{"id":3193,"date":"2014-06-17T23:13:34","date_gmt":"2014-06-17T23:13:34","guid":{"rendered":"http:\/\/www.worldofmastermind.com\/?p=3193"},"modified":"2016-12-09T18:43:30","modified_gmt":"2016-12-09T18:43:30","slug":"%e5%96%9d%e6%b1%bd%e6%b0%b4%e7%ae%97%e8%a1%93%e5%95%8f%e9%a1%8c-%e7%9a%84%e8%a7%a3%e7%ad%94%e8%88%87%e5%95%9f%e7%a4%ba","status":"publish","type":"post","link":"https:\/\/www.worldofmastermind.com\/?p=3193","title":{"rendered":"\u559d\u6c7d\u6c34\u7b97\u8853\u554f\u984c\u7684\u5713\u6eff\u89e3\u7b54\u53ca\u555f\u793a"},"content":{"rendered":"<p><strong><span style=\"color: #993300;\">&#8220;\u559d\u6c7d\u6c34&#8221;\u7b97\u8853\u554f\u984c \u7684\u5713\u6eff\u89e3\u7b54\u53ca\u555f\u793a<\/span><\/strong> \u00a0\u00a0 <strong>\u4fe1\u5805\u53caAllen Tsai<\/strong><\/p>\n<p><strong>\u89e3\u7b54\u4e00\u4e9b\u7c21\u55ae\u667a\u529b\u6e2c\u9a57\u554f\u984c\uff0c\u53ef\u8003\u9a57\u4e00\u4e0b\u81ea\u5df1\u7684\u8010\u529b\uff0c\u601d\u8003\u7684\u9748\u6d3b\u5ea6\uff0c\u5206\u6790\u80fd\u529b\uff0c\u4e5f\u53ef\u6e2c\u8a66\u81ea\u5df1\u5c0d\u4e00\u5207\u4e8b\u7269\u8a8d\u8b58\u7684\u6df1\u5ea6\u3001\u5ee3\u5ea6\u3002\u6240\u6709\u4e00\u5207\u554f\u984c\u8207\u89e3\u7b54\uff0c\u5176\u4e2d\u90fd\u96b1\u542b\u4e7e\u5764\u5999\u7fa9\u3002\u540c\u6642\uff0c\u8207\u540c\u9053\u3001\u670b\u53cb\u4e92\u76f8\u5207\u78cb\u3001\u8a0e\u8ad6\uff0c\u53ef\u4ee5\u6fc0\u767c\u65b0\u601d\u8def\u3001\u65b0\u65b9\u5411\u3002\u4e0d\u7ba1\u61c2\u4e0d\u61c2\uff0c\u6703\u4e0d\u6703\uff0c\u554f\u5c0d\u4e86\u554f\u984c\u4e5f\u662f\u4e00\u7a2e\u89e3\u7b54\u7684\u65b9\u5f0f\uff0c\u6240\u8b02\u554f\u984c\u8207\u7b54\u6848\u662f\u4e00\u9ad4\u7684\u5169\u9762\u3002\u4e92\u6fc0\u3001\u4e92\u767c\uff0c\u662f\u5b78\u7fd2\u589e\u9577\u7684\u5fc5\u8981\u689d\u4ef6\u3002\u4fe1\u5805\u5728\u6b64\uff0c\u4ee5\u4e0b\u9762\u4e00\u500b\u7c21\u55ae\u7684\u7b97\u8853\u554f\u984c\uff0c\u4f86\u95e1\u8aaa\u6b64\u8ad6\u984c\u3002\u77e5\u8b58\u662f\u5c0d\u4e8b\u76f8\u8868\u9762\u819a\u6dfa\u7684\u8a8d\u77e5\uff0c\u5982\u6a39\u4e4b\u679d\u8449\u3002\u667a\u6167\u662f\u5c0d\u4e8b\u76f8\u6df1\u5ee3\u7684\u77ad\u89e3\u8207\u904b\u7528\uff0c\u5982\u6a39\u4e4b\u6839\u5e79\u3002\u4eba\u751f\u7684\u610f\u7fa9\u8207\u76ee\u7684\uff0c\u5728\u65bc\u589e\u9577\u667a\u6167\u3002<\/strong><\/p>\n<p><a href=\"https:\/\/www.worldofmastermind.com\/wp-content\/uploads\/2014\/06\/soda1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-3220 alignleft\" src=\"https:\/\/www.worldofmastermind.com\/wp-content\/uploads\/2014\/06\/soda1.jpg\" alt=\"soda1\" width=\"210\" height=\"158\" \/><\/a><span style=\"color: #ff0000;\"><strong>1. &#8220;\u559d\u6c7d\u6c34&#8221;\u7b97\u8853\u554f\u984c<\/strong><\/span><br \/> <span style=\"color: #993300;\"><strong>\u6709\u4e00\u7fa4\u4eba\u60f3\u8981\u559d\u6c7d\u6c34\u3002\u5047\u5982\u4ed6\u5011\u6709 20 \u584a\u9322\uff0c1 \u74f6\u6c7d\u6c34\u8ce3 2 \u584a\u9322\uff0c\u4ed6\u5011\u53ef\u4ee5\u8cb7\u5230 10 \u74f6\u6c7d\u6c34\uf92d\u559d\u3002\u7576\u4ed6\u5011\u6536\u96c6\u5230 2 \u500b\u74f6\u84cb\uff0c\u5c31\u53ef\u4ee5\u63db 1 \u74f6\u6c7d\u6c34\uff1b\u6536\u96c6\u5230 4 \u500b\u7a7a\u74f6\u7f50\uff0c\u4e5f\u53ef\u4ee5\u63db 1 \u74f6\u6c7d\u6c34\u3002\u8acb\u554f\uff0c\u4ed6\u5011\u6700\u591a\u80fd\u559d\u5230\u5e7e\u74f6\u6c7d\u6c34\uff1f<\/strong><\/span><!