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translation-block\">\u7136\u800c\uff0c\u5713\u4e5f\u53ef\u4ee5\u88ab\u8996\u70ba\u662f\u6d41\u6210\u4e00\u5708\u4e14\u50c5\u5305\u4f4f\u4e86\u4e00\u500b\u9ede\u7684\u6cb3\u3002\u65bc\u662f\u6211\u5011\u53ef\u4ee5\u628a\u4e0a\u9762\u7684\u63cf\u8ff0\u7c21\u5316\u6210\u5982\u4e0b\u578b\u5f0f\uff1a<b>\u6a39\u72c0\u7d50\u69cb\u4e2d\u7684\u6bcf\u4e00\u689d\u908a\uff0c\u7121\u8ad6\u662f\u4e0d\u662f\u8449\u908a\uff0c\u90fd\u5fc5\u9808\u4f54\u64da\u4e00\u689d\u5bec\u5ea6\u7b49\u65bc\u8a72\u908a\u9577\u5ea6\u7684\u6cb3\u3002<\/b><\/p>\n<p>\u540c\u6642\u4e5f\u6ce8\u610f\u5230\uff0c\u6cb3\u7684\u7528\u610f\u662f\u8981\u5206\u96e2\u958b\u5176\u5169\u5074\u7684\u9ede\uff0c\u4ee5\u78ba\u4fdd\u5b83\u5011\u6bcf\u4e00\u5c0d\u4e4b\u9593\u90fd\u6709\u8db3\u5920\u7684\u8ddd\u96e2\u3002\u4e5f\u5c31\u662f\u8aaa\uff0c\u7d66\u5b9a\u6a39\u72c0\u7d50\u69cb\u4e2d\u7684\u4e00\u689d\u908a\uff0c\u5c0d\u65bc\u6a39\u72c0\u7d50\u69cb\u4e0a\u4efb\u4f55\u4e00\u5c0d\u4f4d\u65bc\u8a72\u908a\u5169\u5074\u7684\u9802\u9ede\uff0c\u5b83\u5011\u5728\u7d19\u4e0a\u5c0d\u61c9\u7684\u5169\u500b\u9ede\u3001\u4e5f\u4e00\u5b9a\u5fc5\u9808\u88ab\u5206\u958b\u5230\u81f3\u5c11\u7b49\u65bc\u8a72\u908a\u9577\u5ea6\u7684\u8ddd\u96e2\u3002\u9019\u662f\u57fa\u65bc\u647a\u7d19\u7684\u57fa\u672c\u5b9a\u5f8b\uff1a\u5169\u9ede\u4e4b\u9593\u7684\u8ddd\u96e2\u5728\u7d19\u5f35\u7d93\u904e\u647a\u758a\u4e4b\u5f8c\u4e0d\u53ef\u80fd\u8b8a\u5927\u3002<\/p>\n<p class=\" translation-block\">\u4e8b\u5be6\u4e0a\u9019\u500b\u57fa\u672c\u5b9a\u5f8b\u9069\u7528\u65bc\u4efb\u4f55\u7684\u6a21\u578b\uff0c\u800c\u4e0d\u53ea\u662f\u55ae\u8ef8\u6a21\u578b\u3002\u8003\u616e\u4e00\u822c\u7684\u62bd\u8c61\u5f62\u4e2d\u7684\u4e00\u689d\u908a <code class=\"katex-inline\">\\overline{AB}<\/code> \uff08\u6216\u8005\u662f\u81ea\u6210\u4e00\u7dad\u5143\u4ef6\u3001\u6216\u8005\u662f\u4e8c\u7dad\u5143\u4ef6\u7684\u4e00\u689d\u908a\u3001\u6216\u662f\u4e09\u7dad\u5143\u4ef6\u7684\u4e00\u689d\u908a\uff09\u3002\u6211\u5011\u5b9a\u7fa9\u62bd\u8c61\u5f62\u4e2d\u4e00\u500b\u9802\u9ede\u7684<b>\u8907\u88fd<\/b>\u70ba\u7d19\u5f35\u4e0a\u7684\u4e00\u500b\u9ede\u3001\u8a72\u9ede\u6700\u7d42\u6703\u88ab\u647a\u5230\u8a72\u9802\u9ede\u5728\u57fa\u672c\u5f62\u4e2d\u7684\u5c0d\u61c9\u4f4d\u7f6e\u4e4b\u4e0a\u3002\u6839\u64da\u9019\u500b\u5b9a\u7fa9\u4ee5\u53ca\u57fa\u672c\u5b9a\u5f8b\uff0c\u9802\u9ede <code class=\"katex-inline\">A<\/code> \u7684\u6240\u6709\u8907\u88fd\u90fd\u61c9\u8a72\u8981\u548c\u9802\u9ede <code class=\"katex-inline\">B<\/code> \u7684\u8907\u88fd\u88ab\u5206\u958b\u81f3\u5c11 <code class=\"katex-inline\">\\ell:=\\lvert\\overline{AB}\\rvert<\/code> \u7684\u8ddd\u96e2\uff0c\u4e5f\u5c31\u662f\u8aaa\u5728\u7d19\u5f35\u4e0a\u61c9\u8a72\u8981\u6709\u4e00\u689d\u5bec\u5ea6\u70ba <code class=\"katex-inline\">\\ell<\/code> \u7684\u6cb3\u6d41\u7d93\u9019\u5169\u7d44\u9ede\u4e4b\u9593\u3002\u5c0d\u65bc <code class=\"katex-inline\">A<\/code> \u7684\u4e00\u500b\u8907\u88fd\u548c <code class=\"katex-inline\">B<\/code> \u7684\u4e00\u500b\u8907\u88fd\u3001\u4f7f\u5f97\u5b83\u5011\u4e4b\u9593\u7684\u8ddd\u96e2\u6070\u597d\u70ba <code class=\"katex-inline\">\\ell<\/code> \u8005\uff0c\u5f88\u660e\u986f\u5730\u5b83\u5011\u4e4b\u9593\u7684\u7dda\u6bb5\u5fc5\u7136\u6700\u7d42\u88ab\u647a\u5230\u6700\u7d42\u6a21\u578b\u7684 <code class=\"katex-inline\">\\overline{AB}<\/code> \u985e\u4f3c\u5730\uff0c\u6211\u5011\u5c31\u7a31\u9019\u500b\u7dda\u6bb5\u70ba <code class=\"katex-inline\">\\overline{AB}<\/code> \u7684<b>\u8907\u88fd<\/b>\u3002\u65bc\u662f\u5c0d\u61c9\u65bc <code class=\"katex-inline\">\\overline{AB}<\/code> \u908a\u7684\u6cb3\u5c31\u6703\u6d41\u7d93\u82e5\u5e72\u500b <code class=\"katex-inline\">\\overline{AB}<\/code> \u908a\u7684\u8907\u88fd\u3002\u4f46\u5b83\u8981\u5982\u4f55\u7d42\u7d50\uff1f<\/p>\n<p>\u5728\u5713\u6cb3\u5305\u88dd\u4e2d\uff0c\u4e00\u689d\u6cb3\u53ea\u6709\u5169\u7a2e\u53ef\u80fd\u7684\u7d42\u7d50\u65b9\u5f0f\uff1a\u8ff4\u6d41\u81f3\u81ea\u8eab\u6210\u4e00\u5708\u3001\u6216\u662f\u6d41\u5230\u7d19\u5f35\u7684\u539f\u908a\u3002\u5728\u7b2c\u4e00\u7a2e\u60c5\u6cc1\u7576\u4e2d\uff0c\u8a72\u6cb3\u6700\u7d42\u6703\u88ab\u647a\u6210\u4e00\u500b\u5982\u5716\u56db\u5de6\u908a\u6240\u793a\u7684\u7ba1\u72c0\u7d50\u69cb\uff08\u5176\u4e00\u5074\u53ef\u80fd\u6703\u6536\u7e2e\u6210\u4e00\u9ede\uff09\u3002\u5728\u7b2c\u4e8c\u7a2e\u60c5\u6cc1\u7576\u4e2d\uff0c\u647a\u597d\u7684\u6cb3\u6703\u6709\u4e00\u500b\u958b\uff0c\u5982\u5716\u56db\u7684\u53f3\u908a\u6240\u793a\u3002\u5c0d\u65bc ERM \u62bd\u8c61\u5f62\u4e2d\u7684\u4e00\u7dad\u908a\u4f86\u8aaa\uff0c\u9019\u4e9b\u90fd\u662f\u57fa\u672c\u4e0a\u4e00\u6a23\u7684\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/09\/image-1631837600059.png 