorean tuning\uff09\uff1a\u4ed6\u4e5f\u70ba\u6a02\u7406\u5b78\u5efa\u7acb\u57fa\u790e<\/figcaption><\/figure>\n<p>\u3000\u3000\u5373\u4fbf\u662f\u6700\u63a5\u8fd1\u7d14\u7cb9\u7406\u6027\u7684\u6578\u5b78\u4e5f\u5982\u6b64\u3002\u6839\u64da\u54f2\u5b78\u53f2\u7684\u8a18\u8f09\uff0c\u9805\u6559\u6388\u63a8\u5d07\u7684\u7562\u6c0f\u5b78\u6d3e\u5c31\u5e36\u6709\u795e\u79d8\u4e3b\u7fa9\u7684\u601d\u60f3\u8272\u5f69\u3002\u7562\u6c0f\u5b78\u6d3e\u5373\u4ee5\u6578\u5b571\u70ba\u7406\u6027\u30012\u70ba\u4fd7\u898b\u30015\u70ba\u7d50\u5a5a\u30016\u70ba\u9748\u9b42\uff0c\u8db3\u4ee5\u898b\u5f97\u4ed6\u5011\u7684\u6578\u5b78\u6210\u5c31\u540c\u6642\u53cd\u6620\u4ed6\u5011\u7684\u5b97\u6559\u89c0\u3002\u5f9e\u524d\u7684\u54f2\u5b78\u5bb6\u53ef\u8b02\u540d\u526f\u5176\u5be6\u7684\u611b\u667a\u8005\uff08Philosophy\uff09\uff0c\u76f4\u5230\u725b\u9813\u90fd\u9084\u6709\u9019\u6a23\u7684\u50be\u5411\u3002\u4ed6\u5011\u7121\u6240\u4e0d\u7a76\uff0c\u4ef0\u89c0\u5929\u6587\u4fef\u5bdf\u5730\u7406\u3001\u731c\u5ea6\u5b87\u5b99\u7684\u8d77\u6e90\u4ee5\u53ca\u7269\u8cea\u7684\u7d44\u6210\u90fd\u662f\u4ed6\u5011\u7684\u8208\u8da3\u3002<\/p>\n<p>\u3000\u3000\u56de\u904e\u982d\u4f86\uff0c\u559c\u6b61\u6578\u5b78\u7684\u4eba\u6216\u8a31\u4ecd\u5805\u7a31\u6578\u5f0f\u4e4b\u9593\u56b4\u8b39\u7684\u63a8\u7406\uff0c\u4e43\u662f\u6700\u63a5\u8fd1\u7d14\u7cb9\u7406\u6027\u7684\u5b78\u79d1\uff0c\u56e0\u70ba\u5b83\u53ea\u6191\u85c9\u8457\u4e00\u4e9b\u516c\u8a2d\uff08axioms\uff09\uff0c\u5373\u53ef\u6d69\u6d69\u8569\u8569\u5c55\u958b\u69cb\u601d\u56b4\u5bc6\u4e14\u851a\u7136\u53ef\u89c0\u7684\u7248\u5716\u3002\u7136\u800c\uff0c\u9019\u4e9b\u516c\u8a2d\u76f8\u7576\u76f4\u89c0\uff0c\u6578\u5b78\u767c\u5c55\u53f2\u4e0a\u65e9\u671f\u7684\u6839\u57fa\u53ef\u8b02\u7531\u7d93\u9a57\u3001\u5b87\u5b99\u89c0\u751a\u81f3\u5b97\u6559\u89c0\u800c\u4f86\u3002\u73fe\u4eca\u5927\u591a\u5b78\u7fd2\u6578\u5b78\u7684\u4eba\uff08\u9664\u4e86\u6578\u5b78\u7cfb\u5b78\u751f\u4ee5\u5916\uff09\u5247\u5df2\u7d93\u751a\u5c11\u947d\u7814\u516c\u8a2d\u7684\u6b63\u78ba\u6027\uff0c\u6216\u662f\u5404\u7a2e\u76f4\u89c0\u7684\u884d\u751f\u5b9a\u7406\u5982\u4f55\u7531\u516c\u8a2d\u4e00\u6b65\u4e00\u6b65\u63a8\u5c0e\u2014\u2014\u9019\u662f\u4e00\u500b\u4e00\u822c\u4eba\u671b\u4e4b\u537b\u6b65\u7684\u7169\u5197\u9a57\u8b49\u5de5\u4f5c\u3002\u6578\u5b78\u5c31\u5982\u4eba\u6587\u5b78\u3001\u793e\u6703\u79d1\u5b78\uff0c\u4e5f\u9003\u4e0d\u