--more--><\/p>\n<p><span style=\"color: #ff0000;\"><strong>2. \u5404\u7a2e\u53ef\u80fd\u7684\u89e3\u7b54\u65b9\u6cd5\u8207\u6df1\u5ea6<\/strong><\/span><\/p>\n<p><strong>\u5e95\u4e0b\u662f\u89e3\u7b54\u6b64\u554f\u984c\u7684\u5404\u7a2e\u4eba\u6240\u7528\u65b9\u6cd5:<\/strong><br \/> <strong> 2.1 \u8a31\u591a\u4eba\u4e00\u770b\u9019\u554f\u984c\uff0c\u4ee5\u70ba\u5f88\u7c21\u55ae\uff0c\u5c31\u958b\u59cb\u7528\u5fc3\u7b97\u3002\u7b97\u4e86\u4e00\u9663\u5b50\uff0c\u8d8a\u7b97\u8d8a\u8907\u96dc\uff0c\u5c31\u958b\u59cb\u4f5c\u7b46\u8a18\uff0c\u8d8a\u8a18\u8d8a\u7cca\u5857\uff0c\u5927\u90e8\u4efd\u4eba\u5c31\u653e\u68c4\u4e86\u3002<\/strong><\/p>\n<p><strong>2.2 \u6578\u5b78\u5c08\u5bb6\uff0c\u78b0\u5230\u9019\u554f\u984c\uff0c\u4e5f\u8ddf\u666e\u901a\u4eba\u4e00\u6a23\u675f\u624b\u7121\u7b56\uff0c\u56e0\u70ba\u5b83\u662f\u6574\u6578\u554f\u984c\u3002\u89e3\u7b54\u6b64\u554f\u984c\uff0c\u53ea\u80fd\u7528\u6574\u6578(\u56e0\u70ba\u6c7d\u6c34\u3001\u74f6\u84cb\u3001\u7a7a\u74f6\u662f\u4e0d\u53ef\u5206\u5272\u7684\u6574\u6578)\uff0c\u4e0d\u80fd\u7528\u5c0f\u6578\u6216\u5206\u6578\uff0c\u56e0\u6b64\uff0c\u666e\u901a\u6578\u5b78\u516c\u5f0f\u4e0d\u80fd\u61c9\u7528\u3002[\u9019\u6574\u6578\u554f\u984c(\u4e0d\u80fd\u5206\u5272)\uff0c\u7269\u7406\u540d\u8a5e\u53eb\u91cf\u5b50\u5316(quantization)\uff0c\u662f\u91cf\u5b50\u529b\u5b78(Quantum Mechanics) \u8207\u53e4\u5178\u529b\u5b78(Classical Mechanics)\u7684\u5206\u754c\u5dba\u3002]\u3002<\/strong><\/p>\n<p><strong>2.3 \u8070\u660e\u4e0a\u6839\u4eba\uff0c\u601d\u616e\u6e05\u6790\uff0c\u7a0d\u4f5c\u7b46\u8a18\uff0c\u4e00\u76f4\u7b97\u4e0b\u53bb\uff0c\u5f97\u5230\u7b54\u6848\uff0c\u5c31\u5fc3\u6eff\u610f\u8db3\uff0c\u81ea\u5df1\u62cd\u62cd\u80a9\u8180\uff0c\u5f97\u610f\u81ea\u559c\u3002<\/strong><\/p>\n<p><strong>2.4 \u4e2d\u6839\u4eba\u5c31\u7528\u5be6\u9a57\u65b9\u6cd5\uff0c\u53bb\u8cb7\u4e86\u5341\u74f6\u6c7d\u6c34\uff0c\u4e00\u9762\u559d\uff0c\u4e00\u9762\u4f5c\u7b46\u8a18\uff0c\u7d93\u904e\u4e00\u500b\u9418\u982d\uff0c\u6c7d\u6c34\u559d\u5920\u4e86\uff0c\u7b54\u6848\u4e5f\u7b97\u51fa\u4f86\u4e86\uff0c\u4e5f\u662f\u5fc3\u6eff\u610f\u8db3\u3002\u9084\u6709\u4eba\u4e0d\u8cb7\u6c7d\u6c34\uff0c\u5c31\u5728\u7d19\u4e0a\u756b\u5716\u4f5c\u7b46\u8a18\uff0c\u7d93\u904e\u4e00\u6bb5\u6642\u9593\uff0c\u4e5f\u5f97\u5230\u7b54\u6848\u3002<\/strong><\/p>\n<p><strong>2.5 \u96fb\u8166\u8edf\u9ad4\u5c08\u5bb6\uff0c\u4e00\u770b\u5230\u9019\u554f\u984c\uff0c\u5c31\u958b\u59cb\u5beb\u7a0b\u5f0f\uff0c\u7528\u96fb\u8166\u904b\u4f5c\uff0c\u4e5f\u627e\u5230\u7b54\u6848\u3002<\/strong><\/p>\n<p><strong>2.6.\u53e6\u4e00\u7a2e\u662f\u79d1\u5b78\u5bb6\u6216\u662f\u5de5\u7a0b\u5e2b\uff0c\u4ed6\u5011\u5c07\u8a08\u7b97\u904e\u7a0b\u5217\u8868\uff0c\u5c07\u6240\u6709\u7a0b\u5e8f\u8a18\u9304\uff0c\u4e5f\u5f97\u5230\u7b54\u6848\u3002<\/strong><\/p>\n<p><strong>2.7\u53e6\u4e00\u7a2e\u4eba\uff0c\u6703\u627e\u5230\u4e00\u500b\u5f88\u597d\uff0c\u5f88\u7c21\u55ae\u7684\u65b9\u6cd5\uff0c\u5229\u920d\u5168\u6536\uff0c\u8001\u5c11\u54b8\u5b9c\u3002\u53ef\u5411\u5927\u773e\u89e3\u8aaa\uff0c\u61c2\u4e86\u4e4b\u5f8c\uff0c\u4eba\u4eba\u90fd\u53ef\u4f9d\u6cd5\u904b\u4f5c\u5230\u6240\u6709\u985e\u4f3c\u7684\u554f\u984c\u3002<\/strong><\/p>\n<p><strong>2.8 \u9084\u6709\u4e00\u7a2e\u4eba\uff0c\u6253\u7834\u6c99\u934b\u554f\u5230\u5e95\u3002\u5982\u679c\u4f60\u4e0d\u53ea\u8cb7\u5341\u74f6\uff0c\u800c\u662f\u8cb7\u4e00\u5104\u74f6\uff0c\u7b54\u6848\u662f\u4ec0\u9ebc? \u89e3\u7b54\u9019\u554f\u984c\uff0c\u53ef\u7528\u96fb\u8166\u7a0b\u5f0f\uff0c\u4f46\u4e5f\u53ef\u7528\u7d19\u7b46\uff0c\u4e14\u807d\u4fe1\u5805\u6162\u6162\u9053\u4f86\u3002<\/strong><\/p>\n<p><strong><span style=\"color: #ff0000;\">3. \u5217\u8868\u89e3\u7b54<\/span><\/strong><\/p>\n<p><strong>\u89e3\u7b54\u6b64\u554f\u984c\uff0c\u6211\u5011\u76f4\u89ba\u4e0a\u90fd\u4ee5\u70ba\u61c9\u8a72\u5f88\u5bb9\u6613\u624d\u5c0d\u3002\u601d\u8def\u4f3c\u4e4e\u53ea\u6709\u4e00\u689d\uff0c\u9996\u5148\uff0c\u559d\u5b8c 10 \u74f6\u6c7d\u6c34\uff0c\u5c31\u6709 10 \u500b\u74f6\u84cb\u300110\u500b\u7a7a\u74f6\u3002\u53ef\u4ee5\u7528 10 \u500b\u74f6\u84cb\u63db 5 \u74f6\u6c7d\u6c34\u3001\u7528 8 \u500b\u7a7a\u74f6\u63db 2 \u74f6\u6c7d\u6c34\uff0c\u9019\u6a23\u5c31\u6709 