2x\"><figcaption>\u5716\u56db\uff1a\u55ae\u8ef8\u6a21\u578b\u4e2d\u7684\u6cb3\u3002<\/figcaption><\/figure>\n<p>\u4e0d\u904e\u5c0d\u65bc\u4e8c\u4e09\u7dad\u5143\u4ef6\u7684\u908a\u4f86\u8aaa\uff0c\u4e8b\u60c5\u5c31\u7a0d\u5fae\u6709\u6240\u4e0d\u540c\u4e86\u3002\u5982\u679c\u4e00\u689d\u908a\u6240\u6d89\u53ca\u7684\u3001\u62bd\u8c61\u5f62\u4e2d\u7684\u9762\uff08\u6216\u8005\u81ea\u6210\u4e00\u500b\u4e8c\u7dad\u5143\u4ef6\u3001\u6216\u8005\u662f\u4e09\u7dad\u591a\u9762\u9ad4\u7684\u4e00\u500b\u9762\uff09\u53ea\u6709\u4e00\u500b\uff08\u4f8b\u5982\uff0c\u4e00\u500b\u958b\u8179\u52d5\u7269\u8179\u90e8\u4e0a\u7684\u908a\u3001\u6216\u662f\u9762\u5177\u7684\u908a\u7de3\uff09\uff0c\u90a3\u9ebc\u5176\u6cb3\u7684\u5176\u4e2d\u4e00\u7aef\u5c31\u5fc5\u9808\u9023\u63a5\u81f3\u8a72\u908a\u7684\u4e00\u500b\u8907\u88fd\u3001\u800c\u53e6\u4e00\u7aef\u5247\u5fc5\u9808\u6d41\u81f3\u539f\u908a\u3002\u6700\u7d42\u5b83\u6703\u647a\u6210\u50cf\u5716\u4e94\u5de6\u908a\u7684\u6a23\u5b50\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/09\/image-1631838640190.png 2x\"><figcaption>\u5716\u4e94\uff1a\u4e8c\u4e09\u7dad\u5143\u4ef6\u4e2d\u7684\u908a\u3002<\/figcaption><\/figure>\n<p class=\" translation-block\">\u5982\u679c\u90a3\u662f\u4e00\u500b\u7531\u5169\u500b\u9762\u6240\u5171\u7528\u7684\u908a\uff0c\u90a3\u9ebc\u5176\u6cb3\u5c31\u5fc5\u9808\u9023\u63a5\u5169\u500b\u9762\u7684\u8907\u88fd\uff0c\u4e26\u4e14\u8b8a\u6210\u50cf\u5716\u4e94\u53f3\u908a\u7684\u90a3\u6a23\u3002\u65bc\u662f\u5f88\u5408\u7406\u5730\u53ef\u4ee5\u5c07\u9762\u7684\u8907\u88fd\u7a31\u4e4b\u70ba<b>\u6e56<\/b>\uff0c\u56e0\u70ba\u90a3\u5c31\u662f\u73fe\u5be6\u4e16\u754c\u4e2d\u6cb3\u6240\u9023\u63a5\u7684\u6771\u897f\u3002\u6211\u540c\u6642\u4e5f\u5b9a\u7fa9<b>\u6d77<\/b>\u70ba\u7d19\u5f35\u7684\u539f\u908a\u52a0\u4e0a\u7d19\u5f35\u672a\u4f7f\u7528\u7684\u89d2\u843d\u5340\u57df\uff08\u901a\u5e38\u90a3\u4e9b\u5728\u6536\u5408\u7684\u7b2c\u4e00\u500b\u6b65\u9a5f\u4e2d\u5c31\u6703\u88ab\u647a\u5230\u5e95\u4e0b\u53bb\uff09\u3002\u73fe\u5728\u6211\u5011\u5c31\u53ef\u4ee5\u5c07 ERM \u7684\u6838\u5fc3\u60f3\u6cd5\u63cf\u8ff0\u5982\u4e0b\uff1a<\/p>\n<blockquote>\n<p>\u7d66\u4e88\u4e00\u500b\u6240\u6709\u7684\u9762\u90fd\u662f\u51f8\u591a\u908a\u5f62\u7684\u62bd\u8c61\u5f62\uff0c\u6bcf\u4e00\u500b\u9762\u90fd\u5fc5\u9808\u5c0d\u61c9\u65bc\u4e00\u500b\u5f62\u72c0\u5927\u5c0f\u76f8\u540c\u7684\u6e56\uff0c\u800c\u6bcf\u4e00\u689d\u908a\u90fd\u5fc5\u9808\u4f54\u64da\u4e00\u689d\u5bec\u5ea6\u7b49\u65bc\u8a72\u908a\u9577\u5ea6\u7684\u6cb3\uff08\u9577\u5ea6\u5247\u53ef\u4ee5\u70ba\u96f6\uff0c\u5982\u679c\u5b83\u7acb\u523b\u9023\u63a5\u8457\u5169\u500b\u6e56\u7684\u8a71\uff09\u3002\u9019\u4e9b\u6cb3\u6216\u8457\u8ff4\u6d41\u81f3\u81ea\u8eab\u3001\u9023\u63a5\u81f3\u6e56\u4e0a\u540c\u4e00\u689d\u908a\u7684\u8907\u88fd\uff0c\u6216\u8005\u6d41\u81f3\u6d77\u4e2d\u3002<\/p>\n<\/blockquote>\n<p>\uff08\u6211\u7a0d\u5f8c\u6703\u518d\u8a0e\u8ad6\u5230\u5177\u6709\u51f9\u591a\u908a\u5f62\u9762\u7684\u62bd\u8c61\u5f62\uff0c\u4f8b\u5982\u50cf\u5716\u4e8c\u7684\u8eca\u5b50\u5074\u9762\u90a3\u6a23\u3002\uff09<\/p>\n<p>\u7576\u6211\u9700\u8981\u5340\u5206 ERM \u4e2d\u7684\u6cb3\u548c\u6a39\u72c0\u65b9\u6cd5\u4e2d\u7684\u55ae\u8ef8\u6cb3\u6642\uff0c\u6211\u6703\u7279\u5225\u4f7f\u7528\u300c\u908a\u6cb3\u300d\u9019\u4e00\u5247\u7a31\u547c\u3002\u6211\u5011\u53ef\u80fd\u6703\u4e0d\u7981\u731c\u60f3\u908a\u6cb3\u7684\u884c\u70ba\u8868\u73fe\u8ddf\u55ae\u8ef8\u6cb3\u5f88\u985e\u4f3c\uff0c\u4f8b\u5982\u4e0d\u6703\u91cd\u758a\uff1b\u4f46\u5176\u5be6\u908a\u6cb3\u7684\u884c\u70ba\u6bd4\u8f03\u8907\u96dc\u4e00\u9ede\u3002\u4e0d\u904e\u5728\u6211\u5011\u8a0e\u8ad6\u5230\u90a3\u908a\u4e4b\u524d\uff0c\u8b93\u6211\u5011\u5148\u4f86\u770b\u4e00\u500b\u57fa\u672c\u7684\u4f8b\u5b50\u4f86\u611f\u53d7\u4e00\u4e0b ERM \u7684\u6838\u5fc3\u60f3\u6cd5\u3002<\/p>\n<h2>\u7b2c\u4e00\u500b\u4f8b\u5b50<\/h2>\n<p>\u56de\u5230\u5716\u4e09\u63cf\u7e6a\u7684\u623f\u5b50\u3002\u5982\u679c\u6c92\u6709\u65d7\u5b50\uff0c\u4e14\u4e26\u6c92\u6709\u8981\u6c42\u6211\u5011\u8981\u505a\u51fa\u623f\u5b50\u7684\u5e95\u9762\u7684\u8a71\uff0c\u6eff\u5bb9\u6613\u5c31\u53ef\u4ee5\u60f3\u51fa\u5982\u5716\u516d\u6240\u793a\u7684\u5c55\u958b\u5716\u7684\u3002\u9019\u500b\u6a21\u5f0f\u662f\u76f4\u63a5\u647a\u6210\u4e09\u7dad\u7684\u3001\u4e26\u975e\u53ef\u647a\u5e73\u7684\uff0c\u4e0d\u904e\u5176\u7d50\u69cb\u76f8\u7576\u5730\u55ae\u7d14\u76f4\u622a\u3001\u4e0d\u592a\u9700\u8981\u984d\u5916\u591a\u52a0\u89e3\u91cb\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/09\/image-1631852171224.png 3x\" class=\"lightbox\"><figcaption>\u5716\u516d\uff1a\u7c21\u55ae\u623f\u5c4b\u7684 CP\u3002<\/figcaption><\/figure>\n<p class=\" translation-block\">\u5373\u4f7f\u662f\u9019\u9ebc\u55ae\u7d14\u7684\u5c55\u958b\u5716\uff0c\u6211\u5011\u4e5f\u80fd\u89c0\u5bdf\u5230 ERM \u7684\u904b\u4f5c\u3002\u5728\u5716\u4e03\u7576\u4e2d\uff0c\u6e56\u662f\u756b\u6210\u85cd\u8272\u800c\u6cb3\u662f\u756b\u6210\u6c34\u85cd\u8272\u3002\u5269\u9918\u7684\u9ec3\u8272\u5340\u57df\u7a31\u70ba<b>\u9678\u5730<\/b>\uff0c\u5176\u5b9a\u7fa9\u70ba\u4efb\u4f55\u6c92\u6709\u88ab\u6c34\u57df\u8986\u84cb\u5230\u7684\u5340\u57df\u3002\u9ed1\u8272\u7dda\u689d\u662f\u6e56\u3001\u6cb3\u548c\u9678\u5730\u7684\u908a\u754c\uff0c\u800c\u7d05\u8272\u7dda\u689d\u5247\u662f\u810a\u7dda\u3002\u5f88\u81ea\u7136\u5730\uff0c\u6211\u5011\u6703\u628a\u9019\u6a23\u7684\u4e00\u7a2e\u63cf\u7e6a\u51fa\u9678\u5730\u548c\u6c34\u57df\u5206\u4f48\u7684\u5716\u7a31\u70ba<b>\u5730\u5716<\/b>\u3002\u89c0\u5bdf\u4e00\u4e0b\u62bd\u8c61\u5f62\u7576\u4e2d\u7684\u6bcf\u4e00\u689d\u908a\u90fd\u5c0d\u61c9\u5230\u4e86\u5730\u5716\u4e2d\u7684\u67d0\u4e00\u689d\u6cb3\uff08\u53ef\u80fd\u9577\u5ea6\u70ba\u96f6\uff09\u3001\u6cb3\u5728\u9047\u5230\u810a\u7dda\u7684\u6642\u5019\u6703\u6539\u8b8a\u65b9\u5411\u3001\u4ee5\u53ca\u5b83\u5011\u662f\u5982\u4f55\u9023\u63a5\u540c\u4e00\u689d\u908a\u7684\u4e0d\u540c\u8907\u88fd\u7684\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/09\/image-1631852975491.png 