904e\u7a4d\u7d2f\u6027\u5b78\u79d1\u7684\u7bc4\u7587\uff0c\u5fc5\u6709\u90e8\u4efd\u56e0\u8972\u524d\u4eba\u7684\u6210\u679c\u800c\u4e0d\u518d\u8a73\u52a0\u6aa2\u9a57\u3002\u6240\u4ee5\u8207\u5176\u8aaa\u5927\u591a\u6578\u64c5\u9577\u6578\u5b78\u7684\u4eba\uff0c\u5c0d\u65bc\u6578\u5b78\u7684\u654f\u92b3\u5ea6\u4e43\u662f\u4e00\u7a2e\u7406\u6027\u7684\u6d1e\u898b\uff0c\u4e0d\u5982\u8aaa\u53ea\u662f\u4ef0\u4ed7\u57fa\u672c\u7684\u76f4\u89c0\u8207\u8868\u8c61\u7684\u7d93\u9a57\u800c\u5df2\u3002<\/p>\n<p>\u3000\u3000\u6240\u4ee5\u79d1\u5b78\u9769\u547d\u6642\u671f\u7684\u79d1\u5b78\u5bb6\u904e\u65bc\u5929\u771f\uff1b\u4ee5\u70ba\u77ad\u89e3\u6578\u5b78\u5373\u662f\u63a5\u8fd1\u771f\u7406\u7684\u4eba\uff0c\u537b\u53ef\u80fd\u8207\u771f\u7406\u5931\u4e4b\u4ea4\u81c2\u3002\u5728\u9019\u500b\u79d1\u6280\u3001\u79d1\u5b78\u6210\u679c\u5df2\u6d0b\u6d0b\u53ef\u89c0\u7684\u6642\u4ee3\u4e2d\uff0c\u79d1\u5b78\u5bb6\u8207\u6578\u5b78\u5bb6\u5343\u842c\u4e0d\u80fd\u6cbe\u6cbe\u81ea\u559c\u3002\u5c0d\u65bc\u771f\u7406\u662f\u4ec0\u9ebc\u3001\u9084\u6709\u8ab0\u80fd\u57f7\u8d77\u6469\u897f\u7684\u6756\uff08Moses' rod\uff09\u5f15\u9818\u4eba\u985e\u5b89\u7136\u5ea6\u904e21\u4e16\u7d00\u3002\u9805\u6559\u6388\u5e36\u9818\u6211\u5011\u91cd\u8a2a\u7684\u6b77\u53f2\u544a\u8a34\u6211\u5011\uff0c\u61c9\u62b1\u6301\u8b19\u5351\u3001\u8aa0\u656c\u7684\u5fc3\u9762\u5c0d\u6240\u6709\u672a\u77e5\u7684\u4e00\u5207\u3002<\/p>\n<p>\u3000\u3000\u6839\u64da\u53ef\u4fe1\u7684\u8cc7\u6599\uff0c\u9805\u6b66\u7fa9\u6559\u63881992\u30011993\u5e74\u63d0\u51fa\u523b\u535c\u52d2\u731c\u60f3\u7684\u8b49\u660e\uff0c\u57281994\u5e74\u5c31\u88ab\u99c1\u65a5\uff0c\u8457\u540d\u7684\u6578\u5b78\u767e\u79d1\u5168\u66f8MathWorld\u5f15\u7528J. H. Conway\u8aaa\u9019\u500b\u8b49\u660e\u7684\u6709\u6548\u6027\uff1a\u201c it is nonsense.\u201d\uff0c\u751a\u81f3\u4e00\u4e9b\u6587\u737b\u4e0a\u6709\u8ca0\u9762\u7684\u8a55\u8ff0[\u8a3b4]\u3002\u7136\u800c\u653e\u5728\u6574\u500b\u6578\u5b78\u3001\u79d1\u5b78\u767c\u5c55\u8108\u7d61\u4f86\u770b\uff0c\u6311\u6230\u5931\u6557\u7684\u4eba\u592a\u591a\u4e86[5]\u3002\u9805\u6559\u6388\u5728\u6f14\u8b1b\u4e2d\u63d0\u5230\u81ea\u5df1\u4ecd\u5728\u8457\u624b\u7ffb\u4fee\u9019\u500b\u8b49\u660e\uff0c\u4e14\u8b93\u6211\u5011\u62ed\u76ee\u4ee5\u5f85\uff01<\/p>\n<p>?