7 \u74f6\u6c7d\u6c34\uff0c\u9084\u5269 2 \u500b\u7a7a\u74f6\u3002 \u63a5\u8457\uff0c\u559d\u5b8c\u9019 7 \u74f6\u6c7d\u6c34\uff0c\u9019\u6a23\u7e3d\u5171\u5c31\u559d\u4e86 17 \u74f6\u6c7d\u6c34\uff0c\u800c\u4e14\u65b0\u7522\u751f 7 \u500b\u74f6\u84cb\u30017 \u500b\u7a7a\u74f6\uff0c\u52a0\u4e0a\u525b\u525b\u5269\u4e0b\u7684 2 \u500b\u7a7a\u74f6\uff0c\u5be6\u969b\u4e0a\u5c31\u6709 7 \u500b\u74f6\u84cb\u30019 \u500b\u7a7a\u74f6\u3002\u518d\u63db 5 \u74f6\u6c7d\u6c34\uff0c\u9019\u6a23\u9084\u5269 1 \u500b\u74f6\u84cb\u30011 \u500b\u7a7a\u74f6\u3002\u4f9d\u6b64\u4e00\u76f4\u6f14\u7b97\u4e0b\u53bb\u3002\u9019\u7a0b\u5e8f\u4f3c\u4e4e\u8d8a\u4f86\u8d8a\u8907\u96dc\uff0c\u5f88\u96e3\u8ffd\u5c0b(keep track)\u3002\u5927\u90e8\u4efd\u7684\u4eba\u5c31\u6b64\u505c\u4f4f\u653e\u68c4\u4e86\u3002<\/strong><\/p>\n<p><strong>\u56e0\u6b64\uff0c\u89e3\u7b54\u9019\u554f\u984c\uff0c\u9808\u8981\u6709\u9ede\u6280\u5de7\u3002\u5de5\u7a0b\u5e2b\u6216\u662f\u79d1\u5b78\u5bb6\uff0c\u6703\u904b\u7528\u5c08\u696d\u8a13\u7df4\uff0c\u5c07\u6b64\u554f\u984c\u5217\u8868\uff0c\u5c31\u4e00\u76ee\u4e86\u7136\uff0c\u4efb\u4f55\u4eba\u90fd\u53ef\u4f9d\u6b64\u904b\u4f5c\uff0c\u800c\u5f97\u5230\u7b54\u6848\u3002<\/strong><\/p>\n<p><strong>\u5148\u5c07\u4e00\u5207\u904b\u4f5c\uff0c\u5217\u8868\u5206\u6210\u4e09\u884c:<\/strong><\/p>\n<p><strong>\u6c7d\u6c34\u00a0\u00a0 \u7a7a\u74f6\u00a0\u00a0 \u74f6\u84cb \u00a0 \u00a0 \u00a0 \u8a3b\u89e3<\/strong><br \/> <strong> 10\u00a0\u00a0\u00a0\u00a0\u00a0 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u559d\u5b8c10\u74f6\u6c7d\u6c34\uff0c\u5c31\u670910\u500b\u74f6\u84cb\u300110\u500b\u7a7a\u74f6\u3002<\/strong><\/p>\n<p><strong>5+2\u00a0\u00a0\u00a0 0+7\u00a0\u00a0\u00a0\u00a0\u00a0 2+7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u53ef\u752810\u500b\u7a7a\u74f6\u63db5\u74f6\u6c7d\u6c34\u3001\u75288\u500b\u74f6\u84cb\u63db 2 \u74f6\u6c7d\u6c34\uff0c \u9084\u52692\u500b\u74f6\u84cb\u3002\u9019\u6a23\u5c31\u67097\u74f6\u6c7d\u6c34\uff0c\u9084\u5269 2 \u500b\u74f6\u84cb\u3002<\/strong><strong>\u559d\u5b8c\u90197 \u74f6\u6c7d\u6c34\uff0c\u65b0\u7522\u751f7\u500b\u74f6\u84cb\u30017\u500b\u7a7a\u74f6\uff0c\u52a0\u4e0a\u525b\u525b\u5269\u4e0b \u76842\u500b\u7a7a\u74f6\uff0c\u5be6\u969b\u4e0a\u5c31\u6709 7 \u500b\u7a7a\u74f6\u30019 \u500b\u74f6\u84cb\u3002<\/strong><\/p>\n<p><strong>3+2\u00a0\u00a0\u00a0\u00a0 1+5\u00a0\u00a0\u00a0\u00a0 1+5\u00a0\u00a0\u00a0\u00a0\u00a0 \u518d\u63db 5 \u74f6\u6c7d\u6c34\uff0c\u9084\u5269 1 \u500b\u7a7a\u74f6\u30011 \u500b\u74f6\u84cb\u3002\u559d\u5b8c\u90195\u74f6 \u6c7d\u6c34\uff0c\u65b0\u75225\u500b\u7a7a\u74f6\u30015\u500b\u74f6\u84cb\uff0c\u52a0\u4e0a\u525b\u525b\u5269\u4e0b\u76841\u500b\u7a7a\u74f6\u30011\u500b\u74f6\u84cb\uff0c\u5be6\u969b\u4e0a\u5c31\u67096\u500b\u7a7a\u74f6\u30016\u500b\u74f6\u84cb\u3002<\/strong><strong>\u4f9d\u6b64\u4e00\u76f4\u6f14\u7b97\u4e0b\u53bb\u3002<\/strong><\/p>\n<p><strong>3+1\u00a0\u00a0\u00a0\u00a0\u00a0 0+4\u00a0\u00a0\u00a0\u00a0\u00a0 2+4<\/strong><br \/> <strong> 2+1\u00a0\u00a0\u00a0 \u00a0 0+3\u00a0\u00a0\u00a0\u00a0\u00a0 2+3<\/strong><br \/> <strong> 1+1\u00a0\u00a0\u00a0\u00a0\u00a0 1+2\u00a0\u00a0\u00a0\u00a0\u00a0 1+2<\/strong><br \/> <strong> 1+0\u00a0\u00a0\u00a0\u00a0\u00a0 1+1\u00a0\u00a0\u00a0\u00a0\u00a0 3+1<\/strong><br \/> <strong> 1+1\u00a0\u00a0\u00a0 \u00a0 0+2\u00a0\u00a0\u00a0\u00a0\u00a0 0+2<\/strong><br \/> <strong> 1+0\u00a0\u00a0\u00a0\u00a0\u00a0 0+1\u00a0\u00a0\u00a0\u00a0\u00a0 2+1<\/strong><br \/> <strong> __________________________<\/strong><br \/> <strong> 35\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0 1 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0\u00a0 \u5c07\u6700\u5de6\u908a\u4e00\u884c\u52a0\u8d77\u4f86\uff0c\u5c31\u5f97\u5230\u7e3d\u5171\u559d35\u74f6\u6c7d\u6c34\uff0c\u9084\u5269\u4e0b\u4e00 \u500b\u7a7a\u74f6\u84cb\u548c\u4e09\u500b\u74f6\u84cb\u3002<\/strong><\/p>\n<p><strong><span style=\"color: #ff0000;\">4. \u5217\u8868\u89e3\u7b54\u7684\u597d\u8655<\/span><\/strong><\/p>\n<p><strong>4.1 \u5bb9\u6613\u8a18\u9304\uff0c\u4e0d\u6703\u641e\u7cca\u5857\uff0c\u4efb\u4f55\u4eba\u90fd\u53ef\u4f9d\u6b64\u904b\u4f5c\uff0c\u800c\u5f97\u5230\u7b54\u6848\u3002<\/strong><\/p>\n<p><strong>4.2 \u5982\u679c\u6539\u8b8a\u554f\u984c\uff0c\u4e5f\u53ef\u4f9d\u6a23\u756b\u846b\u8606\u3002\u8b6c\u5982\uff0c\u5982\u679c\u5c07\u554f\u984c\u6539\u70ba\u53ea\u8cb7\u4e866 \u74f6\u6c7d\u6c34\uff0c\u4f9d\u6b64\u5217\u8868\uff0c\u4f60\u53ef\u5f88\u5bb9\u6613\u7b97\u51fa\u7e3d\u5171\u559d\u4e8619\u74f6\u6c7d\u6c34\uff0c\u5269\u4e0b\u4e00\u500b\u74f6\u84cb\u548c\u4e09\u500b\u7a7a\u74f6\u3002\u5982\u679c\u5c07\u554f\u984c\u64f4\u5927\u5230\u4f60\u8cb7\u4e86100\u74f6\u6c7d\u6c34\uff0c\u4e5f\u53ef\u4f9d\u6b64\u5217\u8868\uff0c\u5f97\u5230\u7e3d\u5171\u559d\u4e86395\u74f6\u6c7d\u6c34\uff0c\u9084\u5269\u4e0b\u4e00\u500b\u74f6\u84cb\u548c\u4e09\u500b\u7a7a\u74f6\u3002<\/strong><\/p>\n<p><strong>4.3 \u5982\u679c\u5c07\u554f\u984c\u6539\u70ba\u8cb7\u4e8611\u74f6\uff0c\u6211\u5011\u53ef\u91cd\u65b0\u5217\u8868\uff0c \u4e5f\u53ef\u7531\u4e0a\u8868\u7e7c\u7e8c\u6f14\u7b97\u4e0b\u53bb:<\/strong><br \/> <strong> \u6c7d\u6c34\u00a0\u00a0\u00a0 \u7a7a\u74f6\u00a0\u00a0\u00a0\u00a0 \u74f6\u84cb\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u8a3b\u89e3<\/strong><br \/> <strong> 35\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u9019\u662f\u4e0a\u9762\u8cb710\u74f6\u6c7d\u6c34\u7684\u7b54\u6848<\/strong><br \/> <strong> 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0 1+1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3+1\u00a0\u00a0\u00a0\u00a0\u00a0 \u591a\u8cb71\u74f6\uff0c\u559d\u5b8c\u5f8c\uff0c\u591a\u4e861\u500b\u7a7a\u74f6\u53ca1\u500b\u74f6\u84cb\u3002<\/strong><strong>\u518d\u52a0\u524d\u9762\u5269\u4e0b\u76841\u500b\u7a7a\u74f6\u53ca3\u500b\u74f6\u84cb\u3002<\/strong><br \/> <strong> 1+1\u00a0\u00a0\u00a0\u00a0\u00a0 0+2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0+2<\/strong><br \/> <strong> 1+0\u00a0\u00a0\u00a0 \u00a0 0+1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2+1<\/strong><br \/> <strong> ____________________________________<\/strong><br \/> <strong> 39\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u7b54\u6848\u662f\uff0c\u5982\u679c\u8cb711\u74f6\u6c7d\u6c34\uff0c\u7e3d\u5171\u53ef\u559d39\u74f6\uff0c \u9084\u662f\u5269\u4e0b\u4e00\u500b\u7a7a\u74f6\u548c\u4e09\u500b\u74f6\u84cb\u3002<\/strong><\/p>\n<p><strong>4.4 \u5982\u679c\u5c07\u554f\u984c\u6539\u70ba: \u4f60\u8cb7\u4e86\u5341\u74f6\u6c7d\u6c34\uff0c\u6bcf3\u500b\u74f6\u84cb\u53ef\u63db\u4e00\u74f6\u6c7d\u6c34\uff0c6\u500b\u7a7a\u74f6\u4e5f\u53ef\u63db\u4e00\u74f6\u6c7d\u6c34\uff0c\u7e3d\u5171\u559d\u4e86\u591a\u5c11\u74f6?<\/strong><\/p>\n<p><strong>\u6c7d\u6c34\u00a0\u00a0\u00a0\u00a0 \u7a7a\u74f6\u00a0\u00a0\u00a0\u00a0 \u74f6\u84cb<\/strong><br \/> <strong> 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10<\/strong><br \/> <strong> 3+1\u00a0\u00a0\u00a0\u00a0\u00a0 1+4\u00a0\u00a0\u00a0\u00a0\u00a0 4+4<\/strong><br \/> <strong> 1+1\u00a0\u00a0\u00a0\u00a0\u00a0 2+2\u00a0\u00a0\u00a0\u00a0\u00a0 2+2<\/strong><br \/> <strong> 1+0\u00a0\u00a0\u00a0\u00a0\u00a0 1+1 \u00a0 \u00a0\u00a0 4+1<\/strong><br \/> <strong> ____________________<\/strong><br \/> <strong> 17\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 5<\/strong><\/p>\n<p><strong>\u7b54\u6848\u662f\u7e3d\u5171\u53ef\u559d17\u74f6\uff0c\u5269\u4e0b2\u500b\u7a7a\u74f6\uff0c5\u500b\u74f6\u84cb\u3002<\/strong><\/p>\n<p><span style=\"color: #ff0000;\"><strong>5. \u5982\u679c\u5c07\u554f\u984c\u6539\u70ba\u8cb7\u4e861000000000 (\u4e00\u5104) \u74f6\uff0c\u4f60\u5c07\u600e\u9ebc\u7b97?