2x\" class=\"lightbox\"><figcaption>\u5716\u4e03\uff1a\u7c21\u55ae\u623f\u5c4b\u7684 ERM \u5730\u5716\u3002<\/figcaption><\/figure>\n<h2>\u6982\u5ff5\u5f0f\u5730\u5716<\/h2>\n<p class=\" translation-block\">\u73fe\u5728\u8b93\u6211\u5011\u4f86\u628a ERM 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class=\"lightbox\"><figcaption>\u5716\u516b\uff1a\u65d7\u5b50\u5c4b\u7684\u9802\u9ede\u547d\u540d\u3002<\/figcaption><\/figure>\n<p>\u6982\u5ff5\u5f0f\u5730\u5716\u7528\u7d19\u548c\u925b\u7b46\u5c31\u53ef\u4ee5\u756b\u4e86\uff0c\u4e26\u4e0d\u9700\u8981\u4efb\u4f55\u5de5\u5177\u6216\u8edf\u9ad4\u3002\u56e0\u6b64\uff0c\u5e95\u4e0b\u6211\u5c07\u6545\u610f\u4f7f\u7528\u6211\u7684\u624b\u7e6a\u5716\u7a3f\u4f86\u793a\u7bc4\u3002\u5716\u4e5d\u8ddf\u5716\u4e03\u662f\u4e00\u6a23\u7684\uff0c\u4e0d\u904e\u662f\u4ee5\u6982\u5ff5\u5f0f\u7684\u65b9\u5f0f\u63cf\u7e6a\u3002\u6211\u500b\u4eba\u5728\u624b\u7e6a\u5716\u4e2d\u4f7f\u7528\u96d9\u5411\u7bad\u982d\u4f86\u8868\u793a\u6cb3\u6d41\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1638956470052.png 3x\" class=\"lightbox\"><figcaption>\u5716\u4e5d\uff1a\u7c21\u55ae\u623f\u5c4b\u7684\u6982\u5ff5\u5f0f\u5730\u5716\u3002<\/figcaption><\/figure>\n<p class=\" translation-block\">\u518d\u4f86\uff0c\u8b93\u6211\u60f3\u50cf\u4e00\u4e0b\u5728\u9019\u500b\u8a2d\u8a08\u7576\u4e2d\u52a0\u5165\u4e00\u500b\u65d7\u5b50\uff0c\u7279\u5225\u662f\u8981\u52a0\u5728\u9ede <code class=\"katex-inline\">E<\/code> \u7684\u4f4d\u7f6e\u4e0a\u3002\u5f88\u986f\u7136\u5730\uff0c\u76ee\u524d\u5728\u9ede <code class=\"katex-inline\">E<\/code> \u9644\u8fd1\u4e26\u6c92\u6709\u4efb\u4f55\u7a7a\u9593\u53ef\u4ee5\u8b93\u6211\u5011\u52a0\u5165\u4efb\u4f55\u6771\u897f\u3002\u56e0\u6b64\uff0c\u8b93\u6211\u5011\u628a\u9019\u4e9b\u6e56\u7684\u8ddd\u96e2\u62c9\u958b\u4ee5\u9a30\u51fa\u4e00\u4e9b\u7a7a\u9593\u4f86\u3002\u4f46\u5728\u6211\u5011\u9019\u9ebc\u505a\u7684\u6642\u5019\uff0c\u8981\u8a18\u5f97\u908a\u7684\u8907\u88fd\u9084\u662f\u5f97\u7531\u6cb3\u4f86\u9023\u63a5\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1638956867565.png 4x\" 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translation-block\">\u5728\u5716\u5341\u7576\u4e2d\uff0c\u6211\u5011\u65cb\u8f49\u4e86\u5c0d\u61c9\u65bc\u5c4b\u9802\u7684\u6e56\uff0c\u4e26\u4e14\u5c07\u4e00\u9762\u7246\u79fb\u5230\u9060\u96e2\u5176\u5b83\u6e56\u7684\u5730\u65b9\u53bb\u3002\u5982\u6b64\u4fbf\u5728\u4e2d\u9593\u5275\u9020\u51fa\u4e86\u4e00\u4e9b\u7a7a\u9593\uff0c\u53ef\u80fd\u5920\u6211\u5011\u52a0\u5165\u4e00\u4e9b\u6771\u897f\u9032\u53bb\u3002\u4f46\u5f88\u5bb9\u6613\u770b\u5f97\u51fa\u4f86\u9019\u500b\u6982\u5ff5\u5f0f\u5730\u5716\u662f<b>\u975e\u5e38<\/b>\u6c92\u6709\u6548\u7387\u7684\u3002\u4e0d\u50c5\u73fe\u5728\u6574\u500b\u4f48\u5c40\u770b\u8d77\u4f86\u4e0d\u50cf\u6211\u5011\u6700\u611b\u7684\u6b63\u65b9\u5f62\u800c\u5012\u50cf\u662f\u500b\u9577\u65b9\u5f62\uff0c\u540c\u6642\u4e5f\u89c0\u5bdf\u5230\u90a3\u4e9b\u7528\u4f86\u5c07\u90a3\u9762\u7246\u9023\u63a5\u5230\u5176\u9918\u6e56\u7684\u5197\u9577\u6cb3\u6d41\u3002\u8981\u514b\u670d\u9019\u4e9b\u554f\u984c\uff0c\u95dc\u9375\u5c31\u5728\u65bc\u6ce8\u610f\u5230\u540c\u4e00\u689d\u908a\u7684\u5169\u500b\u8907\u88fd<b>\u672a\u5fc5<\/b>\u7e3d\u662f\u8981\u7531\u540c\u4e00\u689d\u4f55\u4f86\u9023\u63a5\u3002\u53d6\u800c\u4ee3\u4e4b\u5730\uff0c\u5b83\u5011\u53ef\u4ee5\u5404\u81ea\u9023\u63a5\u5230\u4e00\u689d\u6cb3\u3001\u4e14\u5169\u689d\u6cb3\u90fd\u6d41\u5230\u6d77\u88e1\u53bb\u3002\u5728\u5716\u5341\u4e00\u4e2d\uff0c\u6211\u5011\u5c07 <code class=\"katex-inline\">\\overline{EG}<\/code> \u6cb3\u548c <code class=\"katex-inline\">\\overline{GK}<\/code> \u6cb3\u62c6\u4e86\u958b\u4f86\uff0c\u800c\u73fe\u5728\u4e8b\u60c5\u5c31\u597d\u5f97\u591a\u4e86\u3002\u6574\u9ad4\u7684\u4f48\u5c40\u770b\u8d77\u4f86\u66f4\u50cf\u662f\u500b\u6b63\u65b9\u884c\u4e86\uff0c\u4e14\u6211\u5011\u4e5f\u6709\u66f4\u591a\u7684\u7a7a\u9593\u53ef\u4ee5\u4f86\u653e\u65d7\u5b50\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1638958050478.png 4x\" class=\"lightbox\"><figcaption>\u5716\u5341\u4e00\uff1a\u65d7\u5b50\u5c4b\u7684\u7b2c\u4e8c\u6b21\u5617\u8a66\u3002<\/figcaption><\/figure>\n<p class=\" translation-block\">\u73fe\u5728\uff0c\u6211\u5011\u77e5\u9053\u65d7\u7aff\u3001\u4e5f\u5c31\u662f <code class=\"katex-inline\">\\overline{CE}<\/code> 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srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1638964770736.png 