{"id":1103,"date":"2016-11-04T09:27:38","date_gmt":"2016-11-04T01:27:38","guid":{"rendered":"http:\/\/www.xuehelp.cn\/?p=1103"},"modified":"2016-11-04T09:27:38","modified_gmt":"2016-11-04T01:27:38","slug":"%e6%9c%89%e8%b6%a3%e7%9a%84%e6%95%b0%e5%ad%a6%e5%ae%9a%e7%90%86%e4%bd%a0%e7%9f%a5%e9%81%93%e5%90%97%ef%bc%9f","status":"publish","type":"post","link":"http:\/\/www.xuehelp.cn\/index.php\/archives\/1103","title":{"rendered":"\u6709\u8da3\u7684\u6570\u5b66\u5b9a\u7406\u4f60\u77e5\u9053\u5417\uff1f"},"content":{"rendered":"<fieldset class=\"tn-Powered-by-XIUMI\">\n<section class=\"tn-Powered-by-XIUMI\">\u5b9a\u7406\uff1a\u559d\u9189\u7684\u9152\u9b3c\u603b\u80fd\u627e\u5230\u56de\u5bb6\u7684\u8def\uff0c\u559d\u9189\u7684\u5c0f\u9e1f\u5219\u53ef\u80fd\u6c38\u8fdc\u4e5f\u56de\u4e0d\u4e86\u5bb6\u3002<\/section>\n<\/fieldset>\n<p>\u5047\u8bbe\u6709\u4e00\u6761\u6c34\u5e73\u76f4\u7ebf\uff0c\u4ece\u67d0\u4e2a\u4f4d\u7f6e\u51fa\u53d1\uff0c\u6bcf\u6b21\u6709 50% \u7684\u6982\u7387\u5411\u5de6\u8d701\u7c73\uff0c\u670950%\u7684\u6982\u7387\u5411\u53f3\u8d701\u7c73\u3002\u6309\u7167\u8fd9\u79cd\u65b9\u5f0f\u65e0\u9650\u5730\u968f\u673a\u6e38\u8d70\u4e0b\u53bb\uff0c\u6700\u7ec8\u80fd\u56de\u5230\u51fa\u53d1\u70b9\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f\u7b54\u6848\u662f100% \u3002\u5728\u4e00\u7ec4\u968f\u673a\u6e38\u8d70\u8fc7\u7a0b\u4e2d\uff0c\u53ea\u8981\u65f6\u95f4\u8db3\u591f\u957f\uff0c\u6211\u4eec\u6700\u7ec8\u603b\u80fd\u56de\u5230\u51fa\u53d1\u70b9\u3002<!--more--><br class=\"tn-Powered-by-XIUMI\" \/><br class=\"tn-Powered-by-XIUMI\" \/>\u73b0\u5728\u8003\u8651\u4e00\u4e2a\u559d\u9189\u7684\u9152\u9b3c\uff0c\u4ed6\u5728\u8857\u9053\u4e0a\u968f\u673a\u6e38\u8d70\u3002\u5047\u8bbe\u6574\u4e2a\u57ce\u5e02\u7684\u8857\u9053\u5448\u7f51\u683c\u72b6\u5206\u5e03\uff0c\u9152\u9b3c\u6bcf\u8d70\u5230\u4e00\u4e2a\u5341\u5b57\u8def\u53e3\uff0c\u90fd\u4f1a\u6982\u7387\u5747\u7b49\u5730\u9009\u62e9\u4e00\u6761\u8def\uff08\u5305\u62ec\u81ea\u5df1\u6765\u65f6\u7684\u90a3\u6761\u8def\uff09\u7ee7\u7eed\u8d70\u4e0b\u53bb\u3002\u90a3\u4e48\u4ed6\u6700\u7ec8\u80fd\u591f\u56de\u5230\u51fa\u53d1\u70b9\u7684\u6982\u7387\u662f\u591a\u5c11\u5462\uff1f\u7b54\u6848\u4e5f\u8fd8\u662f 