<\/p>\n<hr size=\"1\" \/>[\u8a3b1] Johannes Kepler\u65bc1611\u5e74\u63d0\u51fa\u5982\u679c\u8981\u5728\u4e09\u7dad\u7a7a\u9593\u4e2d\u5806\u7a4d\u5927\u5c0f\u76f8\u540c\u7684\u7403\u9ad4\uff0c\u6700\u7bc0\u7701\u7a7a\u9593\u65b9\u6cd5\u662f\u5e02\u5834\u5c0f\u8ca9\u5806\u758a\u6a58\u5b50\u6216\u756a\u8304\u7684\u65b9\u5f0f\uff0c\u5982\u6587\u7ae0\u4e00\u958b\u59cb\u7684\u5716\u4e00\u3002\u9019\u6a23\u7684\u65b9\u6cd5\u53c8\u7a31\u70ba\u9762\u5fc3\u5806\u7a4d\uff0c\u7b49\u6548\u4e0a\u5982\u4e0b\u5716\u4e4b\u7acb\u65b9\u9ad4\u3002<\/p>\n<p><a href=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2010\/04\/399px-Lattice_face_centered_cubic.svg1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-2699 alignleft\" title=\"Lattice_face_centered_cubic\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2010\/04\/399px-Lattice_face_centered_cubic.svg1.png\" alt=\"Lattice_face_centered_cubic\" width=\"114\" height=\"102\" \/><\/a><\/p>\n<p>\u3000\u3000\u5de6\u5716\u6240\u793a\u70ba\u4e00\u500b\u7acb\u65b9\u9ad4\uff0c\u5728\u5316\u5b78\u7a31\u70ba\u300c\u6676\u683c\u300d\uff08lattice\uff09\u3002\u6bcf\u500b\u9ede\u90fd\u662f\u4e00\u500b\u7403\u7684\u7403\u5fc3\uff0c\u7acb\u65b9\u9ad4\u76846\u500b\u9762\u9084\u67098\u500b\u9802\u9ede\u7686\u5404\u81ea\u6709\u4e00\u500b\u3002\u6bcf\u500b\u9762\u4e0a\u7684\u9ede\u6240\u4ee3\u8868\u7684\u7403\u6709\u4e00\u534a\u7684\u9ad4\u7a4d\u843d\u5728\u7acb\u65b9\u9ad4\u5167\uff0c\u9802\u9ede\u6240\u4ee3\u8868\u7684\u7403\u5247\u67091\/8\u843d\u5728\u7acb\u65b9\u9ad4\u5167\u3002\u56e0\u6b64\u7b49\u6548\u4e0a\u7acb\u65b9\u9ad4\u5167\u5171\u6709<sup>1<\/sup>?<sub>8<\/sub>?\u00d7?8+<sup>1<\/sup>?<sub>2<\/sub>?\u00d7?6 = 4\u500b\u7403\u3002\u9032\u4e00\u6b65\u7684\u6578\u5b78\u8a08\u7b97\u53ef\u4ee5\u8aaa\u660e\u7403\u7684\u9ad4\u7a4d\uff084\u9846\u7403\uff09\u7d04\u4f54\u4e86\u6574\u9ad4\u7a7a\u9593\uff08\u4e00\u500b\u6676\u683c\uff09\u768474\uff05\u3002<\/p>\n<p>[\u8a3b2] \u5176\u4ee3\u8868\u4eba\u5c31\u662f\u8457\u540d\u7684\u7562\u9054\u54e5\u62c9\u65af\uff08Pythagoras\uff09\uff0c\u50b3\u8aaa\u4e2d\u4ed6\u767c\u73fe\u7562\u6c0f\u5b9a\u7406\uff0c\u7136\u800c\u5728\u6578\u5b78\u53f2\u3001\u54f2\u5b78\u53f2\u4e0a\u4e26\u6c92\u6709\u8db3\u5920\u7684\u8cc7\u6599\u53ef\u4ee5\u8b49\u660e\u3002\u56e0\u6b64\u672c\u6587\u4ee5\u7562\u9054\u54e5\u62c9\u65af\u5b78\u6d3e\u7a31\u547c\u3002<\/p>\n<p>[\u8a3b3] \u53c3\u52a0\u6f14\u8b1b\u7684\u807d\u773e\u6709\u4e00\u4e9b\u9ad8\u4e2d\u751f\uff0c\u76f8\u4fe1\u9019\u4e9b\u670b\u53cb\u5011\u5728\u300c\u6578\u8207\u5750\u6a19\u7cfb\u300d\u7684\u55ae\u5143\u4e2d\u6709\u5b78\u5230\uff0c\u221a2\u5c31\u7121\u6cd5\u5316\u70ba\u7c21\u55ae\u6574\u6578\u6bd4\u3002\u9805\u6559\u6388\u5728\u6f14\u8b1b\u4e2d\uff0c\u5247\u8209\u4e86\u53e6\u4e00\u500b\u4f8b\u5b50\u3002<\/p>\n<p>[\u8a3b4] \u53c3\u898bMathWorld\u4e2d\u95dc\u65bcKepler