4x\" class=\"lightbox\"><figcaption>\u5716\u5341\u4e09\uff1a\u7b2c\u4e8c\u6b21\u5617\u8a66\u65d7\u5b50\u3002<\/figcaption><\/figure>\n<p>\u5982\u4eca\u4e0d\u4f46\u6cb3\u6d41\u66f4\u52a0\u7dca\u5bc6\u4e86\uff0c\u6574\u9ad4\u4f48\u5c40\u770b\u8d77\u4f86\u4e5f\u80fd\u5920\u5f88\u7406\u60f3\u5730\u653e\u5230\u4e00\u500b\u5c0d\u89d2\u7dda\u653e\u7f6e\u7684\u6b63\u65b9\u5f62\u7576\u4e2d\u3002\u7167\u8457\u9019\u500b\u6982\u5ff5\u5f0f\u5730\u5716\u6709\u5f88\u591a\u65b9\u6cd5\u53ef\u4ee5\u9020\u51fa CP\uff0c\u800c\u5176\u4e2d\u4e00\u7a2e\u65b9\u6cd5\u5982\u5716\u5341\u56db\u6240\u793a\uff0c\u5176\u4e2d\u6211\u7a0d\u5fae\u8abf\u6574\u4e86\u4e00\u4e0b\u6bd4\u4f8b\u4ee5\u4fbf\u6240\u6709\u7684\u6771\u897f\u80fd\u5920\u5f88\u5b8c\u7f8e\u5730\u4ee5 22.5\u00b0 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class=\"lightbox\"><figcaption>\u5716\u5341\u4e94\uff1a\u5b8c\u6210\u7684\u65d7\u5b50\u5c4b\u3002<\/figcaption><\/figure>\n<p>\u9019\u908a\u7684\u91cd\u9ede\u4e0d\u662f\u5728\u65bc\u5982\u4f55\u628a\u5730\u5716\u8f49\u63db\u6210 CP \u7684\u7d30\u7bc0\uff0c\u800c\u662f\u5728\u65bc\u5c55\u793a\u6982\u5ff5\u5f0f\u5730\u5716\u53ef\u4ee5\u5982\u4f55\u5730\u5e6b\u52a9\u6211\u5011\u60f3\u50cf\u53ef\u80fd\u7684\u914d\u7f6e\u3001\u800c\u4e0d\u7528\u7169\u60f1\u4e00\u4e9b\u7d30\u7bc0\uff0c\u4ee5\u53ca\u6cb3\u7684\u6d41\u52d5\u6539\u8b8a\u5982\u4f55\u5730\u5f71\u97ff\u8457\u6211\u5011\u7684\u5305\u88dd\u3002<\/p>\n<h2>\u9678\u5730<\/h2>\n<p class=\" translation-block\">\u6bcf\u4e00\u689d\u6cb3\u90fd\u6709\u5169\u500b\u6cb3\u5cb8\uff08\u4e5f\u5c31\u662f\u5176\u5074\u908a\u7684\u908a\u754c\u7dda\uff09\uff0c\u5404\u81ea\u5c0d\u61c9\u65bc\u8a72\u6cb3\u6240\u5c0d\u61c9\u7684\u908a\u7684\u4e00\u500b\u7aef\u9ede\u3002\u5728\u5716\u5341\u56db\u4e2d\u6709\u82e5\u5e72\u584a\u7684\u9678\u5730\uff0c\u6bcf\u4e00\u584a\u9678\u5730\u90fd\u662f\u7531\u82e5\u5e72\u6cb3\u5cb8\u6240\u5305\u570d\u8457\u7684\uff0c\u800c\u6ce8\u610f\u5230\u5c0d\u65bc\u7279\u5b9a\u4e00\u584a\u9678\u5730\u4f86\u8aaa\uff0c\u5176\u5468\u570d\u7684\u6cb3\u5cb8\u90fd\u662f\u5c0d\u61c9\u65bc\u62bd\u8c61\u5f62\u7576\u4e2d\u7684\u540c\u4e00\u500b\u9802\u9ede\u3002\u4f8b\u5982\uff0c\u5716\u5341\u56db\u4e2d\u6700\u5927\u7684\u5169\u584a\u9678\u5730\u90fd\u662f\u7531 <code class=\"katex-inline\">E<\/code>-\u6cb3\u5cb8\u6240\u5305\u570d\u7684\u3002\u6b64\u6642\uff0c\u6211\u5011\u6703\u7a31\u4e4b\u70ba <code class=\"katex-inline\">E<\/code>-\u9678\u5730\u3002\u6982\u5ff5\u4e0a\u4f86\u8aaa\uff0c\u4e00\u584a\u9678\u5730\u4ee3\u8868\u8457\u90a3\u4e00\u500b\u9802\u9ede\u7684\u6536\u5408\uff0c\u4e5f\u5c31\u662f\u8aaa\uff0c\u5927\u81f4\u4e0a\uff0c\u8a72\u90e8\u4efd\u7684\u7d19\u5f35\u6700\u7d42\u6703\u88ab\u6536\u5408\u6210\u4e00\u500b\u5c0d\u61c9\u9802\u9ede\u9644\u8fd1\u7684\u4e00\u500b\u5c0f\u7d50\u69cb\u3002\u9019\u5c0d\u65bc\u525b\u624d\u63d0\u5230\u7684 <code class=\"katex-inline\">E<\/code>-\u9678\u5730\u4f86\u8aaa\u5c24\u5176\u5bb9\u6613\u89c0\u5bdf\u51fa\u4f86\uff0c\u53ea\u8981\u5982\u5716\u5341\u516d\u9019\u6a23\u6a19\u51fa\u6240\u6709\u9678\u5730\u5468\u570d\u7684\u9ede <code class=\"katex-inline\">E<\/code> \u8907\u88fd\u5373\u53ef\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639106034561.png 2x\" class=\"lightbox\"><figcaption class=\" translation-block\">\u5716\u5341\u516d\uff1a\u4e00\u584a <code class=\"katex-inline\">E<\/code>-\u9678\u5730\uff0c\u4e26\u6a19\u51fa\u4e86\u9ede <code class=\"katex-inline\">E<\/code> \u7684\u8907\u88fd\u3002<\/figcaption><\/figure>\n<p>\u9678\u5730\u5177\u6709\u5404\u7a2e\u4e0d\u540c\u7684\u5927\u5c0f\u8207\u540d\u7a31\u3002\u5f88\u5c0f\u7684\u9678\u5730\u7a31\u70ba\u5cf6\uff08\u4e00\u500b\u5e38\u898b\u7684\u4f8b\u5b50\u662f\u7bb1\u5f62\u8936\u4e2d\u4f7f\u7528\u7684\u4e00\u55ae\u4f4d\u585e\u5b50\uff09\uff0c\u5927\u584a\u7684\u9678\u5730\u7a31\u70ba\u5927\u9678\uff0c\u90a3\u770b\u4f3c\u662f\u6548\u7387\u7684\u6d6a\u8cbb\u4f46\u6709\u7684\u6642\u5019\u662f\u4e0d\u53ef\u907f\u514d\u7684\u3002\u4e00\u500b\u5927\u9678\u7684\u4f8b\u5b50\u53ef\u898b\u65bc\u5716\u5341\u4e03\u7684 12 \u9762\u9810\u5099\u57fa\u672c\u5f62\uff08\u90a3\u6709\u9ede\u50cf Montroll \u7684\u4e94\u9762\u65b9\u5f62\uff0c\u4f46\u6709\u8457 12 \u500b\u9762\uff1b\u5b83\u4f8b\u5982\u53ef\u4ee5\u88ab\u7528\u4f86\u647a\u51fa\u4e00\u500b\u5177\u6709\u4e5d\u500b\u982d\u7684\u7d19\u9db4\uff09\uff0c\u5176\u4e2d\u4e2d\u592e\u7684\u5927\u9678\u5c0d\u61c9\u65bc\u57fa\u672c\u5f62\u4e2d\u6700\u4e0a\u9762\u7684\u90a3\u500b\u9802\u9ede\u3002\u96d6\u7136\u6709\u8457\u9019\u500b\u5927\u9678\u7684\u5b58\u5728\uff0c\u9019\u500b\u4f48\u5c40\u5be6\u969b\u4e0a\u5df2\u7d93\u662f\u6700\u4f73\u7684\u4e86\uff0c\u53ea\u662f\u525b\u597d\u6211\u5011\u5c0d\u65bc\u9019\u500b\u62bd\u8c61\u5f62\u4f86\u8aaa\u5728\u90a3\u500b\u5730\u65b9\u4e0d\u9700\u8981\u9020\u51fa\u984d\u5916\u7684\u7279\u5fb5\u7f77\u4e86\u3002\u5c0d\u65bc\u50cf\u9019\u6a23\u7684\u6a21\u578b\uff0c\u4e3b\u8981\u7684\u6311\u6230\u5728\u65bc\u5982\u4f55\u5c07\u5927\u9678\u6536\u5408\u3001\u4f7f\u5f97\u7522\u751f\u7684\u7d50\u69cb\u76e1\u53ef\u80fd\u5730\u8584\u3001\u4f46\u540c\u6642\u53c8\u5c0f\u5230\u4e0d\u81f3\u65bc\u5e72\u64fe\u5230\u5176\u5b83\u7684\u7d50\u69cb\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639106285661.png 2x\" class=\"lightbox\"><figcaption>\u5716\u5341\u4e03\uff1a\u6211\u7684 12 \u9762\u9810\u5099\u57fa\u672c\u5f62\u7684\u7248\u672c\u3002<\/figcaption><\/figure>\n<p class=\" translation-block\">\u4f46\u5728 ERM \u4e2d\u6700\u91cd\u8981\u7684\u9678\u5730\u985e\u578b\u5247\u662f\u534a\u5cf6\uff0c\u5b83\u8ddf\u62bd\u8c61\u5f62\u4e2d\u7684\u51f9\u9ede\u7684\u6982\u5ff5\u6709\u5bc6\u5207\u7684\u95dc\u806f\u3002\u5728\u4e8c\u7dad\u7684\u60c5\u6cc1\u4e2d\uff0c\u6211\u5011\u8aaa\u62bd\u8c61\u5f62\u4e2d\u7684\u5169\u689d\u908a\u69cb\u6210\u4e86\u4e00\u500b\u51f9\u9ede\u3001\u5982\u679c\u5b83\u5011\u4e4b\u9593\u7684\u89d2\u5ea6\uff08\u6cbf\u8457\u6a21\u578b\u7684\u90a3\u4e00\u5074\uff09\u5927\u65bc 180\u00b0 \u7684\u8a71\u3002\uff08\u5728\u4e09\u7dad\u7684\u60c5\u6cc1\u4e2d\u7684\u5b9a\u7fa9\u6bd4\u8f03\u8907\u96dc\uff0c\u6211\u5011\u5728\u6b64\u7701\u7565\u3002\uff09\u5716\u5341\u516b\u662f\u4e00\u500b\u62bd\u8c61\u5f62\u7684\u4f8b\u5b50\u3001\u5176\u4e2d <code class=\"katex-inline\">\\overline{AB}<\/code> \u908a\u548c <code class=\"katex-inline\">\\overline{AC}<\/code> \u908a\u5728\u9802\u9ede <code class=\"katex-inline\">A<\/code> \u8655\u69cb\u6210\u4e86\u4e00\u500b\u51f9\u9ede\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639052725449.png 2x\" class=\"lightbox\"><figcaption>\u5716\u5341\u516b\uff1a\u51f9\u9ede\u7684\u4f8b\u5b50\u3002<\/figcaption><\/figure>\n<p>\u5728\u5927\u90e8\u5206\u7684\u60c5\u6cc1\u4e2d\uff0c\u7576\u62bd\u8c61\u5f62\u4e2d\u6709\u51f9\u9ede\u6642\uff0c\u6211\u5011\u96b1\u7d04\u5c31\u662f\u6307\u5b9a\u4e86\u90a3\u500b\u8ca0\u7a7a\u9593\u61c9\u8a72\u8981\u88ab\u5b8c\u5168\u5730\u6de8\u7a7a\u3001\u800c\u4e0d\u8a72\u6709\u984d\u5916\u7684\u5c64\u6b21\u88ab\u66b4\u9732\u51fa\u4f86\u3002\u6b64\u6642\uff0c\u5c0d\u61c9\u65bc\u5f62\u6210\u51f9\u9ede\u7684\u5169\u689d\u908a\u7684\u5169\u689d\u6cb3\u4e00\u5b9a\u4e0d\u80fd\u5171\u7528\u6cb3\u5cb8\uff08\u9019\u5169\u689d\u6cb3\u53ef\u4ee5\u5141\u8a31\u5728\u4e00\u9ede\u4e0a\u78b0\u89f8\uff0c\u4f46\u662f\u4e0d\u80fd\u5920\u6709\u4e00\u6bb5\u975e\u96f6\u9577\u5ea6\u7684\u5171\u7528\u6cb3\u5cb8\uff09\uff0c\u5426\u5247\u8981\u6de8\u7a7a\u8ca0\u7a7a\u9593\u5c31\u662f\u4e0d\u53ef\u80fd\u7684\uff08\u5047\u5b9a\u6211\u5011\u8981\u6c42\u6a21\u578b\u8981\u647a\u5e73\u7684\u8a71\uff09\u3001\u800c\u4e00\u5b9a\u6703\u6709\u984d\u5916\u7684\u5c64\u6b21\u88ab\u66b4\u9732\u51fa\u4f86\uff0c\u7121\u8ad6\u6211\u5011\u600e\u9ebc\u647a\u90fd\u4e00\u6a23\u3002\u7279\u5225\u662f\uff0c\u5982\u679c\u9019\u5169\u689d\u6cb3\u5e73\u884c\u5730\u6d41\u52d5\uff0c\u90a3\u9ebc\u6211\u5011\u4e00\u5b9a\u8981\u5728\u5b83\u5011\u4e2d\u9593\u4fdd\u7559\u4e00\u500b\u9593\u9694\u4ee5\u907f\u514d\u90a3\u4e9b\u6211\u7a31\u4e4b\u70ba\u9023\u7247\u7684\u5c64\u6b21\uff0c\u5176\u5b9a\u7fa9\u70ba\u4efb\u4f55\u4e0d\u5c6c\u65bc\u539f\u672c\u7684\u62bd\u8c61\u5f62\u4e2d\u7684\u53ef\u898b\u5c64\u6b21\u3002\u9019\u500b\u9593\u9694\u81ea\u7136\u6703\u5728\u5169\u689d\u6cb3\u4e4b\u9593\u5f62\u6210\u4e00\u500b\u72f9\u9577\u7684\u9678\u5730\uff0c\u4e5f\u5c31\u662f\u6211\u6240\u8b02\u7684\u534a\u5cf6\u3002<\/p>\n<p>\u4e00\u500b\u6709\u8da3\u7684\u554f\u984c\u662f\uff0c\u9019\u500b\u534a\u5cf6\u5fc5\u9808\u8981\u591a\u5bec\u624d\u5920\uff1f\u6216\u8a31\u5f88\u4ee4\u4eba\u9a5a\u8a1d\u7684\u662f\uff0c\u53ea\u8981\u6709\u4e00\u500b\u5bec\u5ea6\u975e\u96f6\u7684\u534a\u5cf6\uff0c\u4e0d\u7ba1\u591a\u7a84\uff0c\u7e3d\u662f\u5b58\u5728\u4e00\u500b CP \u53ef\u4ee5\u5c07\u5b83\u647a\u5e73\u4e14\u6c92\u6709\u9023\u7247\uff01\u7136\u800c\uff0c\u4f46\u66f8\u5728\u65bc\uff0c\u9019\u500b\u534a\u5cf6\u8d8a\u662f\u72f9\u7a84\uff0c\u5c31\u6703\u9700\u8981\u8d8a\u591a\u7684\u647a\u75d5\u624d\u80fd\u5920\u64fa\u812b\u9023\u7247\uff0c\u800c\u4e14\u96a8\u8457\u534a\u5cf6\u7684\u5bec\u5ea6\u8da8\u8fd1\u65bc\u96f6\u3001\u5c40\u90e8\u7684\u6a21\u578b\u539a\u5ea6\u53ef\u4ee5\u8da8\u8fd1\u65bc\u7121\u7aae\u5927\uff01\u6240\u4ee5\u96d6\u7136\u8f03\u7a84\u7684\u534a\u5cf6\u610f\u5473\u8457\u8f03\u597d\u7684\u6548\u7387\u3001\u4ea6\u5373\u6280\u8853\u4e0a\u4f86\u8aaa\u6a21\u578b\u76f8\u5c0d\u65bc\u7d19\u5f35\u9762\u7a4d\u4f86\u8aaa\u7684\u5e73\u5747\u539a\u5ea6\u6703\u6bd4\u8f03\u5c11\uff0c\u53ef\u662f\u5728\u9019\u908a\u4e00\u76f4\u8ffd\u6c42\u6548\u7387\u53cd\u800c\u6703\u5c0e\u81f4\u5c40\u90e8\u8b8a\u5f97\u66f4\u539a\uff01<\/p>\n<p class=\" translation-block\">\u6240\u4ee5\u4e00\u822c\u4f86\u8aaa\uff0c\u6211\u5011\u6703\u8b93\u534a\u5cf6\u4e0d\u8981\u592a\u5bec\u4ee5\u514d\u6d6a\u8cbb\u4e86\u592a\u591a\u6548\u7387\u3001\u4f46\u4e5f\u4e0d\u6703\u8b93\u5b83\u592a\u7a84\u4ee5\u514d\u592a\u904e\u96e3\u647a\u3002\u5c0d\u65bc\u7bb1\u5f62\u8936\u4f86\u8aaa\uff0c\u5408\u7406\u5730\u5c31\u662f\u63a1\u7528\u4e00\u55ae\u4f4d\u5bec\u7684\u534a\u5cf6 <sup id=\"fnref1:p\"><a href=\"p\" class=\"footnote-ref\" target=\"_self\">1<\/a><\/sup>\u3002\u4f5c\u70ba\u7bc4\u4f8b\uff0c\u8003\u616e\u5c07\u5716\u5341\u516b\u7684\u62bd\u8c61\u5f62\u5728 8 \u00d7 8 \u7684\u683c\u5b50\u4e2d\u7528\u7bb1\u5f62\u8936\u4f86\u647a\u51fa\u3002\u65e2\u7136 <code class=\"katex-inline\">\\lvert\\overline{AB}\\rvert=3<\/code> \u4e14 <code class=\"katex-inline\">\\lvert\\overline{AC}\\rvert=3<\/code>\uff0c\u4e4d\u770b\u4e4b\u4e0b\u4f3c\u4e4e\u8b93\u9019\u5169\u689d\u908a\u9023\u63a5\u81f3\u5bec\u5ea6\u70ba 