{"id":17377,"date":"2014-04-25T06:09:18","date_gmt":"2014-04-24T22:09:18","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=17377"},"modified":"2017-03-31T23:19:31","modified_gmt":"2017-03-31T15:19:31","slug":"%e3%80%90%e6%95%b8%e5%8f%b2%e5%9b%9e%e9%a1%a7%e3%80%91%e6%94%b9%e8%ae%8a%e6%ad%b7%e5%8f%b2%e9%80%b2%e7%a8%8b%e7%9a%8417%e5%80%8b%e6%96%b9%e7%a8%8b%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=17377","title":{"rendered":"\u3010\u6578\u53f2\u56de\u9867\u3011\u6539\u8b8a\u6b77\u53f2\u9032\u7a0b\u768417\u500b\u65b9\u7a0b\u5f0f"},"content":{"rendered":"<p><span style=\"color: #333399;\"><strong>\u25a0\u6578\u5b78\u570d\u7e5e\u5728\u6211\u5011\u56db\u5468\uff0c\u5b83\u5728\u8a31\u591a\u65b9\u9762\u578b\u5851(shaped)\u6211\u5011\u5c0d\u9019\u500b\u4e16\u754c\u7684\u7406\u89e3\u3002<\/strong><\/span><\/p>\n<p style=\"text-align: left;\"><strong><a href=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/395.png\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-17396\" style=\"border: 0px;\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/395.png\" alt=\"395\" width=\"600\" height=\"415\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/395.png 600w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/395-300x207.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/a>\u4f5c\u8005\uff5c<\/strong>ANDY KIERSZ<br \/>\n<strong>\u7de8\u8b6f\uff5c<\/strong>\u8607\u4fca\u9d3b<\/p>\n<p>\u3000\u30002013\u5e74\uff0c\u8eab\u70ba\u6578\u5b78\u5bb6\uff0c\u4e5f\u662f\u79d1\u666e\u4f5c\u8005\u7684\u4f0a\u6069\uff0e\u53f2\u90fd\u83ef(Ian Stewart)\u51fa\u7248\u4e86\u300a\u6539\u8b8a\u4e16\u754c\u768417\u500b\u65b9\u7a0b\u5f0f\u300b(The 17 Equations that Changed the World)\u4e00\u66f8\u3002\u8fd1\u4f86\uff0c\u6211\u5011\u5728Dr. Paul Coxon\u7684Twitter (\u7531\u6578\u5b78\u8f14\u5c0e\u8001\u5e2b\uff0c\u4e5f\u662f\u90e8\u843d\u5ba2\u7684Larry Phillips\u6240\u8a3b\u518a)\u4e0a\u767c\u73fe\u9019\u500b\u4ed6\u6458\u9304\u66f8\u4e2d\u65b9\u7a0b\u5f0f\u6240\u6210\u7684\u7c21\u4fbf\u8868\u683c\uff1a<!--more--><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/01.png\"><img decoding=\"async\" class=\"aligncenter wp-image-17384\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/01.png\" alt=\"01\" width=\"675\" height=\"905\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/01.png 750w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/01-223x300.png 223w\" sizes=\"(max-width: 675px) 100vw, 675px\" \/><\/a><\/p>\n<p style=\"text-align: center;\">\u00a0* \u8b6f\u8005\u6309\uff1a\u539f\u6587\u8868\u4e2d\u6709\u8aa4\uff0c\u5747\u5df2\u66f4\u6b63\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u5c0d\u65bc\u9019\u4e9b\u5851\u9020\u6578\u5b78\u53ca\u4eba\u985e\u6b77\u53f2\u7684\u7f8e\u5999\u65b9\u7a0b\u5f0f\uff0c\u4e0b\u9762\u6709\u66f4\u591a\u7684\u4ecb\u7d39\uff1a<br \/>\n<a href=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m1.jpg\"><img decoding=\"async\" class=\"alignright wp-image-17385\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m1.jpg\" alt=\"m1\" width=\"320\" height=\"240\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m1.jpg 400w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m1-300x225.jpg 