100% \u3002\u521a\u5f00\u59cb\uff0c\u8fd9\u4e2a\u9189\u9b3c\u53ef\u80fd\u4f1a\u8d8a\u8d70\u8d8a\u8fdc\uff0c\u4f46\u6700\u540e\u4ed6\u603b\u80fd\u627e\u5230\u56de\u5bb6\u8def\u3002<\/p>\n<p>\u4e0d\u8fc7\uff0c\u9189\u9152\u7684\u5c0f\u9e1f\u5c31\u6ca1\u6709\u8fd9\u4e48\u5e78\u8fd0\u4e86\u3002\u5047\u5982\u4e00\u53ea\u5c0f\u9e1f\u98de\u884c\u65f6\uff0c\u6bcf\u6b21\u90fd\u4ece\u4e0a\u3001\u4e0b\u3001\u5de6\u3001\u53f3\u3001\u524d\u3001\u540e\u4e2d\u6982\u7387\u5747\u7b49\u5730\u9009\u62e9\u4e00\u4e2a\u65b9\u5411\uff0c\u90a3\u4e48\u5b83\u5f88\u6709\u53ef\u80fd\u6c38\u8fdc\u4e5f\u56de\u4e0d\u5230\u51fa\u53d1\u70b9\u4e86\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5728\u4e09\u7ef4\u7f51\u683c\u4e2d\u968f\u673a\u6e38\u8d70\uff0c\u6700\u7ec8\u80fd\u56de\u5230\u51fa\u53d1\u70b9\u7684\u6982\u7387\u53ea\u6709\u5927\u7ea6 34% \u3002<\/p>\n<p>\u8fd9\u4e2a\u5b9a\u7406\u662f\u8457\u540d\u6570\u5b66\u5bb6\u6ce2\u5229\u4e9a\uff08George P\u00f3lya\uff09\u5728 1921 \u5e74\u8bc1\u660e\u7684\u3002\u968f\u7740\u7ef4\u5ea6\u7684\u589e\u52a0\uff0c\u56de\u5230\u51fa\u53d1\u70b9\u7684\u6982\u7387\u5c06\u53d8\u5f97\u8d8a\u6765\u8d8a\u4f4e\u3002\u5728\u56db\u7ef4\u7f51\u683c\u4e2d\u968f\u673a\u6e38\u8d70\uff0c\u6700\u7ec8\u80fd\u56de\u5230\u51fa\u53d1\u70b9\u7684\u6982\u7387\u662f 19.3% \uff0c\u800c\u5728\u516b\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u8fd9\u4e2a\u6982\u7387\u53ea\u6709 7.3% \u3002<\/p>\n<fieldset class=\"tn-Powered-by-XIUMI\"><\/fieldset>\n<p class=\"tn-Powered-by-XIUMI\">\n<fieldset class=\"tn-Powered-by-XIUMI\">\n<section class=\"tn-Powered-by-XIUMI\">\u5b9a\u7406\uff1a\u628a\u4e00\u5f20\u5f53\u5730\u7684\u5730\u56fe\u5e73\u94fa\u5728\u5730\u4e0a\uff0c\u5219\u603b\u80fd\u5728\u5730\u56fe\u4e0a\u627e\u5230\u4e00\u70b9\uff0c\u8fd9\u4e2a\u70b9\u4e0b\u9762\u7684\u5730\u4e0a\u7684\u70b9\u6b63\u597d\u5c31\u662f\u5b83\u5728\u5730\u56fe\u4e0a\u6240\u8868\u793a\u7684\u4f4d\u7f6e\u3002<\/section>\n<\/fieldset>\n<p class=\"tn-Powered-by-XIUMI\">\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u5728\u5546\u573a\u7684\u5730\u677f\u4e0a\u753b\u4e86\u4e00\u5f20\u6574\u4e2a\u5546\u573a\u7684\u5730\u56fe\uff0c\u90a3\u4e48\u4f60\u603b\u80fd\u5728\u5730\u56fe\u4e0a\u7cbe\u786e\u5730\u4f5c\u4e00\u4e2a\u201c\u4f60\u5728\u8fd9\u91cc\u201d\u7684\u6807\u8bb0\u3002<\/p>\n<p>1912\u5e74\uff0c\u8377\u5170\u6570\u5b66\u5bb6\u5e03\u52b3\u5a01\u5c14\uff08Luitzen Brouwer\uff09\u8bc1\u660e\u4e86\u8fd9\u4e48\u4e00\u4e2a\u5b9a\u7406\uff1a\u5047\u8bbe D \u662f\u67d0\u4e2a\u5706\u76d8\u4e2d\u7684\u70b9\u96c6\uff0cf \u662f\u4e00\u4e2a\u4ece D \u5230\u5b83\u81ea\u8eab\u7684\u8fde\u7eed\u51fd\u6570\uff0c\u5219\u4e00\u5b9a\u6709\u4e00\u4e2a\u70b9x\uff0c\u4f7f\u5f97 f(x) = x \u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u8ba9\u4e00\u4e2a\u5706\u76d8\u91cc\u7684\u6240\u6709\u70b9\u505a\u8fde\u7eed\u7684\u8fd0\u52a8\uff0c\u5219\u603b\u6709\u4e00\u4e2a\u70b9\u53ef\u4ee5\u6b63\u597d\u56de\u5230\u8fd0\u52a8\u4e4b\u524d\u7684\u4f4d\u7f6e\u3002\u8fd9\u4e2a\u5b9a\u7406\u53eb\u505a\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u5b9a\u7406\uff08Brouwer fixed point theorem\uff09\u3002<br \/>\n<br class=\"tn-Powered-by-XIUMI\" \/> \u9664\u4e86\u4e0a\u9762\u7684\u201c\u5730\u56fe\u5b9a\u7406\u201d\uff0c\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u5b9a\u7406\u8fd8\u6709\u5f88\u591a\u5176\u4ed6\u5947\u5999\u7684\u63a8\u8bba\u3002\u5982\u679c\u53d6\u4e24\u5f20\u5927\u5c0f\u76f8\u540c\u7684\u7eb8\uff0c\u628a\u5176\u4e2d\u4e00\u5f20\u7eb8\u63c9\u6210\u4e00\u56e2\u4e4b\u540e\u653e\u5728\u53e6\u4e00\u5f20\u7eb8\u4e0a\uff0c\u6839\u636e\u5e03\u52b3\u5a01\u5c14\u4e0d\u52a8\u70b9\u5b9a\u7406\uff0c\u7eb8\u56e2\u4e0a\u4e00\u5b9a \u5b58\u5728\u4e00\u70b9\uff0c\u5b83\u6b63\u597d\u4f4d\u4e8e\u4e0b\u9762\u90a3\u5f20\u7eb8\u7684\u540c\u4e00\u4e2a\u70b9\u7684\u6b63\u4e0a\u65b9\u3002<\/p>\n<p>\u8fd9\u4e2a\u5b9a\u7406\u4e5f\u53ef\u4ee5\u6269\u5c55\u5230\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u53bb\uff1a\u5f53\u4f60\u6405\u62cc\u5b8c\u5496\u5561\u540e\uff0c\u4e00\u5b9a\u80fd\u5728\u5496\u5561\u4e2d\u627e\u5230\u4e00\u4e2a\u70b9\uff0c\u5b83\u5728\u6405\u62cc\u524d\u540e\u7684\u4f4d\u7f6e\u76f8\u540c\uff08\u867d\u7136\u8fd9\u4e2a\u70b9\u5728\u6405\u62cc\u8fc7\u7a0b\u4e2d\u53ef \u80fd\u5230\u8fc7\u522b\u7684\u5730\u65b9\uff09\u3002\n<\/p>\n<fieldset class=\"tn-Powered-by-XIUMI\">\n<section class=\"tn-Powered-by-XIUMI\">\u5b9a\u7406\uff1a\u4f60\u6c38\u8fdc\u4e0d\u80fd\u7406\u987a\u6930\u5b50\u4e0a\u7684\u6bdb\u3002<\/section>\n<\/fieldset>\n<p>\u60f3\u8c61\u4e00\u4e2a\u8868\u9762\u957f\u6ee1\u6bdb\u7684\u7403\u4f53\uff0c\u4f60\u80fd\u628a\u6240\u6709\u7684\u6bdb\u5168\u90e8\u68b3\u5e73\uff0c\u4e0d\u7559\u4e0b\u4efb\u4f55\u50cf\u9e21\u51a0\u4e00\u6837\u7684\u4e00\u64ae\u6bdb\u6216\u8005\u50cf\u5934\u53d1\u4e00\u6837\u7684\u65cb\u5417\uff1f\u62d3\u6251\u5b66\u544a\u8bc9\u4f60\uff0c\u8fd9\u662f\u529e\u4e0d\u5230\u7684\u3002\u8fd9\u53eb\u505a\u6bdb\u7403\u5b9a\u7406\uff08hairy ball