<\/strong><\/span><\/p>\n<p><strong>\u7531\u4e0a\u97624.3, \u6211\u5011\u89c0\u5bdf\u5230\uff0c\u8cb7\u4e8610 \u74f6\u5f8c\uff0c\u6bcf\u591a\u8cb71\u74f6\uff0c\u53ef\u559d4\u74f6 (39 &#8211; 35 = 4)\u3002\u800c\u4e14\u4e00\u76f4\u91cd\u8986\u4e0b\u53bb\u3002<\/strong><\/p>\n<p><strong>\u518d\u56de\u5230\u8d77\u982d\uff0c\u5982\u679c\u8cb7\u4e862\u74f6\u6c7d\u6c34\uff0c\u7e3d\u5171\u53ef\u559d\u4e09\u74f6\uff0c\u5269\u4e0b\u4e00\u500b\u7a7a\u84cb\u53ca\u4e09\u500b\u7a7a\u74f6\u3002<\/strong><br \/> <strong> \u6c7d\u6c34\u00a0\u00a0 \u7a7a\u74f6\u00a0\u00a0\u00a0 \u74f6\u84cb<\/strong><br \/> <strong> 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 2<\/strong><br \/> <strong> 1+0\u00a0\u00a0\u00a0\u00a0\u00a0 0+1\u00a0\u00a0\u00a0\u00a0 2+1<\/strong><br \/> <strong> ______________________________<\/strong><br \/> <strong> 3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3<\/strong><\/p>\n<p><strong>\u4f46\u5f9e\u6b64\u4ee5\u4e0b\uff0c\u6bcf\u591a\u8cb7\u4e00\u74f6\uff0c\u5c31\u53ef\u559d\u56db\u74f6\u6c7d\u6c34\uff0c\u90fd\u662f\u5269\u4e0b\u4e00\u500b\u7a7a\u84cb\u53ca\u4e09\u500b\u7a7a\u74f6\u3002\u4e5f\u662f\u4e00\u76f4\u91cd\u8986\u3002<\/strong><\/p>\n<p><strong>\u56e0\u6b64\uff0c\u6211\u5011\u5c31\u53ef\u5927\u81bd\u7684\u5047\u8a2d\u4e00\u500b\u516c\u5f0f: (n \u662f\u8d77\u521d\u8cb7\u7684\u6c7d\u6c34\u74f6\u6578\uff0cn \u2265 2 )<\/strong><br \/> <strong>Total N = 3 + (n-2) * 4 = 4n &#8211; 5.<\/strong><br \/> <strong> \u90fd\u662f\u5269\u4e0b\u4e00\u500b\u7a7a\u74f6\u53ca\u4e09\u500b\u74f6\u84cb\u3002<\/strong><\/p>\n<p><strong>\u56e0\u6b64\uff0c\u5982\u679c\u8cb7\u4e86\u4e00\u5104\u74f6 (n = 10000000000)\uff0c\u7b54\u6848\u662f\u7e3d\u5171(N)\u53ef\u559d3999999995\u74f6\u6c7d\u6c34\u3002<\/strong><\/p>\n<p><span style=\"color: #ff0000;\"><strong>6. \u9019\u8ddf\u666e\u901a\u6578\u5b78\u6240\u7528\u65b9\u6cd5\uff0c\u6709\u4f55\u5206\u5225\u5462?<\/strong><\/span><\/p>\n<p><strong>\u666e\u901a\u7684\u6578\u5b78\u89e3\u6cd5\u662f (\u4e0d\u7406\u5b83\u662f\u6c7d\u6c34\u554f\u984c\uff0c\u5047\u8a2d\u5b83\u662fn\u500b\u7269\u4ef6)\uff0c<\/strong><br \/> <strong> \u8d77\u9996\u662fn,<\/strong><br \/> <strong> \u518d\u7b97\u4e0b\u53bb\u662f \u00bd n + \u00bc n = \u00be n ,<\/strong><br \/> <strong> \u518d\u7b97\u4e0b\u53bb\u662f \u00be * \u00be n, \u2026\u2026 \u7b49\u7b49<\/strong><\/p>\n<p><strong>\u7e3d\u548c\u662f N&#8217; = (1 + \u00be + \u00be * \u00be + \u2026) n = n\/(1- \u00be) = 4n.<\/strong><br \/> <strong> (\u61c9\u7528\u6578\u5b78\u516c\u5f0f: 1 + x + x^2 + x^3 + x^4 + &#8230;. = 1\/(1-x) ]<\/strong><\/p>\n<p><strong>\u9019\u8ddf\u4e0a\u9762\u7684\u6b63\u78ba\u516c\u5f0f\uff0cN = 4n &#8211; 5\uff0c\u5dee\u4e86\u4e00\u9ede\u3002\u5176\u539f\u56e0\u662f\u6211\u5011\u5ffd\u7565\u4e86 &#8220;\u559d\u6c7d\u6c34\u554f\u984c&#8221; \u88e1\u7684\u6c7d\u6c34\u3001\u74f6\u84cb\u3001\u7a7a\u74f6\u90fd\u662f\u91cf\u5b50\u5316\u7269\u4ef6 (quantized object)\u3002\u5ffd\u7565\u4e86\u9019\u4e8b\u5be6\uff0c\u6211\u5011\u5f9e\u4e0d\u6574\u6578\u7684\u6c7d\u6c34\u3001\u74f6\u84cb\u3001\u7a7a\u74f6\u591a\u63db\u4e86\u5e7e\u74f6\u3002\u9019\u5c31\u662f\u6709\u540d\u7684&#8221;quantization correction&#8221;\u3002<\/strong><\/p>\n<p><strong>This is the fine distinction between Quantum Mechanics and Classical Mechanics. <\/strong><strong>[\u9019\u662f\u4e8c\u5341\u4e16\u7d00\u5049\u5927\u7684\u7269\u7406\u767c\u73fe\uff0c\u6240\u6709\u7269\u8cea\u90fd\u662f\u91cf\u5b50\u5316 (quantized)\uff0c thus introduced quantum correction.]