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/a><br \/>\n1) \u7562\u6c0f\u5b9a\u7406\uff1a\u9019\u500b\u5b9a\u7406\u662f\u6211\u5011\u7406\u89e3\u5e7e\u4f55\u7684\u57fa\u790e\u3002\u5b83\u63cf\u8ff0\u5e73\u9762\u4e0a\u4e00\u500b\u76f4\u89d2\u4e09\u89d2\u5f62\u4e09\u908a\u4e4b\u9593\u7684\u95dc\u4fc2\uff1a\u5169\u500b\u77ed\u908a(a\u548cb)\u5e73\u65b9\u76f8\u52a0\uff0c\u53ef\u4ee5\u5f97\u5230\u9577\u908a(c)\u7684\u5e73\u65b9\u3002<br \/>\n\u5728\u67d0\u4e9b\u65b9\u9762\uff0c\u9019\u500b\u95dc\u4fc2\u78ba\u5be6\u5c07\u6211\u5011\u719f\u77e5\u7684\u5e73\u9762\u6b50\u6c0f\u5e7e\u4f55\u548c\u66f2\u9762\u7684\u975e\u6b50\u5e7e\u4f55\u5206\u958b\u4f86\u3002\u4f8b\u5982\uff0c\u756b\u5728\u7403\u9762\u4e0a\u7684\u76f4\u89d2\u4e09\u89d2\u5f62\u5c31\u4e0d\u7528\u9075\u5b88\u7562\u6c0f\u5b9a\u7406\u3002<\/p>\n<p>2) \u5c0d\u6578\uff1a\u5c0d\u6578(\u51fd\u6578)\u662f\u6307\u6578\u51fd\u6578\u7684\u53cd\u51fd\u6578\u3002\u4e00\u500b\u7279\u5b9a\u5e95\u6578\u7684\u5c0d\u6578\uff0c\u544a\u8a34\u4f60\u7528\u9019\u500b\u5e95\u6578\u4f86\u8868\u793a\u9019\u500b\u6578\u6240\u9700\u8981\u7684\u6307\u6578(power)\u3002\u8b6c\u598210\u00b0=1\uff0c\uff0c\u6240\u4ee5\u5e95\u6578\u70ba10\u76841\u4e4b\u5c0d\u6578log1=0\uff1b10\u00b9=10\uff0c\u6240\u4ee5log10=1\uff1b10\u00b2=100\uff0c\u6240\u4ee5log100=2\u3002<\/p>\n<p>\u65b9\u7a0b\u5f0flogab=loga+logb\uff0c\u5c55\u793a\u5c0d\u6578\u6700\u6709\u7528\u7684\u61c9\u7528\uff1a\u5c07\u4e58\u6cd5\u8b8a\u6210\u52a0\u6cd5\u3002<br \/>\n\u4e00\u76f4\u5230\u8a08\u7b97\u6a5f\u767c\u5c55\u4e4b\u524d\uff0c\u9019\u662f\u5feb\u901f\u9032\u884c\u5927\u6578\u5b57\u76f8\u4e58\u6700\u5e38\u7528\u7684\u65b9\u6cd5\uff0c\u5927\u5927\u5730\u52a0\u5feb\u5728\u7269\u7406\u3001\u5929\u6587\uff0c\u4ee5\u53ca\u5de5\u7a0b\u4e0a\u7684\u8a08\u7b97\u3002<\/p>\n<p>3) \u5fae\u7a4d\u5206\uff1a\u9019\u88cf\u7d66\u7684\u516c\u5f0f\u662f\u5fae\u7a4d\u5206\u4e0a\u5c0e\u6578\u7684\u5b9a\u7fa9\uff0c\u5c0e\u6578\u662f\u8861\u91cf\u5169\u500b\u91cf\u4e4b\u9593\u8b8a\u5316\u95dc\u4fc2\u7684\u6bd4\u7387\u3002\u6bd4\u65b9\u8aaa\uff0c\u6211\u5011\u8003\u616e\u901f\u5ea6\uff0c\u9019\u662f\u4f4d\u7f6e\u5c0d\u6642\u9593\u7684\u5c0e\u6578 \u2500 \u5047\u5982\u4f60\u6bcf\u5c0f\u6642\u75283\u82f1\u91cc\u7684\u901f\u5ea6\u884c\u8d70\uff0c\u8868\u793a\u4f60\u4ee5\u6bcf\u500b\u5c0f\u66423\u82f1\u91cc\u6539\u8b8a\u4f60\u7684\u4f4d\u7f6e\u3002<br \/>\n\u4e00\u822c\u800c\u8a00\uff0c\u591a\u6578\u79d1\u5b78\u5bb6\u6709\u8208\u8da3\u7684\u662f\u77ad\u89e3\u4e8b\u7269\u5982\u4f55\u6539\u8b8a\uff0c\u5c0e\u6578\u548c\u7a4d\u5206 \u2500 \u5fae\u7a4d\u5206\u53e6\u4e00\u500b\u57fa\u790e \u2500 \u6b63\u662f\u6578\u5b78\u5bb6\u8207\u79d1\u5b78\u5bb6\u7406\u89e3\u8b8a\u5316\u7684\u95dc\u9375\u3002<\/p>\n<p>4) \u842c\u6709\u5f15\u529b\u5b9a\u5f8b\uff1a\u725b\u9813\u7684\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u63cf\u8ff0\u5169\u500b\u7269\u9ad4\u9593\u7684\u5438\u5f15\u529bF\uff0c\u7531\u5e38\u6578G\u3001\u5169\u7269\u9ad4\u7684\u8cea\u91cfm1\u548cm2\uff0c\u4ee5\u53ca\u5169\u7269\u9ad4\u4e4b\u9593\u7684\u8ddd\u96e2r\u800c\u6c7a\u5b9a\u3002\u725b\u9813\u7684\u5b9a\u5f8b\u662f\u79d1\u5b78\u53f2\u975e\u5e38\u51fa\u8272\u7684\u90e8\u4efd \u2500 \u5b83\u5e7e\u4e4e\u5b8c\u7f8e\u5730\u89e3\u91cb\u884c\u661f\u70ba\u4f55\u4f9d\u7167\u4ed6\u5011\u6240\u9075\u5faa\u7684\u65b9\u5f0f\u79fb\u52d5\u3002\u540c\u6a23\u51fa\u8272\u7684\u662f\u5b83\u7684\u666e\u904d\u6027 \u2500 \u4e0d\u53ea\u662f\u9069\u7528\u65bc\u5730\u7403\u4e0a\u7684\u91cd\u529b\u5982\u4f55\u4f5c\u7528\uff0c\u6216\u662f\u5728\u6211\u5011\u7684\u592a\u967d\u7cfb\uff0c\u4e5f\u5305\u62ec\u5b87\u5b99\u7684\u4efb\u4f55\u89d2\u843d\u3002<\/p>\n<p>\u725b\u9813\u7684\u5f15\u529b\u6709\u6548\u7dad\u6301\u4e86200\u5e74\uff0c\u76f4\u5230\u88ab\u611b\u56e0\u65af\u5766\u7684\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u53d6\u4ee3\u70ba\u6b62\u3002<\/p>\n<p>5) -1 \u7684\u5e73\u65b9\u6839\uff1a\u6578\u5b78\u5bb6\u7e3d\u662f\u5728\u64f4\u5c55\u6578\u5b57\u5230\u5e95\u662f\u4ec0\u9ebc\u7684\u6982\u5ff5\uff0c\u5f9e\u81ea\u7136\u6578\uff0c\u5230\u8ca0\u6578\u3001\u5206\u6578\u3001\u548c\u5be6\u6578\u3002-1\u7684\u5e73\u65b9\u6839(\u7d93\u5e38\u88ab\u5beb\u4f5ci)\uff0c\u5b8c\u6210\u9019\u500b\u904e\u7a0b\uff0c\u4e26\u4e14\u5f15\u51fa\u8907\u6578\u3002<br \/>\n\u5728\u6578\u5b78\u4e0a\uff0c\u8907\u6578\u662f\u975e\u5e38\u512a\u96c5\u7684\u3002\u4ee3\u6578\u80fd\u5b8c\u7f8e\u4f9d\u5faa\u6211\u5011\u6240\u8981\u7684\u65b9\u5f0f\u904b\u4f5c \u2500 \u4efb\u4f55\u65b9\u7a0b\u5f0f\u90fd\u6709\u8907\u6578\u89e3\uff0c\u4e0d\u4e00\u5b9a\u6709\u5be6\u6578\u89e3\uff1a\u50cfx\u00b2+4=0\u6c92\u6709\u5be6\u6578\u89e3\uff0c\u4f46\u5b83\u6709\u5169\u500b\u8907\u6578\u7684\u89e3\uff1a\u00b12i\u3002\u5fae\u7a4d\u5206\u53ef\u4ee5\u64f4\u5c55\u5230\u8907\u6578\uff0c\u7d93\u7531\u9019\u9ebc\u505a\uff0c\u6211\u5011\u767c\u73fe\u9019\u4e9b\u6578\u5b57\u4e00\u4e9b\u9a5a\u4eba\u7684\u5c0d\u7a31\u6027\u548c\u6027\u8cea\uff0c\u9019\u4e9b\u6027\u8cea\u4f7f\u5f97\u8907\u6578\u5728\u96fb\u8def\u548c\u4fe1\u865f\u8655\u7406\u4e0a\u8b8a\u5f97\u4e0d\u53ef\u6216\u7f3a\u3002<\/p>\n<p>6) \u6b50\u62c9\u7684\u591a\u9762\u9ad4\u516c\u5f0f\uff1a<\/p>\n<p>\u591a\u9762\u9ad4\u662f\u591a\u908a\u5f62\u4e09\u7dad\u7684\u7248\u672c\uff0c\u50cf\u7acb\u65b9\u9ad4\u5c31\u662f\u5176\u4e2d\u4e00\u500b\u4f8b\u5b50\u3002\u591a\u9762\u9ad4\u7684\u89d2\u843d\u5c31\u7a31\u70ba\u9802\u9ede\uff0c\u9023\u63a5\u9802\u9ede\u7684\u7dda\u6bb5\u7a31\u70ba\u908a\uff0c\u8986\u84cb\u5b83\u7684\u591a\u908a\u5f62\u5c31\u7a31\u70ba\u9762\u3002<br \/>\n\u4e00\u500b\u7acb\u65b9\u9ad4\u67098\u500b\u9802\u9ede\uff0c12\u689d\u908a\uff0c\u548c6\u500b\u9762\u3002\u5018\u82e5\u5c07\u9802\u9ede\u6578\u548c\u9762\u6578\u52a0\u8d77\u4f86\uff0c\u518d\u6e1b\u53bb\u908a\u6578\uff0c\u5f97\u52308+6-12=2\u3002<br \/>\n\u6b50\u62c9\u7684\u516c\u5f0f\u6307\u51fa\uff0c\u53ea\u8981\u4f60\u7684\u591a\u9762\u9ad4\u662f\u826f\u614b\u7684(well behaved)\uff0c\u5c07\u9802\u9ede\u6578\u548c\u9762\u6578\u76f8\u52a0\uff0c\u518d\u6e1b\u53bb\u908a\u6578\uff0c\u4f60\u7e3d\u6703\u5f97\u52302\u3002\u7121\u8ad6\u4f60\u7684\u591a\u9762\u9ad4\u67094\u30018\u300112\u300120\u6216\u662f\u4efb\u610f\u9762\u6578\uff0c\u90fd\u5c07\u70ba\u771f\u3002<br \/>\n\u6b50\u62c9\u7684\u767c\u73fe\u662f\u73fe\u5728\u88ab\u7a31\u70ba\u62d3\u6a38\u4e0d\u8b8a\u91cf\u7684\u6700\u521d\u4f8b\u5b50\u4e4b\u4e00 \u2500 \u540c\u985e\u5f62\u72c0\u6240\u5171\u4eab\u7684\u67d0\u4e9b\u6578\u5b57\u548c\u6027\u8cea\u5f7c\u6b64\u90fd\u76f8\u4f3c\u3002\u826f\u614b\u7684\u591a\u9762\u9ad4\u90fd\u6709V+F-1=2\u3002\u9019\u500b\u767c\u73fe\uff0c\u9023\u540c\u6b50\u62c9\u54e5\u5c3c\u65af\u5821\u4e03\u6a4b\u554f\u984c(the Bridges of Konigsburg Problem)\u7684\u89e3\u6cd5\uff0c\u4e00\u8d77\u70ba\u73fe\u4ee3\u7269\u7406\u5b78\u4e0d\u53ef\u6216\u7f3a\u7684\u6578\u5b78\u5206\u652f\u62d3\u6a38\u5b78\u7684\u767c\u5c55\u92ea\u597d\u9053\u8def\u3002<\/p>\n<p>7) \u5e38\u614b\u5206\u5e03\uff1a\u6709\u8457\u719f\u77e5\u9418\u5f62\u66f2\u7dda\u5716\u5f62\u7684\u5e38\u614b\u6a5f\u7387\u5206\u5e03\uff0c\u5728\u7d71\u8a08\u5b78\u4e2d\u7121\u8655\u4e0d\u5728\u3002<\/p>\n<p>\u7269\u7406\u3001\u751f\u7269\u4ee5\u53ca\u793e\u6703\u79d1\u5b78\u4e0a\u7d93\u5e38\u904b\u7528\u5e38\u614b\u5206\u5e03\u4f86\u6a21\u5f0f\u5316\u5404\u7a2e\u6027\u8cea\uff0c\u539f\u56e0\u4e4b\u4e00\u662f\u5e38\u614b\u66f2\u7dda\u53ef\u4ee5\u7528\u4f86\u63cf\u8ff0\u5927\u91cf\u7368\u7acb\u904e\u7a0b(independent processes)\u7684\u884c\u70ba\u3002<\/p>\n<figure id=\"attachment_17392\" aria-describedby=\"caption-attachment-17392\" style=\"width: 400px\" class=\"wp-caption aligncenter\"><a style=\"text-align: -webkit-center;\" href=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m4.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-17392\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m4.jpg\" alt=\"m4\" width=\"400\" height=\"300\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m4.jpg 400w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m4-300x225.jpg 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/a><figcaption id=\"caption-attachment-17392\" class=\"wp-caption-text\">\u5e38\u614b\u5206\u4f48<\/figcaption><\/figure>\n<p style=\"text-align: -webkit-center;\"><span style=\"color: #0000ee;\"><span style=\"text-decoration: underline;\">\u00a0<\/span><\/span><\/p>\n<p>8) \u6ce2\u52d5\u65b9\u7a0b\u5f0f\uff1a\u9019\u662f\u4e00\u500b\u5fae\u5206\u65b9\u7a0b\uff0c\u898f\u7bc4\u6ce2\u51fd\u6578\u5c0d\u6642\u9593\u8207\u7a7a\u9593\u8b8a\u6578\u7684\u4e8c\u6b21\u5fae\u5206\u7684\u65b9\u7a0b\u5f0f\uff0c\u5176\u4e2d\u00a0<i>C\u00a0<\/i>\u4ee3\u8868\u6ce2\u7684\u50b3\u905e\u901f\u7387\u3002\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u53ef\u63cf\u8ff0\u6ce2\u7684\u884c\u70ba \u5982\u632f\u52d5\u7684\u5409\u4ed6\u5f26\uff0c\u77f3\u584a\u4e1f\u51fa\u5f8c\u6c60\u5858\u7522\u751f\u7684\u6f23\u6f2a\uff0c\u767d\u71be\u71c8\u6ce1\u7522\u751f\u7684\u5149\u7b49\u3002\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u96d6\u7136\u53ea\u662f\u4e00\u500b\u5fae\u5206\u65b9\u7a0b\u5f0f\uff0c\u89e3\u6c7a\u9019\u500b\u65b9\u7a0b\u6240\u767c\u5c55\u51fa\u7684\u6280\u5de7\u958b\u555f\u4e86\u7406\u89e3\u5176\u4ed6\u5fae\u5206\u65b9\u7a0b\u7684\u5927\u9580\u3002<\/p>\n<p>9) \u5085\u7acb\u8449\u8b8a\u63db\uff1a\u60f3\u8981\u7406\u89e3\u8907\u96dc\u7684\u6ce2\u52d5\u7d50\u69cb\uff0c\u50cf\u662f\u4eba\u7684\u8aaa\u8a71\uff0c\u5085\u7acb\u8449\u8b8a\u63db\u662f\u4e0d\u53ef\u7f3a\u5c11\u7684\u3002\u7d66\u5b9a\u4e00\u500b\u8907\u96dc\u3001\u51cc\u4e82\u7684\u6ce2\u52d5\u7d50\u69cb\uff0c\u4f8b\u5982\u4eba\u7684\u8ac7\u8a71\u9304\u97f3\uff0c\u5085\u7acb\u8449\u8b8a\u63db\u5141\u8a31\u6211\u5011\u5c07\u9019\u51cc\u4e82\u7684\u7d50\u69cb\u5206\u89e3\u6210\u4e00\u4e9b\u7c21\u55ae\u6ce2\u7684\u5408\u6210\uff0c\u5927\u5927\u5730\u7c21\u5316\u5206\u6790\u7684\u5de5\u4f5c\u3002<br \/>\n\u5085\u7acb\u8449\u8b8a\u63db\u662f\u73fe\u4ee3\u4fe1\u865f\u8655\u7406\u548c\u5206\u6790\uff0c\u4ee5\u53ca\u6578\u64da\u58d3\u7e2e\u7684\u6838\u5fc3\u3002<\/p>\n<p>10) \u7d0d\u7dad-\u65af\u6258\u514b\u65af\u65b9\u7a0b\u5f0f\uff1a\u548c\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u76f8\u540c\uff0c\u9019\u4e5f\u662f\u4e00\u500b\u5fae\u5206\u65b9\u7a0b\u3002\u7d0d\u7dad-\u65af\u6258\u514b\u65af\u65b9\u7a0b\u5f0f\u63cf\u8ff0\u6d41\u9ad4\u7684\u884c\u70ba \u2500 \u6c34\u5728\u7ba1\u9053\u7684\u6d41\u52d5\uff0c\u7a7a\u6c23\u6d41\u904e\u6a5f\u7ffc\uff0c\u6216\u662f\u7159\u5f9e\u9ede\u71c3\u7684\u9999\u7159\u4e0a\u5347\u8d77\u3002\u5118\u7ba1\u5229\u7528\u96fb\u8166\u6a21\u64ec\u6d41\u9ad4\u904b\u52d5\uff0c\u6211\u5011\u53ef\u4ee5\u5f97\u5230\u7d0d\u7dad-\u65af\u6258\u514b\u65af\u65b9\u7a0b\u5f0f\u6975\u4f73\u7684\u8fd1\u4f3c\u89e3\uff0c\u4f46\u80fd\u5426\u69cb\u9020\u51fa\u9019\u500b\u65b9\u7a0b\u5f0f\u6578\u5b78\u7684\u7cbe\u78ba\u89e3\uff0c\u4ecd\u7136\u662f\u5f85\u89e3\u7684\u554f\u984c(\u6709\u767e\u842c\u7f8e\u5143\u734e\u91d1)\u3002<\/p>\n<p>11) \u99ac\u514b\u58eb\u5a01\u65b9\u7a0b\u7d44\uff1a\u9019\u662f\u7531\u56db\u500b\u63cf\u8ff0\u96fb(E)\u8207\u78c1(H)\u7684\u884c\u70ba\u548c\u95dc\u4fc2\u4e4b\u5fae\u5206\u65b9\u7a0b\u6240\u7d44\u6210\u7684\u65b9\u7a0b\u7d44\u3002\u99ac\u514b\u58eb\u5a01\u65b9\u7a0b\u7d44\u4e4b\u65bc\u53e4\u5178\u96fb\u78c1\u5b78\uff0c\u5982\u540c\u725b\u9813\u7684\u904b\u52d5\u5b9a\u5f8b\u548c\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u4e4b\u65bc\u53e4\u5178\u529b\u5b78 \u2500 \u4ed6\u5011\u662f\u6211\u5011\u89e3\u91cb\u96fb\u78c1\u5b78\u5728\u65e5\u5e38\u5c3a\u5ea6\u4e0b\u5982\u4f55\u4f5c\u7528\u7684\u57fa\u790e\u3002\u5982\u8981\u63a8\u5ee3\u5230\u539f\u5b50\u7684\u5c3a\u5ea6\uff0c\u5c31\u6709\u8cf4\u91cf\u5b50\u529b\u5b78\u7684\u4fee\u6b63\uff0c\u9019\u9580\u5b78\u554f\u7a31\u70ba\u91cf\u5b50\u96fb\u52d5\u529b\u5b78\u3002\u6e05\u695a\u7684\u662f\uff0c\u9019\u4e9b\u512a\u7f8e\u7684\u99ac\u514b\u58eb\u5a01\u65b9\u7a0b\u5f0f\u662f\u5728\u4eba\u985e\u5c3a\u5ea6\u4e0b\uff0c\u96fb\u78c1\u5b78\u4ee5\u53ca\u5149\u5b78\u2500\u5149\u5373\u96fb\u78c1\u6ce2\u2500\u80fd\u5920\u88ab\u826f\u597d\u63cf\u8ff0\u7684\u8fd1\u4f3c\u65b9\u7a0b\u7d44\u3002<\/p>\n<p>12) \u71b1\u529b\u5b78\u7b2c\u4e8c\u5b9a\u5f8b\uff1a\u5728\u4e00\u500b\u5c01\u9589\u7684\u7cfb\u7d71\u4e2d\uff0c\u71b5 (<i>S<\/i>) \u7e3d\u662f\u4fdd\u6301\u7a69\u5b9a\u6216\u9010\u6f38\u589e\u52a0\uff0c\u800c\u6ce2\u8332\u66fc\u5beb\u4e0b\u7684\u65b9\u7a0b\u5f0f\u66f4\u8ce6\u4e88\u4e86\u71b5\u7d71\u8a08\u7684\u610f\u7fa9\u3002\u7c21\u55ae\u5730\u8aaa\uff0c\u71b1\u529b\u5b78\u7684\u71b5\u662f\u5ea6\u91cf\u4e00\u500b\u7cfb\u7d71\u7684\u7d0a\u4e82\u7a0b\u5ea6\u3002\u4e00\u500b\u958b\u59cb\u6642\u6709\u5e8f\uff0c\u4f46\u4e0d\u5e73\u8861\u7684\u7cfb\u7d71 \u2500 \u4f8b\u5982\uff0c\u9760\u8fd1\u5bd2\u51b7\u5340\u57df\u7684\u71b1\u9ede\u5340\u57df \u2500 \u7e3d\u662f\u8da8\u5411\u5e73\u8861\u7684\u7d0a\u4e82\u72c0\u614b\uff0c\u71b1\u6703\u5f9e\u71b1\u5340\u6d41\u5411\u51b7\u5340\uff0c\u76f4\u5230\u5747\u52fb\u5206\u4f48\u70ba\u6b62\u3002\u5927\u591a\u6578\u7684\u7269\u7406\u904e\u7a0b\u90fd\u662f\u4e0d\u53ef\u9006\u7684 \u2500 \u4ea6\u5373\u5b87\u5b99\u7684\u71b5\u6703\u4e00\u76f4\u8b8a\u5927\uff0c\u9019\u96b1\u542b\u4e86\u6642\u9593\u662f\u6709\u65b9\u5411\u6027\u7684\u3002\u4f8b\u5982\u6211\u5011\u5c07\u51b0\u584a\u653e\u5165\u4e00\u676f\u71b1\u5496\u5561\u4e2d\uff0c\u6211\u5011\u7e3d\u662f\u770b\u5230\u51b0\u584a\u878d\u5316\uff0c\u537b\u672a\u66fe\u898b\u904e\u4e00\u676f\u5496\u5561\u751f\u51fa\u51b0\u584a\u800c\u5496\u5561\u81ea\u5df1\u8b8a\u71b1\u3002<\/p>\n<p>13)\u00a0 \u76f8\u5c0d\u8ad6\uff1a\u611b\u56e0\u65af\u5766\u7528\u72f9\u7fa9\u548c\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u5f9e\u6839\u672c\u4e0a\u6539\u8b8a\u4e86\u7269\u7406\u7684\u9032\u7a0b\uff0c\u7d93\u5178\u7684\u65b9\u7a0b\u5f0f E=mc\u00b2\u00a0\u8aaa\u660e\u8cea\u91cf\u8207\u80fd\u91cf\u7684\u8f49\u63db\u95dc\u4fc2\u3002\u72f9\u7fa9\u76f8\u5c0d\u8ad6\u5f15\u9032\u5149\u5728\u771f\u7a7a\u4e2d\u7684\u901f\u5ea6\u662f\u56fa\u5b9a\u4e0d\u8b8a\u7684\uff0c\u4ee5\u53ca\u4e0d\u540c\u901f\u5ea6\u79fb\u52d5\u7684\u4eba\u5c0d\u6642\u9593\u6d41\u901d\u53ca\u7a7a\u9593\u8ddd\u96e2\u611f\u53d7\u4e26\u4e0d\u76f8\u540c\u7684\u6982\u5ff5\u3002<\/p>\n<p>\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u5247\u8a8d\u70ba\u91cd\u529b\u662f\u6642\u9593\u8207\u7a7a\u9593\u672c\u8eab\u7684\u5f4e\u66f2\u548c\u647a\u758a\uff0c\u81ea\u725b\u9813\u7684\u5b9a\u5f8b\u4ee5\u4f86\uff0c\u9019\u662f\u6211\u5011\u5c0d\u91cd\u529b\u7684\u7406\u89e3\u9996\u6b21\u5de8\u5927\u7684\u6539\u8b8a\uff0c\u5c0d\u65bc\u6211\u5011\u4e86\u89e3\u5b87\u5b99\u7684\u8d77\u6e90\u3001\u69cb\u9020\uff0c\u548c\u6700\u7d42\u7d50\u5c40\uff0c\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u662f\u4e0d\u53ef\u6216\u7f3a\u7684\u3002<\/p>\n<figure id=\"attachment_17393\" aria-describedby=\"caption-attachment-17393\" style=\"width: 574px\" class=\"wp-caption aligncenter\"><a style=\"text-align: center;\" href=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m5.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-17393\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m5-1024x768.jpg\" alt=\"m5\" width=\"574\" height=\"430\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m5-1024x768.jpg 1024w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m5-300x225.jpg 300w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m5.jpg 1200w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/a><figcaption id=\"caption-attachment-17393\" class=\"wp-caption-text\">\u611b\u56e0\u65af\u5766<\/figcaption><\/figure>\n<p>14)\u00a0 \u859b\u4e01\u683c\u65b9\u7a0b\u5f0f\uff1a\u9019\u662f\u5728\u91cf\u5b50\u529b\u5b78\u4e0a\u6700\u4e3b\u8981\u7684\u65b9\u7a0b\u5f0f\uff0c\u5982\u540c\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u5728\u6700\u5927\u5c3a\u5ea6\u4e0a\u8aaa\u660e\u6211\u5011\u7684\u5b87\u5b99\uff0c\u9019\u500b\u65b9\u7a0b\u5247\u662f\u652f\u914d\u539f\u5b50\u548c\u6b21\u539f\u5b50\u7c92\u5b50\u7684\u884c\u70ba\u3002<br \/>\n\u73fe\u4ee3\u91cf\u5b50\u529b\u5b78\u662f\u6b77\u53f2\u4e0a\u975e\u5e38\u6210\u529f\u7684\u79d1\u5b78\u7406\u8ad6 \u2500 \u6240\u6709\u6211\u5011\u505a\u7684\u5be6\u9a57\u7d50\u679c\u90fd\u548c\u91cf\u5b50\u529b\u5b78\u7684\u9810\u6e2c\u5b8c\u5168\u4e00\u81f4\u3002\u6700\u73fe\u4ee3\u7684\u6280\u8853\u4e5f\u9700\u8981\u91cf\u5b50\u529b\u5b78\uff0c\u8209\u51e1\u6838\u80fd\u3001\u8087\u57fa\u65bc\u534a\u5c0e\u9ad4\u7684\u96fb\u8166\uff0c\u4ee5\u53ca\u96f7\u5c04\u7b49\u90fd\u5efa\u7acb\u5728\u91cf\u5b50\u73fe\u8c61\u4e0a\u3002<\/p>\n<p>15)\u00a0 \u8cc7\u8a0a\u7406\u8ad6\uff1a\u9019\u88cf\u7d66\u51fa\u7684\u65b9\u7a0b\u5f0f\u662f\u70ba\u4e86\u590f\u8fb2\u8cc7\u8a0a\u71b5(Shannon information entropy)\u3002\u5982\u540c\u524d\u8ff0\uff0c\u71b1\u529b\u5b78\u7684\u71b5\u662f\u5c0d\u7d0a\u4e82\u7684\u4e00\u7a2e\u5ea6\u91cf\uff0c\u9019\u88cf\u6307\u7684\u662f\u5c0d\u8a0a\u606f\u8cc7\u8a0a\u91cf\u7684\u5ea6\u91cf \u2500 \u4e00\u672c\u66f8\uff0c\u4e00\u5f35\u7db2\u8def\u4e0a\u5bc4\u9001\u7684JPEG\u5716\u7247\uff0c\u6216\u662f\u4efb\u4f55\u53ef\u7528\u7b26\u865f\u8868\u793a\u7684\u4e8b\u7269\u3002\u8a0a\u606f\u7684\u590f\u8fb2\u71b5\u8aaa\u7684\u662f\u5728\u4e0d\u6f0f\u5931\u5167\u5bb9\u7684\u60c5\u5f62\u4e0b\uff0c\u8a0a\u606f\u53ef\u4ee5\u88ab\u58d3\u7e2e\u591a\u5c11\u7684\u4e0b\u9650\u3002<br \/>\n\u590f\u8fb2\u7684\u71b5\u5ea6\u91cf\u5f15\u8d77\u8cc7\u8a0a\u7406\u8ad6\u7684\u6578\u5b78\u7814\u7a76\uff0c\u4ed6\u7684\u6210\u679c\u662f\u4eca\u65e5\u6211\u5011\u5982\u4f55\u5728\u7db2\u8def\u4e0a\u6e9d\u901a\u7684\u6838\u5fc3\u3002<\/p>\n<p>16)\u00a0 \u6df7\u6c8c\u7406\u8ad6\uff1a\u9019\u500b\u65b9\u7a0b\u5f0f\u662f\u6885\u7684\u4e8c\u6b21\u591a\u9805\u5f0f\u6620\u5c04(May\u2019s logistic map)\uff0c\u5b83\u63cf\u8ff0\u4e00\u7a2e\u901a\u904e\u6642\u9593\u6f14\u8b8a\u7684\u904e\u7a0b \u2500x\u7684\u4e0b\u4e00\u500b\u6642\u9593\u4e16\u4ee3 x\u03c4+1\u2500 \u7531\u65b9\u7a0b\u5f0f\u7684\u53f3\u908a\u7d66\u51fa\uff0c\u4f9d\u8cf4x\u76ee\u524d\u7684\u4e16\u4ee3x\u03c4\u3002k\u662f\u4e00\u500b\u9078\u64c7\u7684\u5e38\u6578\uff0c\u5c0d\u65bc\u67d0\u4e9bk\u503c\uff0c\u6620\u5c04\u6703\u986f\u793a\u6df7\u6c8c\u7684\u884c\u70ba\uff1a\u5982\u679c\u5f9e\u67d0\u4e9b\u7279\u6b8a\u7684\u521d\u59cb\u503cx\u958b\u59cb\uff0c\u904e\u7a0b\u5c07\u6f14\u5316\u51fa\u4e00\u7a2e\u7d50\u679c\uff0c\u5982\u679c\u7531\u5176\u4ed6\u7684\u521d\u59cb\u503c\u958b\u59cb\uff0c\u751a\u81f3\u975e\u5e38\u975e\u5e38\u9760\u8fd1\u7b2c\u4e00\u500b\u503c\uff0c\u904e\u7a0b\u5c07\u6f14\u5316\u51fa\u5b8c\u5168\u4e0d\u540c\u7684\u7d50\u679c\u3002<br \/>\n\u6211\u5011\u6240\u898b\u7684\u6df7\u6c8c\u884c\u70ba \u2500 \u5c0d\u521d\u59cb\u689d\u4ef6\u975e\u5e38\u654f\u611f \u2500 \u5728\u8a31\u591a\u9818\u57df\u90fd\u662f\u5982\u6b64\u3002\u5929\u6c23\u662f\u500b\u5178\u578b\u7684\u4f8b\u5b50 \u2500\u5927\u6c23\u689d\u4ef6\u7684\u4e00\u500b\u5fae\u5c0f\u6539\u8b8a\u53ef\u4ee5\u5c0e\u81f4\u5e7e\u5929\u5f8c\u5b8c\u5168\u4e0d\u540c\u7684\u5929\u6c23\u7cfb\u7d71\uff0c\u9019\u500b\u6982\u5ff5\u6700\u5e38\u63d0\u53ca\u7684\u8aaa\u6cd5\u5c31\u662f\u300c\u8774\u8776\u6548\u61c9\u300d\u3002<\/p>\n<p>17)\u00a0 \u5e03\u840a\u514b-\u4f11\u65af\u65b9\u7a0b\u5f0f\uff1a\u53e6\u4e00\u500b\u5fae\u5206\u65b9\u7a0b\uff0c\u5e03\u840a\u514b-\u4f11\u65af\u65b9\u7a0b\u5f0f\u63cf\u8ff0\u91d1\u878d\u5c08\u5bb6\u548c\u5546\u4eba\u5982\u4f55\u627e\u5230\u884d\u751f\u6027\u5546\u54c1\u7684\u50f9\u683c\u3002\u884d\u751f\u6027\u5546\u54c1 \u2500 \u57fa\u65bc\u67d0\u4e9b\u6f5b\u5728\u8cc7\u7522\u7684\u91d1\u878d\u5546\u54c1\uff0c\u4f8b\u5982\u80a1\u7968 \u2500 \u4e00\u500b\u73fe\u4ee3\u91d1\u878d\u9ad4\u7cfb\u7684\u4e3b\u8981\u90e8\u4efd\u3002<br \/>\n\u5e03\u840a\u514b-\u4f11\u65af\u65b9\u7a0b\u5f0f\u5141\u8a31\u91d1\u878d\u5c08\u5bb6\u5229\u7528\u884d\u751f\u6027\u5546\u54c1\u7684\u7279\u6027\u548c\u6f5b\u5728\u8cc7\u7522\u4f86\u8a08\u7b97\u9019\u4e9b\u91d1\u878d\u5546\u54c1\u7684\u50f9\u503c\u3002<\/p>\n<figure id=\"attachment_17394\" aria-describedby=\"caption-attachment-17394\" style=\"width: 614px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m6.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-17394\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m6-1024x615.jpg\" alt=\"m6\" width=\"614\" height=\"369\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m6-1024x615.jpg 1024w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m6-300x180.jpg 300w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/m6.jpg 1200w\" sizes=\"(max-width: 614px) 100vw, 614px\" \/><\/a><figcaption id=\"caption-attachment-17394\" class=\"wp-caption-text\">\u9019\u4e9b\u662f\u829d\u52a0\u54e5\u671f\u4ea4\u6240\u6a19\u6e96\u666e\u723e500\u6307\u6578\u7684\u4ea4\u6613\u54e1\uff0c\u4f60\u4e0d\u6703\u767c\u73fe\u6709\u4eba\u6c92\u807d\u904e\u5e03\u840a\u514b-\u4f11\u65af\u65b9\u7a0b\u5f0f\u3002<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>--<\/p>\n<pre><span style=\"color: #333333;\">\u7814\u7a76\u51fa\u8655\uff1a<strong><a href=\"http:\/\/www.businessinsider.com.au\/17-equations-that-changed-the-world-2014-3\" target=\"_blank\">The 17 Equations That Changed The Course Of History\/a&gt;<\/a><\/strong><\/span><\/pre>\n<p><span style=\"color: #333399;\"><strong><strong>\u8b6f\u8005\uff1a\u8607\u4fca\u9d3b \u73fe\u70ba\u5317\u4e00\u5973\u6559\u5e2b\u3002<\/strong><\/strong><\/span><br \/>\n<span style=\"color: #333399;\"><strong><strong>\u8cac\u4efb\u7de8\u8f2f\uff1a\u81fa\u5927\u7269\u7406\u7cfb \u738b\u540d\u5112\u6559\u6388<\/strong><\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0\u6578\u5b78\u570d\u7e5e\u5728\u6211\u5011\u56db\u5468\uff0c\u5b83\u5728\u8a31\u591a\u65b9\u9762\u578b\u5851(<\/p>\n","protected":false},"author":20,"featured_media":17716,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,148],"tags":[1229,1227,1228,611,81,1230],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2014\/04\/2\u3010\u6578\u53f2\u56de\u9867\u3011\u6539\u8b8a\u6b77\u53f2\u9032\u7a0b\u768417\u500b\u65b9\u7a0b\u5f0f.png","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/17377"}],"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=17377"}],"version-history":[{"count":24,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/17377\/revisions"}],"predecessor-version":[{"id":17869,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/17377\/revisions\/17869"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/17716"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=17377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=17377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=17377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}