theorem\uff09\uff0c\u5b83\u4e5f\u662f\u7531\u5e03\u52b3\u5a01\u5c14\u9996\u5148\u8bc1\u660e\u7684\u3002\u7528\u6570\u5b66\u8bed\u8a00\u6765\u8bf4\u5c31\u662f\uff0c\u5728\u4e00\u4e2a\u7403\u4f53\u8868\u9762\uff0c\u4e0d\u53ef\u80fd\u5b58\u5728\u8fde\u7eed\u7684\u5355\u4f4d\u5411\u91cf\u573a\u3002\u8fd9\u4e2a\u5b9a\u7406\u53ef\u4ee5\u63a8\u5e7f\u5230\u66f4\u9ad8\u7ef4\u7684\u7a7a\u95f4\uff1a\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u5076\u6570\u7ef4\u7684\u7403\u9762\uff0c\u8fde\u7eed\u7684\u5355\u4f4d\u5411\u91cf\u573a\u90fd\u662f\u4e0d\u5b58\u5728\u7684\u3002<\/p>\n<p>\u6bdb\u7403\u5b9a\u7406\u5728\u6c14\u8c61\u5b66\u4e0a\u6709\u4e00\u4e2a\u6709\u8da3\u7684\u5e94\u7528\uff1a\u7531\u4e8e\u5730\u7403\u8868\u9762\u7684\u98ce\u901f\u548c\u98ce\u5411\u90fd\u662f\u8fde\u7eed\u7684\uff0c\u56e0\u6b64\u7531\u6bdb\u7403\u5b9a\u7406\uff0c\u5730\u7403\u4e0a\u603b\u4f1a\u6709\u4e00\u4e2a\u98ce\u901f\u4e3a 0 \u7684\u5730\u65b9\uff0c\u4e5f\u5c31\u662f\u8bf4\u6c14\u65cb\u548c\u98ce\u773c\u662f\u4e0d\u53ef\u907f\u514d\u7684\u3002<\/p>\n<fieldset class=\"tn-Powered-by-XIUMI\"><\/fieldset>\n<p class=\"tn-Powered-by-XIUMI\">\n<fieldset class=\"tn-Powered-by-XIUMI\">\n<section class=\"tn-Powered-by-XIUMI\">\u5b9a\u7406\uff1a\u5728\u4efb\u610f\u65f6\u523b\uff0c\u5730\u7403\u4e0a\u603b\u5b58\u5728\u5bf9\u79f0\u7684\u4e24\u70b9\uff0c\u4ed6\u4eec\u7684\u6e29\u5ea6\u548c\u5927\u6c14\u538b\u7684\u503c\u6b63\u597d\u90fd\u76f8\u540c\u3002<\/section>\n<\/fieldset>\n<p>\u6ce2\u5170\u6570\u5b66\u5bb6\u4e4c\u62c9\u59c6\uff08Stanis\u0142aw Marcin Ulam\uff09\u66fe\u7ecf\u731c\u60f3\uff0c\u4efb\u610f\u7ed9\u5b9a\u4e00\u4e2a\u4ece n \u7ef4\u7403\u9762\u5230 n \u7ef4\u7a7a\u95f4\u7684\u8fde\u7eed\u51fd\u6570\uff0c\u603b\u80fd\u5728\u7403\u9762\u4e0a\u627e\u5230\u4e24\u4e2a\u4e0e\u7403\u5fc3\u76f8\u5bf9\u79f0\u7684\u70b9\uff0c\u4ed6\u4eec\u7684\u51fd\u6570\u503c\u662f\u76f8\u540c\u7684\u30021933 \u5e74\uff0c\u6ce2\u5170\u6570\u5b66\u5bb6\u535a\u82cf\u514b\uff08Karol Borsuk\uff09\u8bc1\u660e\u4e86\u8fd9\u4e2a\u731c\u60f3\uff0c\u8fd9\u5c31\u662f\u62d3\u6251\u5b66\u4e2d\u7684\u535a\u82cf\u514b-\u4e4c\u62c9\u59c6\u5b9a\u7406\uff08Borsuk\u2013Ulam theorem\uff09\u3002<br class=\"tn-Powered-by-XIUMI\" \/><br class=\"tn-Powered-by-XIUMI\" \/>\u535a\u82cf\u514b-\u4e4c\u62c9\u59c6\u5b9a\u7406\u6709\u5f88\u591a\u63a8\u8bba\uff0c\u5176\u4e2d\u4e00\u4e2a\u63a8\u8bba\u5c31\u662f\uff0c\u5728\u5730\u7403\u4e0a\u603b\u5b58\u5728\u5bf9\u79f0\u7684\u4e24\u70b9\uff0c\u4ed6\u4eec\u7684\u6e29\u5ea6\u548c\u5927\u6c14\u538b\u7684\u503c\u6b63\u597d\u90fd\u76f8\u540c\uff08\u5047\u8bbe\u5730\u7403\u8868\u9762\u5404\u5730\u7684\u6e29\u5ea6\u5dee\u5f02\u548c\u5927\u6c14\u538b\u5dee