Conjecture\u7684\u689d\u76ee\u3002\u8ca0\u9762\u8a55\u8ff0\u7684\u4f8b\u5b50\u8acb\u898b\u300a\u523b\u535c\u52d2\u7684\u731c\u60f3\u300b\uff0c\u5929\u4e0b\u6587\u5316\u51fa\u7248<\/p>\n<p>[\u8a3b5] \u57281998\u5e74Thomas Hales\u4ee5\u7aae\u8209\u6cd5\uff08Proof by exhaustion\uff09\u914d\u5408\u73fe\u4ee3\u96fb\u8166\u8655\u7406\u4e865000\u7a2e\u53ef\u80fd\u7684\u60c5\u5f62\u3002\u4f46\u53f0\u5927\u6578\u5b78\u7cfb\u5f35\u6d77\u6f6e\u6559\u6388\u9762\u5c0d\u9805\u6559\u6388\u7684\u6279\u8a55\u8005\uff0c\u66fe\u53cd\u99c1Hales\u7684\u65b9\u6cd5\u592a\u904e\u8907\u96dc\uff0c\u5728\u4ea4\u7d66\u96fb\u8166\u7684\u540c\u6642\uff0c\u5df2\u7d93\u963b\u7d55\u4e86\u4e00\u822c\u6578\u5b78\u5bb6\u5c0d\u9019\u554f\u984c\u7684\u4e86\u89e3\u3002\uff08\u300a\u79d1\u5b78\u4eba\u96dc\u8a8c\u300b\u66f8\u8a55\u3008\u6578\u5b78\u63a5\u529b\u8cfd\u3009\uff0c2005\u5e7411\u6708\u865f\uff09<\/p>\n<p>?<\/p>\n<p><strong><span style=\"color: #003366;\">\u8cac\u4efb\u7de8\u8f2f\uff1aMissZoe<\/span><\/strong><br \/>\n<a type=\"box_count\" name=\"fb_share\" href=\"http:\/\/www.facebook.com\/sharer.php\">\u5206\u4eab\u5230facebook <\/a><br \/>\n<script src=\"http:\/\/static.ak.fbcdn.net\/connect.php\/js\/FB.Share\" type=\"text\/javascript\"><\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0 \u4eba\u985e\u4e08\u91cf\u5929\u7a7a\u7684\u5927\u5922\u5982\u4f55\u8207\u6578\u5b78\u548c\u6587\u660e\u6709<\/p>\n","protected":false},"author":20,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,148,22],"tags":[80,47,2251,277,81],"aioseo_notices":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/2692"}],"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=2692"}],"version-history":[{"count":5,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/2692\/revisions"}],"predecessor-version":[{"id":2982,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/2692\/revisions\/2982"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2692"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2692"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2692"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}