<\/strong><\/p>\n<p><strong>\u4f46\u4e0a\u9762\u7684N&#8217; = 4n \uff0c\u7576 n &gt;&gt; 1\u6642\uff0c\u662f\u500b\u5f88\u597d\u7684\u8fd1\u4f3c\u503c\u3002<\/strong><\/p>\n<p><span style=\"color: #ff0000;\"><strong><strong>7. \u4e00\u822c\u554f\u984c\u7684\u8fd1\u4f3c\u516c\u5f0f<\/strong><\/strong><\/span><\/p>\n<p><strong>\u7531\u4e0a\u9762\u7684\u8a0e\u8ad6\uff0c\u6211\u5011\u53ef\u89e3\u7b54\u4e00\u822c\u554f\u984c\u7684\u8fd1\u4f3c\u503c\u3002\u5982\u679c\u5c07\u559d\u6c7d\u6c34\u554f\u984c\u6539\u6210\u4e00\u822c\u7684\u554f\u984c:<\/strong><br \/> <strong> \u4f60\u8cb7\u4e86n \u74f6\u6c7d\u6c34\uff0c a \u7a7a\u74f6\u63db\u4e00\u74f6\u6c7d\u6c34\uff0cb\u74f6\u84cb\u63db\u4e5f\u53ef\u4e00\u74f6\u6c7d\u6c34\uff0c\u90a3\u7e3d\u5171\u53ef\u559d\u5e7e\u74f6?<\/strong><\/p>\n<p><strong>\u4f9d\u4e0a\u9762\u89e3\u8aaa\uff0c\u8d77\u9996\u662fn, <\/strong><strong>\u518d\u7b97\u4e0b\u53bb\u662f(1\/a + 1\/b) n ,<\/strong><br \/> <strong> \u518d\u7b97\u4e0b\u53bb\u662f(1\/a + 1\/b)* (1\/a + 1\/b) n, \u2026\u2026 \u7b49\u7b49<\/strong><\/p>\n<p><strong>\u7e3d\u5171\u7684\u8fd1\u4f3c\u7b54\u6848\u662f N\u2019 =n* 1\/(1-1\/a- 1\/b) = n* ab\/(ab-a-b).<\/strong><\/p>\n<p><strong>\u8b6c\u5982, \u7576 a=2, b=4 \u6642, N\u2019= 4n. \u7576 a = 3, b=6 \u6642, N\u2019 = 2n.<\/strong><\/p>\n<p><span style=\"color: #ff0000;\"><strong>8. \u5713\u6eff\u89e3\u8aaa &#8211; \u5b8c\u7d50\u7bc7<\/strong><\/span><\/p>\n<p><strong>\u5f9e\u9019\u500b\u7c21\u55ae\u7684&#8221;\u559d\u6c7d\u6c34\u7b97\u8853\u554f\u984c&#8221;\uff0c\u6211\u5011\u5b78\u5230\u4e86\u5f88\u591a\u7d93\u9a57\u3002\u4f46\u81f3\u4eca\u4ecd\u4e0d\u53ef\u8b02\u5713\u6eff\uff0c\u56e0\u70ba\u7b54\u6848\u88e1\uff0c\u90fd\u9084\u5269\u4e0b\u4e00\u500b\u74f6\u84cb\u53ca\u4e09\u500b\u7a7a\u74f6\u672a\u7528\uff0c\u6d6a\u8cbb\u4e86\u6c92\u7528\uff0c\u5be6\u5728\u53ef\u60dc\u3002\u540c\u6642\uff0c\u6211\u5011\u81f3\u6b64\uff0c\u4e5f\u6c92\u6709\u5713\u6eff\u89e3\u8aaa\u5982\u4f55\u6d88\u89e3&#8221;\u6574\u6578(\u91cf\u5b50\u5316\u3001quantization)\u5217\u8868&#8221;\u8207&#8221;\u5206\u6578(fraction)\u7b97\u6cd5&#8221;\u4e4b\u9593\u7684\u77db\u76fe\u3002<\/strong><\/p>\n<p><strong>\u5c0d\u6b64\uff0c\u592a\u6975\u5510\u5e2b\u7236\uff0c\u9001\u4f86\u4e86\u4e00\u500b\u65b0\u767c\u73fe\u3001\u65b0\u89e3\u8aaa\u3002\u4ed6\u8aaa\uff0c\u5269\u4e0b\u4e86\u4e00\u500b\u74f6\u84cb\u53ca\u4e09\u500b\u7a7a\u74f6\u672a\u7528\uff0c\u5be6\u5728\u592a\u53ef\u60dc\u4e86\u3002\u56e0\u6b64\u4ed6\u5047\u8a2d\uff0c\u5982\u679c\u80fd\u501f\u3001\u80fd\u9084\uff0c\u5230\u6700\u5f8c\u5c07\u6240\u5269\u7684\u74f6\u84cb\u53ca\u7a7a\u74f6\u90fd\u76e1\u91cf\u5229\u7528(\u5411\u9280\u884c\u8cb8\u6b3e\u5468\u8f49)\uff0c\u90a3\u9ebc\uff0c\u7e3d\u5171\u53ef\u559d\u5e7e\u74f6? (*\u5373\u74f6\u84cb\u8207\u7a7a\u74f6\u5747\u53ef\u501f\u4f86, \u4ee5\u63cd\u6578\u6d3e\u7528\u5834, \u4f46\u5fc5\u9808\u6709\u501f\u3001\u6709\u9084\uff0c\u4f46\u6700\u5f8c\u4e0d\u80fd\u7a7a\u6b20\u3002)<\/strong><\/p>\n<p><strong>\u7b54\u6848\u662f\u53ef\u518d\u591a\u559d\u4e94\u74f6\uff0c\u6c92\u5269\u4e0b\u74f6\u84cb\u53ca\u7a7a\u74f6\u3002\u56e0\u6b64\u7e3d\u5171\u53ef\u559d35 + 5 = 40\u74f6\u3002\u9019\u5c31\u662f\u4fe1\u5805\u4e0a\u6b21\u6240\u8aaa\u7684\uff0c\u7528\u4ee3\u6578\u65b9\u6cd5\u6240\u5f97\u5230\u7684\u7b54\u6848 4n = 4*10 = 40\u3002[\u9019\u5c31\u5713\u878d\u4e86 \u53e4\u5178\u529b\u5b78(classical mechanics) and \u91cf\u5b50\u7269\u7406 (quantum physics) \u4e4b\u9593\u7684\u77db\u76fe (conflict)]\u3002<\/strong><\/p>\n<p><strong>\u7b97\u6cd5\u5982\u4e0b: \u4f9d\u7167\u7b2c\u4e09\u7bc0\u7684\u5217\u8868\u89e3\u8aaa\uff0c\u7e7c\u7e8c\u4f9d\u4e0a\u9762\u6240\u8aaa\u7684\u65b0\u898f (\u53ef\u5411\u9280\u884c\u8cb8\u6b3e\u5468\u8f49)\uff0c\u7b97\u4e0b\u53bb:<\/strong><br \/> <strong> \u6c7d\u6c34\u00a0\u00a0\u00a0 \u7a7a\u74f6\u00a0\u00a0\u00a0\u00a0 \u74f6\u84cb\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u8a3b\u89e3<\/strong><br \/> <strong> 35\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u9019\u662f\u4e0a\u9762\u8cb710\u74f6\u6c7d\u6c34\u7684\u7b54\u6848<\/strong><\/p>\n<p><strong>1+1\u00a0\u00a0\u00a0\u00a0 \u00a0 -1+2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -1+2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u5411\u9280\u884c\u501f1\u500b\u74f6\u84cb\u53ca1\u500b\u7a7a\u74f6\u3002\u53ef\u591a\u63db2\u74f6\u6c7d\u6c34\u3002\u559d\u5b8c\u5f8c\uff0c\u591a\u4e862\u500b\u74f6\u84cb\u53ca2\u500b\u7a7a\u74f6\u3002\u9084\u9280\u884c\u6240\u6b20\u7684\u4e00\u500b\u74f6\u84cb\u53ca1\u500b\u7a7a\u74f6\uff0c\u73fe\u5728\u5c31\u5269\u4e0b1\u500b\u74f6\u84cb\u53ca1\u500b\u7a7a\u74f6\u3002<\/strong><\/p>\n<p><strong>1+0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -1+1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1+1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u518d\u5411\u9280\u884c\u501f1\u500b\u74f6\u84cb\u3002\u53ef\u591a\u63db1\u74f6\u6c7d\u6c34\u3002\u559d\u5b8c\u5f8c\uff0c\u591a\u4e861\u500b\u74f6\u84cb\u53ca1\u500b\u7a7a\u74f6\u3002\u9084\u9280\u884c\u6240\u6b20\u7684\u4e00\u500b\u74f6\u84cb\uff0c\u73fe\u5728\u53ea\u5269\u4e0b2\u500b\u7a7a\u74f6\u3002<\/strong><\/p>\n<p><strong>0+1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0+1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -2+1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u518d\u5411\u9280\u884c\u501f2\u500b\u7a7a\u74f6\u3002\u53ef\u591a\u63db1\u74f6\u6c7d\u6c34\u3002\u559d\u5b8c\u5f8c\uff0c\u591a\u4e861\u500b\u74f6\u84cb\u53ca1\u500b\u7a7a\u74f6\u3002\u73fe\u5728\u5c31\u5269\u4e0b1\u500b\u74f6\u84cb\u53ca\u6b20\u9280\u884c1\u500b\u7a7a\u74f6\u3002<\/strong><\/p>\n<p><strong>1+0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -1+1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -1+1\u00a0\u00a0\u00a0\u00a0\u00a0 \u518d\u5411\u9280\u884c\u501f1\u500b\u74f6\u84cb\u3002\u53ef\u591a\u63db1\u74f6\u6c7d\u6c34\u3002\u559d\u5b8c\u5f8c\uff0c\u591a\u4e861\u500b\u74f6\u84cb\u53ca1\u500b\u7a7a\u74f6\u3002\u9084\u9280\u884c\u6240\u6b20\u76841\u500b\u74f6\u84cb\u53ca1\u500b\u7a7a\u74f6\u3002\u73fe\u5728\u6c7d\u6c34\u559d\u98fd\u4e86\uff0c\u4e5f\u6c92\u5269\u4e0b\u74f6\u84cb\u53ca\u7a7a\u74f6!<\/strong><br \/> <strong> ____________________________________<\/strong><br \/> <strong> 40\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u7e3d\u7b54\u6848\u662f\uff0c\u4f9d\u7167\u65b0\u898f\u5247\uff0c\u5982\u679c\u8cb710\u74f6\u6c7d\u6c34\uff0c\u7e3d\u5171\u53ef\u559d40\u74f6\uff0c \u4e00\u5207\u7686\u7a7a\u3002<\/strong><\/p>\n<p><strong>\u9644\u8a3b: \u89e3\u7b54\u9019\u554f\u984c\uff0c\u5982\u679c\u525b\u958b\u59cb\u5148\u501f5\u500b\u74f6\u84cb\u53ca5\u500b\u7a7a\u74f6\uff0c\u5247\u53ef\u4e00\u6b21\u5b8c\u6210\u3002<\/strong><\/p>\n<p><strong>\u6c7d\u6c34\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u7a7a\u74f6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u74f6\u84cb\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u8a3b\u89e3<\/strong><br \/> <strong> 35\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u9019\u662f\u4e0a\u9762\u8cb710\u74f6\u6c7d\u6c34\u7684\u7b54\u6848<\/strong><\/p>\n<p><strong>3+2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -5+5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -5+5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u5411\u9280\u884c\u501f5\u500b\u74f6\u84cb\u53ca5\u500b\u7a7a\u74f6\u3002\u53ef\u591a\u63db5\u74f6\u6c7d\u6c34\u3002\u559d\u5b8c\u5f8c\uff0c\u591a\u4e865\u500b\u74f6\u84cb\u53ca5\u500b\u7a7a\u74f6\u3002\u9084\u9280\u884c\u6240\u6b20\u76845\u500b\u74f6\u84cb\u53ca5\u500b\u7a7a\u74f6\uff0c\u73fe\u5728\u6c7d\u6c34\u559d\u98fd\u4e86\uff0c\u4e5f\u6c92\u5269\u4e0b\u74f6\u84cb\u53ca\u7a7a\u74f6!