3 \u7684\u6cb3\u3001\u4e26\u4e14\u8b93 <code class=\"katex-inline\">B<\/code> \u9ede\u8907\u88fd\u548c <code class=\"katex-inline\">C<\/code> \u9ede\u7684\u8907\u88fd\u7dad\u6301 6 \u7684\u8ddd\u96e2\u5c31\u8db3\u5920\u4e86\uff1b\u4f46\u4e8b\u5be6\u4e0a\u9019\u662f\u4e0d\u5920\u7684\uff0c\u56e0\u70ba <code class=\"katex-inline\">A<\/code> \u9ede\u662f\u4e00\u500b\u51f9\u9ede\u3002\u56e0\u6b64\u6211\u5011\u5728\u5b83\u5011\u4e2d\u9593\u52a0\u4e0a\u4e86\u4e00\u500b\u4e00\u55ae\u4f4d\u7684\u534a\u5cf6\uff0c\u800c\u85c9\u7531\u5728 <code class=\"katex-inline\">B<\/code> \u548c <code class=\"katex-inline\">C<\/code>\u4e4b\u9593\u4f7f\u7528\u7562\u6c0f\u4f38\u5c55\uff0c8 \u00d7 8 \u7684\u7d19\u5f35\u525b\u597d\u6709\u8457\u8db3\u5920\u7684\u7a7a\u9593\u53ef\u4ee5\u653e\u5f97\u4e0b\u5b83\u5011\u5168\u90e8\u3002\u5176\u7d50\u679c\u5982\u5716\u5341\u4e5d\u6240\u793a\u3002\u6ce8\u610f\u5230\u534a\u5cf6\u901a\u5e38\u90fd\u6703\u5728 CP \u4e2d\u88ab\u586b\u5165 Z \u5b57\u5f62\u7684\u647a\u75d5\uff08\u4f46\u4e5f\u6709\u53ef\u80fd\u56e0\u70ba\u647a\u75d5\u8b8a\u5316\u800c\u6c92\u6709\uff09\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639266669550.png 2x\" class=\"lightbox\"><figcaption>\u5716\u5341\u4e5d\uff1a\u5716\u5341\u516b\u7684\u62bd\u8c61\u5f62\u7684\u5730\u5716\u548c CP\u3002\u6df1\u85cd\u8272\u5340\u57df\u70ba\u6d77\u3002<\/figcaption><\/figure>\n<p class=\" translation-block\">\u5728\u6211\u7684<a href=\"https:\/\/origami.abstreamace.com\/zh\/2021\/09\/15\/sauwastika-2021\/\" target=\"_self\">\u534d\u5b57\u7b26\u865f<\/a>\uff08\u5982\u5716\u4e8c\u5341\u6240\u793a\uff09\u4e2d\uff0c\u53ef\u4ee5\u770b\u5230\u62bd\u8c61\u5f62\u4e2d\u516b\u500b\u6a19\u793a\u51fa\u4f86\u7684\u51f9\u9ede\u6703\u5c0d\u61c9\u5230\u5730\u5716\u4e2d\u7684\u516b\u500b\u534a\u5cf6\u3002\u540c\u6642\u4e5f\u6ce8\u610f\u5230\u5728\u56db\u500b\u5730\u65b9\u4e2d\u3001\u69cb\u6210\u51f9\u9ede\u7684\u5169\u689d\u6cb3\u5728\u4e00\u500b\u89d2\u843d\u4e0a\u6709\u78b0\u5230\uff0c\u9019\u5982\u540c\u524d\u8ff0\u662f\u53ef\u4ee5\u5141\u8a31\u7684\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639109193409.png\" class=\"lightbox\"><figcaption>\u5716\u4e8c\u5341\uff1a\u534d\u5b57\u7b26\u865f\u7684\u62bd\u8c61\u5f62\u3001\u5730\u5716\u8207 CP\u3002<\/figcaption><\/figure>\n<h2>\u91cd\u758a\u6cb3\u8207\u7011\u5e03<\/h2>\n<p>\u6216\u8a31\u6bd4\u534a\u5cf6\u66f4\u52a0\u4ee4\u4eba\u610f\u5916\u7684\u662f\uff0c\u5728\u53e6\u5916\u4e00\u4e9b\u60c5\u6cc1\u4e2d\uff0c\u908a\u6cb3\u5176\u5be6\u53ef\u4ee5\u91cd\u758a\u3002\u9019\u7576\u62bd\u8c61\u5f62\u4e2d\u7684\u5143\u4ef6\u90fd\u662f\u4e00\u7dad\u7684\u6642\u5019\uff08\u4ea6\u5373\u62bd\u8c61\u5f62\u662f\u4e00\u500b\u6a39\u72c0\u7d50\u69cb\uff09\u662f\u4e0d\u53ef\u80fd\u7684\uff0c\u4f46\u53ea\u8981\u5b83\u5177\u6709\u4e8c\u7dad\u6216\u4e09\u7dad\u7684\u5143\u4ef6\uff0c\u6211\u5011\u5c31\u6709\u6a5f\u6703\u53ef\u4ee5\u5229\u7528\u9019\u4e9b\u5143\u4ef6\u7684\u5167\u90e8\u4f86\u8b93\u9019\u4e9b\u6cb3\u91cd\u758a\u4ee5\u589e\u9032\u6548\u7387\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639360039841.png\" class=\"lightbox\"><figcaption>\u5716\u4e8c\u5341\u4e00\uff1a\u91cd\u758a\u6cb3\u7684\u4f8b\u5b50\u3002<\/figcaption><\/figure>\n<p class=\" translation-block\">\u4e00\u500b\u4f8b\u5b50\u5982\u5716\u4e8c\u5341\u4e00\u6240\u793a\u3002\u5728\u9019\u908a\u6211\u5011\u60f3\u8981\u5728 8 \u00d7 8 \u7684\u683c\u5b50\u4e0a\u9020\u51fa\u5de6\u908a\u7684\u62bd\u8c61\u5f62\u3002\u85c9\u7531\u6211\u5011\u524d\u9762\u5c0d\u65bc\u51f9\u9ede\u7684\u7406\u89e3\uff0c\u6211\u5011\u53ef\u4ee5\u5f88\u5feb\u5730\u78ba\u8a8d\u51fa\u914d\u7f6e\u9019\u4e9b\u6e56\u7684\u552f\u4e00\u65b9\u6cd5\uff08\u5047\u8a2d\u4e00\u5207\u90fd\u5fc5\u9808\u7167\u8457\u7bb1\u5f62\u8936\u7684\u6846\u67b6\u8d70\uff09\u5c31\u662f\u628a\u5b83\u5011\u653e\u5728\u5982\u4e2d\u9593\u7684\u5716\u6240\u793a\u7684\u4f4d\u7f6e\u4e4b\u4e0a\u3002\u7136\u800c\uff0c\u9019\u9ebc\u4e00\u4f86 <code class=\"katex-inline\">\\overline{AB}<\/code> \u6cb3\u548c <code class=\"katex-inline\">\\overline{AC}<\/code> \u6cb3\u770b\u8d77\u4f86\u4f3c\u4e4e\u662f\u5728\u9670\u5f71\u8655\u91cd\u758a\u4e86\u3002\u5947\u5999\u7684\u662f\uff0c\u9019\u6a23\u7684\u91cd\u758a\u5176\u5be6\u662f\u5408\u6cd5\u7684\uff0c\u56e0\u70ba <code class=\"katex-inline\">B<\/code> \u9ede\u548c <code class=\"katex-inline\">C<\/code> \u9ede\u4e4b\u9593\uff08\u6cbf\u8457\u6a21\u578b\u4e0a\u8d70\u7684\uff09\u6700\u77ed\u8ddd\u96e2\u4e26\u4e0d\u662f 4\u3001\u800c\u662f <code class=\"katex-inline\">\\sqrt{8}<\/code>\uff0c\u56e0\u6b64\u53ea\u8981 <code class=\"katex-inline\">B<\/code> \u9ede\u548c <code class=\"katex-inline\">C<\/code> \u9ede\u7684\u8907\u88fd\u4e4b\u9593\u4fdd\u6301\u8457\u90a3\u6a23\u7684\u8ddd\u96e2\uff0c\u6cb3\u7684\u91cd\u758a\u662f\u5b8c\u5168\u6c92\u554f\u984c\u7684\u3002\u6700\u7d42\u7684 CP \u5982\u53f3\u5716\u6240\u793a\u3002<\/p>\n<p>\u63db\u53e5\u8a71\u8aaa\uff0c\u5982\u679c\u5169\u689d\u908a\u4e4b\u9593\u7684\u89d2\u5ea6\u5c0f\u65bc 