\u5f02\u662f\u8fde\u7eed\u53d8\u5316\u7684\uff09\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u6e29\u5ea6\u503c\u548c\u5927\u6c14\u538b\u503c\u6240\u6709\u53ef\u80fd\u7684\u7ec4\u5408\u770b\u6210\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e0a\u7684\u70b9\uff0c\u4e8e\u662f\u5730\u7403\u8868\u9762\u5404\u70b9\u7684\u6e29\u5ea6\u548c\u5927\u6c14\u538b\u53d8\u5316\u60c5\u51b5\u5c31\u53ef\u4ee5\u770b\u4f5c\u662f\u4e8c\u7ef4\u7403\u9762\u5230\u4e8c\u7ef4\u5e73\u9762\u7684\u51fd\u6570\uff0c\u7531\u535a\u82cf\u514b-\u4e4c\u62c9\u59c6\u5b9a\u7406\u4fbf\u53ef\u63a8\u51fa\uff0c\u4e00\u5b9a\u5b58\u5728\u4e24\u4e2a\u51fd\u6570\u503c\u76f8\u7b49\u7684\u5bf9\u79f0\u70b9\u3002<br \/>\n<br class=\"tn-Powered-by-XIUMI\" \/>\u5f53 n = 1 \u65f6\uff0c\u535a\u82cf\u514b-\u4e4c\u62c9\u59c6\u5b9a\u7406\u5219\u53ef\u4ee5\u8868\u8ff0\u4e3a\uff0c\u5728\u4efb\u4e00\u65f6\u523b\uff0c\u5730\u7403\u7684\u8d64\u9053\u4e0a\u603b\u5b58\u5728\u6e29\u5ea6\u76f8\u7b49\u7684\u4e24\u4e2a\u70b9\u3002\u5bf9\u4e8e\u8fd9\u4e2a\u5f31\u5316\u7248\u7684\u63a8\u8bba\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u975e\u5e38\u76f4\u89c2\u7684\u8bc1\u660e\u65b9\u6cd5\uff1a\u5047\u8bbe\u8d64\u9053\u4e0a\u6709 A\u3001B \u4e24\u4e2a\u4eba\uff0c\u4ed6\u4eec\u7ad9\u5728\u5173\u4e8e\u7403\u5fc3\u5bf9\u79f0\u7684\u4f4d\u7f6e\u4e0a\u3002\u5982\u679c\u6b64\u65f6\u4ed6\u4eec\u6240\u5728\u5730\u65b9\u7684\u6e29\u5ea6\u76f8\u540c\uff0c\u95ee\u9898\u5c31\u5df2\u7ecf\u89e3\u51b3\u4e86\u3002\u4e0b\u9762\u6211\u4eec\u53ea\u9700\u8981\u8003\u8651\u4ed6\u4eec\u6240\u5728\u5730\u70b9\u7684\u6e29\u5ea6\u4e00\u9ad8\u4e00\u4f4e\u7684\u60c5\u51b5\u3002\u4e0d\u59a8\u5047\u8bbe\uff0cA \u6240\u5728\u7684\u5730\u65b9\u662f 10 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\u7684\u8303\u56f4\uff09\uff0c\u6700\u7ec8\u53d8\u6210\u4e86 20\uff1b\u800c B \u7ecf\u5386\u7684\u6e29\u5ea6\u5219\u4ece 20 \u51fa\u53d1\uff0c\u6700\u7ec8\u8fde\u7eed\u53d8\u5316\u5230\u4e86 10\u3002\u90a3\u4e48\uff0c\u4ed6\u4eec\u6240\u62a5\u7684\u6e29\u5ea6\u503c\u5728\u4e2d\u95f4\u4e00\u5b9a\u6709\u201c\u76f8\u4ea4\u201d\u7684\u4e00\u523b\uff0c\u8fd9\u6837\u4e00\u6765\u6211\u4eec\u4e5f\u5c31\u627e\u5230\u4e86\u8d64\u9053\u4e0a\u4e24\u4e2a\u6e29\u5ea6\u76f8\u7b49\u7684\u5bf9\u79f0\u70b9\u3002<\/p>\n<fieldset class=\"tn-Powered-by-XIUMI\"><\/fieldset>\n<p class=\"tn-Powered-by-XIUMI\">\n<fieldset class=\"tn-Powered-by-XIUMI\">\n<section 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