<\/strong><br \/> ____________________________________<br \/> <strong> 40\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u7e3d\u7b54\u6848\u662f\uff0c\u4f9d\u7167\u65b0\u898f\u5247\uff0c\u5982\u679c\u8cb710\u74f6\u6c7d\u6c34\uff0c\u7e3d\u5171\u53ef\u559d40\u74f6\uff0c \u4e00\u5207\u7686\u7a7a\u3002<\/strong><\/p>\n<p><strong>\u9019\u5269\u9918\u554f\u984c\uff0c\u4e5f\u53ef\u53ef\u7528\u4ee3\u6578\u8a08\u7b97\u3002\u5269\u4e0b1\u500b\u74f6\u84cb\uff0c3\u500b\u7a7a\u74f6\u7684\u5229\u7528:<\/strong><\/p>\n<p><strong>First iteration: 1\/2 +3\/4 = 5\/4\uff0c<\/strong><br \/> <strong> Second iteration: 1\/2 *5\/4 +1\/4*5\/4 = (1\/2 +1\/4)* 5\/4 = 3\/4*5\/4<\/strong><br \/> <strong> Third iteration: 3\/4*(3\/4* 5\/4 )\uff0c etc&#8230;.<\/strong><\/p>\n<p><strong>Total extra sodas = (1 + 3\/4 + 3\/4*3\/4 + &#8230;&#8230;) * 5\/4 = [1\/(1-3\/4)]*5\/4 = 4 * 5\/4 = 5.<\/strong><\/p>\n<p><strong><strong>(\u5373\u7531\u4e0a\u9762\u516c\u5f0f\uff0cN\u2019 = n* ab\/(ab-a-b)\uff0c\u4ee3\u5165n = 5\/4, a=2, b=4, \u5c31\u53ef\u5f97 N&#8217; = 5. )<\/strong><br \/> <\/strong><\/p>\n<p><strong>\u9019\u5c31\u5713\u6eff\u89e3\u8aaa\uff0c\u70ba\u4f55\u7528\u4ee3\u6578\u65b9\u6cd5\uff0c\u7b54\u6848\u6703\u591a\u51fa5\u74f6\u7684\u539f\u56e0\u3002<\/strong><\/p>\n<p><span style=\"color: #ff0000;\"><strong>9. \u7d93\u9a57\u8207\u555f\u793a<\/strong><\/span><\/p>\n<p><strong>\u5982\u4e0a\u6240\u8aaa\uff0c\u89e3\u7b54\u4e00\u4e9b\u7c21\u55ae\u667a\u529b\u6e2c\u9a57\u554f\u984c\uff0c\u53ef\u8003\u9a57\u4e00\u4e0b\u81ea\u5df1\u7684\u8010\u529b\uff0c\u601d\u8003\u7684\u9748\u6d3b\u5ea6\uff0c\u5206\u6790\u80fd\u529b\uff0c\u4e5f\u53ef\u6e2c\u8a66\u81ea\u5df1\u5c0d\u4e00\u5207\u4e8b\u7269\u8a8d\u8b58\u7684\u6df1\u5ea6\u3001\u5ee3\u5ea6\u3002\u6240\u6709\u4e00\u5207\u554f \u984c\u8207\u89e3\u7b54\uff0c\u5176\u4e2d\u90fd\u96b1\u542b\u4e7e\u5764\u5999\u7fa9\u3002\u540c\u6642\uff0c\u8207\u540c\u9053\u3001\u670b\u53cb\u4e92\u76f8\u5207\u78cb\u3001\u8a0e\u8ad6\uff0c\u53ef\u4ee5\u6fc0\u767c\u65b0\u601d\u8def\u3001\u65b0\u65b9\u5411\u3002\u4e0d\u7ba1\u61c2\u4e0d\u61c2\uff0c\u6703\u4e0d\u6703\uff0c\u554f\u5c0d\u4e86\u554f\u984c\u4e5f\u662f\u4e00\u7a2e\u89e3\u7b54\u7684\u65b9\u5f0f\uff0c\u6240\u8b02\u554f \u984c\u8207\u7b54\u6848\u662f\u4e00\u9ad4\u7684\u5169\u9762\u3002\u4e92\u6fc0\u3001\u4e92\u767c\uff0c\u662f\u5b78\u7fd2\u589e\u9577\u7684\u5fc5\u8981\u689d\u4ef6\u3002<\/strong><\/p>\n<p><strong>\u5f9e\u89e3\u7b54\u9019\u554f\u984c\u7684\u6df1\u5165\u3001\u6dfa\u51fa\uff0c\u6211\u5011\u5f97\u5230\u4e0b\u9762\u7684\u7d93\u9a57\u8207\u555f\u793a:<\/strong><\/p>\n<p><strong>9.1 \u5982\u679c\u53ea\u60f3\u5f97\u5230\u7b54\u6848\uff0c\u5247\u65b9\u4fbf\u6709\u591a\u9580\uff0c\u689d\u689d\u5927\u8def\u901a\u7f85\u99ac\u3002<\/strong><\/p>\n<p><strong>9.2 \u5de5\u6b32\u5584\u5176\u4e8b\uff0c\u5fc5\u5148\u5229\u5176\u5668\u3002\u8981\u6709\u4e00\u500b\u842c\u5168\u7684\u89e3\u6c7a\u4e4b\u7b56\uff0c\u624d\u80fd\u589e\u5ee3\u898b\u8b58\u3002<\/strong><\/p>\n<p><strong>9.3 \u9047\u5230\u554f\u984c\uff0c\u61c9\u591a\u65b9\u9762\u89c0\u5bdf\uff0c\u7528\u4e0d\u540c\u65b9\u6cd5\u89e3\u7b54\uff0c\u5c31\u6703\u6709\u65b0\u7684\u4e86\u89e3\uff0c\u8207\u66f4\u6df1\u5165\u7684\u8a8d\u8b58\u3002<\/strong><\/p>\n<p><strong>9.4 \u4f46\u4e0d\u80fd\u5f97\u5c11\u70ba\u8db3\u3002\u61c9\u7576\u66f4\u52a0\u6df1\u5165\u4e86\u89e3\u3001\u63a8\u5ee3\u6240\u77e5\uff0c\u6478\u7d22\u51fa\u5176\u4e2d\u6240\u542b\u7684\u898f\u5f8b\u6cd5\u5247\u3002\u800c\u5f97\u5230\u4e00\u822c\u901a\u7528\u516c\u5f0f\uff0c\u6216\u8005\u8fd1\u4f3c\u516c\u5f0f\u3002<\/strong><\/p>\n<p><strong>9.5 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