180\u00b0\uff0c\u90a3\u9ebc\u8996\u89d2\u5ea6\u800c\u5b9a\uff0c\u5b83\u5011\u4e4b\u9593\u5c31\u53ef\u4ee5\u88ab\u5141\u8a31\u4e0d\u540c\u7a0b\u5ea6\u7684\u91cd\u758a\u3002\u9019\u4ef6\u4e8b\u5f88\u503c\u5f97\u8a18\u5728\u5fc3\u4e0a\uff0c\u56e0\u70ba\u5b83\u5e38\u5e38\u80fd\u5e6b\u52a9\u6211\u5011\u5728\u72f9\u7a84\u7684\u7a7a\u9593\u4e2d\u585e\u5165\u6cb3\u6d41\u3002\u7136\u800c\uff0c\u9019\u4e5f\u53ef\u80fd\u4f7f\u5f97\u5730\u5716\u8b8a\u5f97\u96e3\u4ee5\u95b1\u8b80\uff0c\u56e0\u70ba\u4efb\u4f55\u90e8\u4efd\u7684\u7d19\u5f35\u90fd\u6709\u53ef\u80fd\u6703\u6709\u8d85\u904e\u4e00\u7a2e\u7684\u8eab\u4efd\u3002\u5728\u67d0\u4e9b\u5176\u6cc1\u4e2d\uff0c\u53ef\u4ee5\u7c21\u55ae\u5730\u50cf\u6211\u5011\u5728\u5716\u4e8c\u5341\u4e00\u4e2d\u505a\u7684\u90a3\u6a23\u7528\u9670\u5f71\u4f86\u8868\u793a\u91cd\u758a\u3001\u800c\u4e0d\u81f3\u65bc\u9020\u6210\u592a\u591a\u7591\u60d1\uff1b\u4f46\u5728\u53e6\u5916\u7684\u4e00\u4e9b\u60c5\u6cc1\u4e2d\uff0c\u91cd\u758a\u6709\u53ef\u80fd\u6703\u53c8\u5927\u53c8\u8907\u96dc\uff0c\u751a\u81f3\u6709\u53ef\u80fd\u6703\u51fa\u73fe\u6cb3\u8ddf\u534a\u5cf6\u91cd\u758a\u7684\u60c5\u6cc1\uff08\u770b\u6211\u5011\u600e\u9ebc\u53bb\u89e3\u8b80\u90a3\u90e8\u4efd\u7684\u7d19\u5f35\u8eab\u4efd\u800c\u5b9a\uff09\u3002<\/p>\n<p>\u70ba\u4e86\u8b93\u8907\u96dc\u7684\u91cd\u758a\u5bb9\u6613\u88ab\u7406\u89e3\uff0c\u6211\u63d0\u51fa\u4e86\u7011\u5e03\u7684\u6982\u5ff5\u3002\u7011\u5e03\u662f\u5730\u5716\u4e0a\u7684\u4e00\u689d\u7dda\uff0c\u5b83\u5177\u6709\u8457\u5947\u5999\u7684\u6027\u8cea\u3001\u53ef\u4ee5\u8b93\u4e00\u689d\u6cb3\u5f9e\u4e00\u500b\u5730\u65b9\u77ac\u9593\u79fb\u52d5\u5230\u53e6\u5916\u4e00\u500b\u5730\u65b9\u3002\u793a\u7bc4\u8d77\u898b\uff0c\u8003\u616e\u5716\u4e8c\u5341\u4e8c\u5de6\u908a\u7684\u62bd\u8c61\u5f62\uff0c\u4ee5\u53ca\u4e2d\u9593\u7684\u90a3\u500b\u53ef\u4ee5\u5c07\u5b83\u647a\u5e73\u7684 CP\uff08\u5c0d\u65bc\u9019\u500b\u62bd\u8c61\u5f62\u4f86\u8aaa\uff0c\u9019\u500b CP \u4f3c\u4e4e\u6548\u7387\u4e26\u975e\u6700\u4f73\u7684\uff0c\u4e0d\u904e\u9019\u662f\u56e0\u70ba\u9019\u500b\u4f8b\u5b50\u662f\u5f9e\u4e00\u500b\u66f4\u5927\u7684\u8a2d\u8a08\u4e2d\u64f7\u53d6\u51fa\u4f86\u7684\uff0c\u800c\u5728\u5916\u9762\u6709\u8457\u5176\u5b83\u7684\u8003\u91cf\uff09\u3002\u9019\u500b CP \u80cc\u5f8c\u7684 ERM \u5730\u5716\u61c9\u8a72\u9577\u4ec0\u9ebc\u6a23\u5b50\uff1f<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639214778099.png\" class=\"lightbox\"><figcaption>\u5716\u4e8c\u5341\u4e8c\uff1a\u793a\u7bc4\u7011\u5e03\u7684\u7bc4\u4f8b\u3002<\/figcaption><\/figure>\n<p class=\" translation-block\">\u62bd\u8c61\u5f62\u4e2d\u5927\u90e8\u4efd\u7684\u908a\u90fd\u5f88\u5bb9\u6613\u5c0d\u61c9\u5230\u53f3\u908a\u6240\u793a\u7684\u90e8\u4efd\u5b8c\u6210\u5730\u5716\u4e4b\u4e0a\uff0c\u9664\u4e86 <code class=\"katex-inline\">\\overline{AB}<\/code> \u908a\u548c <code class=\"katex-inline\">\\overline{AC}<\/code> \u908a\u4e4b\u5916\u3002\u6211\u5011\u53ef\u80fd\u6703\u731c\u60f3\u5b83\u5011\u5c0d\u61c9\u5230\u5169\u689d\u6cb3\u3001\u5b83\u5011\u4ee5\u67d0\u7a2e\u65b9\u5f0f\u6d41\u7d93\u53f3\u908a\u6240\u793a\u7684\u554f\u865f\u5340\u57df\u3001\u4e26\u9023\u63a5\u8457\u90a3\u5169\u689d\u908a\u7684\u8907\u88fd\u3002\u4f46\u5982\u679c\u6211\u5011\u4ed4\u7d30\u6aa2\u8996\u5f9e\u9019\u500b CP \u647a\u51fa\u7684\u5be6\u969b\u7d50\u69cb\uff0c\u6211\u5011\u6703\u767c\u73fe\u9019\u5169\u689d\u908a\u7684\u8907\u88fd\u5404\u81ea\u90fd\u9023\u51fa\u4e86\u4e00\u689d\u6d41\u5230\u6d77\u88e1\u53bb\u7684\u6cb3\uff0c\u4e26\u4e14\u5728\u6d41\u52d5\u904e\u7a0b\u4e2d\u4ee5\u5716\u4e8c\u5341\u4e09\u5de6\u908a\u6240\u793a\u7684\u8907\u96dc\u65b9\u5f0f\u8ddf\u53e6\u5916\u7684\u6cb3\u91cd\u758a\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639215619393.png 1.5x\" class=\"lightbox\"><figcaption>\u5716\u4e8c\u5341\u4e09\uff1a\u91cd\u758a\u8868\u793a\u6cd5 vs \u7011\u5e03\u8868\u793a\u6cd5\u3002<\/figcaption><\/figure>\n<p class=\" translation-block\">\u9019\u6a23\u7684\u8868\u793a\u65b9\u5f0f\u660e\u986f\u5730\u5f88\u5dee\uff0c\u56e0\u70ba\u5b83\u9700\u8981\u7528\u5f88\u591a\u7684\u7bad\u982d\u4f86\u8868\u793a\u51fa\u6cb3\u5230\u5e95\u662f\u600e\u9ebc\u6d41\u52d5\u7684\u3002\u76f8\u8f03\u4e4b\u4e0b\uff0c\u53f3\u908a\u7684\u7011\u5e03\u8868\u793a\u6cd5\u5c31\u4e7e\u6de8\u5f97\u591a\u3001\u4e14\u4e5f\u5bb9\u6613\u7406\u89e3\u3002\u5728\u9019\u5f35\u5716\u4e2d\uff0c\u7011\u5e03\u4ee5\u7d2b\u8272\u7dda\u689d\u8868\u793a\u3002\u6211\u5011\u60f3\u50cf\u7576\u6cb3\u9032\u5165\u7011\u5e03\u7684\u5176\u4e2d\u4e00\u90e8\u4efd\u6642\uff0c\u5b83\u6703\u88ab\u50b3\u9001\u5230\u7011\u5e03\u7684\u53e6\u5916\u4e00\u7aef\uff0c\u9019\u9ebc\u4e00\u4f86 <code class=\"katex-inline\">\\overline{AB}<\/code> \u908a\u548c <code class=\"katex-inline\">\\overline{AC}<\/code> 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   <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639218447387.png 1.5x\" class=\"lightbox\"><figcaption>\u5716\u4e8c\u5341\u56db\uff1a\u80cc\u9762\u6e56\u3002<\/figcaption><\/figure>\n<p>\u5728\u5716\u4e8c\u5341\u56db\u5de6\u908a\u7684\u62bd\u8c61\u5f62\u4e2d\uff0c\u5176\u4e2d\u4e00\u500b\u9762\u770b\u8d77\u4f86\u662f\u51f9\u7684\uff0c\u4f46\u5982\u679c\u6211\u5011\u53bb\u60f3\u50cf\u3001\u5b83\u5176\u5be6\u6709\u4e00\u500b\u96b1\u85cf\u7684\u90e8\u4efd\u662f\u5728\u53e6\u5916\u4e00\u500b\u9762\u7684\u4e0b\u5c64\uff08\u5982\u865b\u7dda\u6240\u793a\uff1b\u901a\u5e38\u6211\u4e0d\u6703\u5728\u62bd\u8c61\u5f62\u4e2d\u628a\u865b\u7dda\u756b\u51fa\u4f86\uff0c\u9019\u908a\u53ea\u662f\u89e3\u8aaa\u65b9\u4fbf\uff09\uff0c\u90a3\u9ebc\u6211\u5011\u5c31\u53ef\u4ee5\u628a\u5b83\u7576\u6210\u662f\u51f8\u7684\u9762\u4e26\u4e14\u4e00\u6a23\u7167\u8457 ERM 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target=\"_self\">2<\/a><\/sup>\u3002\u56e0\u6b64\u53d6\u800c\u4ee3\u4e4b\u5730\uff0c\u6211\u5011\u5c07\u80cc\u9762\u5206\u89e3\u6210\u6cbc\u6fa4\uff0c\u5982\u6df1\u7da0\u8272\u5340\u57df\u6240\u793a\u3002\u9019\u500b\u5340\u57df\u6700\u7d42\u6703\u88ab\u647a\u6210\u8a72\u80cc\u9762\uff0c\u4e0a\u9762\u6709\u4e00\u9053\u7e2b\u7dda\u3002\u5c0d\u61c9\u7684 CP \u5982\u53f3\u5716\u6240\u793a\u3002<\/p>\n<p>\u88dc\u5145\u4e00\u63d0\uff0c\u5404\u4f4d\u53ef\u80fd\u6703\u6ce8\u610f\u5230\u5716\u4e8c\u5341\u4e00\u7684\u91cd\u758a\u6cb3\u4e5f\u53ef\u4ee5\u7528\u80cc\u9762\u6e56\u4f86\u91cd\u65b0\u8a6e\u91cb\u3002\u78ba\u5be6\u5728\u5f88\u591a\u60c5\u6cc1\u4e2d\uff0c\u540c\u6a23\u7684 CP \u53ef\u4ee5\u88ab\u8a6e\u91cb\u6210\u4e0d\u540c\u7684\u6a23\u5b50\u3002\u4e4b\u6240\u4ee5\u6211\u500b\u4eba\u6703\u9078\u64c7\u4f7f\u7528\u91cd\u758a\u6cb3\u7684\u8a6e\u91cb\uff0c\u662f\u56e0\u70ba\u5c0d\u6211\u4f86\u8aaa\uff0c\u90a3\u6a23\u7684\u80cc\u9762\u6e56\u4e26\u6c92\u6709\u88ab\u62bd\u8c61\u5f62\u6697\u793a\u51fa\u4f86\uff0c\u800c\u6211\u4e0d\u60f3\u8b93\u4eba\u6709\u4e00\u7a2e\u300c\u975e\u5f97\u8981\u80fd\u9810\u898b\u8a72\u80cc\u9762\u6e56\u7684\u4f7f\u7528\u624d\u80fd\u5920\u60f3\u51fa\u90a3\u6a23\u7684\u5730\u5716\u300d\u7684\u932f\u8aa4\u5370\u8c61\u3002<\/p>\n<h2>\u61c9\u7528<\/h2>\n<p>\u7576\u6211\u5011\u8a66\u8457\u5728\u8a2d\u8a08\u4e2d\u5957\u7528 ERM \u7684\u6642\u5019\uff0c\u7b2c\u4e00\u500b\u6b65\u9a5f\u662f\u756b\u51fa\u62bd\u8c61\u5f62\u3002\u5728\u67d0\u4e9b\u60c5\u6cc1\u4e2d\uff08\u4f8b\u5982\u7576\u5957\u7528\u5230  22.5\u00b0 \u7cfb\u7d71\u7684\u6642\u5019\uff09\u62bd\u8c61\u5f62\u4e5f\u53ef\u662f\u6982\u5ff5\u5f0f\u7684\uff0c\u4f46\u662f\u5c0d\u65bc\u50cf\u7bb1\u5f62\u8936\u6216\u516d\u89d2\u8936\u9019\u7a2e\u683c\u5b50\u7cfb\u7d71\u4f86\u8aaa\uff0c\u6bd4\u8f03\u7406\u60f3\u7684\u662f\u7cbe\u78ba\u5b9a\u7fa9\u7684\u62bd\u8c61\u5f62\u3002\u70ba\u4e86\u8981\u627e\u51fa\u62bd\u8c61\u5f62\u7684\u7406\u60f3\u5c3a\u5ea6\uff0c\u6211\u5e38\u5e38\u6703\u7528\u526a\u5200\u548c\u9ecf\u81a0\u505a\u51fa\u7d19\u96d5\u6a21\u578b\u3001\u4f86\u78ba\u8a8d\u57fa\u672c\u5f62\u53ef\u4ee5\u88ab\u5851\u5f62\u6210\u70ba\u5c0d\u8ab2\u984c\u4f86\u8aaa\u6bd4\u4f8b\u6070\u7576\u7684\u6a21\u578b\u3002\u6211\u5011\u540c\u6642\u4e5f\u9700\u8981\u6307\u5b9a\u62bd\u8c61\u5f62\u4e2d\u6240\u6709\u96b1\u85cf\u7684\u7d30\u7bc0\uff0c\u4f8b\u5982\u80cc\u9762\u548c\u91cd\u758a\u5206\u652f\u7684\u6578\u91cf\u7b49\u7b49\u3002<\/p>\n<p>\u7b2c\u4e8c\u500b\u6b65\u9a5f\u662f\u898f\u5283\u4f48\u5c40\uff0c\u5148\u5f9e\u756b\u51fa\u6982\u5ff5\u5f0f\u5730\u5716\u958b\u59cb\u3002\u4e00\u65e6\u4e00\u500b\u6982\u5ff5\u5f0f\u5730\u5716\u770b\u8d77\u4f86\u597d\u50cf\u53ef\u884c\u4e86\uff0c\u6211\u5011\u5c31\u53ef\u4ee5\u958b\u59cb\u5617\u8a66\u7cbe\u78ba\u5730\u5c07\u5143\u7d20\u914d\u7f6e\u5728\u6211\u5011\u7684\u7d19\u5f35\u4e0a\u3002\u6e56\u7684\u7cbe\u78ba\u4f4d\u7f6e\u53ef\u4ee5\u85c9\u7531\u8003\u616e\u9802\u9ede\u4e4b\u9593\u7684\u5fc5\u8981\u8ddd\u96e2\uff08\u4e5f\u5c31\u662f\u53bb\u8003\u616e\u5f9e\u4e00\u500b\u9802\u9ede\u6cbf\u8457\u6a21\u578b\u4e0a\u8d70\u5230\u53e6\u5916\u4e00\u500b\u9802\u9ede\u8981\u591a\u9060\u3001\u518d\u52a0\u4e0a\u5c0d\u61c9\u65bc\u51f9\u9ede\u7684\u984d\u5916\u5fc5\u8981\u8ddd\u96e2\uff09\u4f86\u6c7a\u5b9a\u51fa\u4f86\u3002\u5728\u7bb1\u5f62\u8936\u7576\u4e2d\uff0c\u6211\u5011\u4e5f\u5fc5\u9808\u8981\u8003\u616e\u5947\u5076\u6027\u539f\u7406\u7684\u6548\u61c9\uff0c\u8a72\u539f\u7406\u8aaa\u7684\u662f\uff0c\u540c\u4e00\u500b\u9802\u9ede\u7684\u4efb\u5169\u500b\u8907\u88fd\u4e4b\u9593\u7684\u8a08\u7a0b\u8eca\u8ddd\u96e2\u5fc5\u9808\u662f\u5076\u6578\uff08\u5426\u5247\u5c31\u6703\u5fc5\u9808\u7528\u4e0a\u534a\u55ae\u4f4d\u7684\u7d50\u69cb\uff0c\u9019\u6709\u53ef\u80fd\u4e0d\u662f\u6a02\u898b\u7684\u4e8b\uff09\u3002<\/p>\n<p>\u6700\u5f8c\u4e00\u500b\u6b65\u9a5f\u5c31\u662f\u5c07\u5730\u5716\u8f49\u63db\u6210\u5c71\u647a\u8c37\u647a\u7684 CP\uff0c\u800c\u9019\u90e8\u4efd\u7684\u7d30\u7bc0\u8d85\u904e\u672c\u7c21\u4ecb\u7684\u7bc7\u5e45\u4e86\u3002\u4e0d\u904e\u81f3\u5c11\u5c0d\u65bc\u7bb1\u5f62\u8936\u4f86\u8aaa\uff0c\u5f88\u591a\u7684\u647a\u75d5\u6a21\u5f0f\u90fd\u662f\u70ba\u4eba\u719f\u77e5\u7684\uff0c\u4f8b\u5982\u6cb3\u6703\u8b8a\u6210\u9032\u9032\u51fa\u51fa\u7684\u8936\u7247\u3001\u800c\u534a\u5cf6\u901a\u5e38\u6703\u6709 Z \u5b57\u5f62\u7684\u647a\u75d5\u3002\u5982\u679c\u4e0d\u78ba\u5b9a\u7684\u8a71\uff0c\u6211\u5011\u7e3d\u662f\u53ef\u4ee5\u5c0d\u9078\u64c7\u6027\u7684\u5c40\u90e8\u9032\u884c\u8a66\u647a\u3001\u4e26\u4e14\u7528\u8a66\u8aa4\u6cd5\u4f86\u627e\u51fa\u53ef\u884c\u7684 CP\u3002\u800c\u5728\u6700\u4e00\u822c\u7684\u60c5\u6cc1\u4e2d\uff0c\u7e3d\u662f\u6709\u500b\u53ef\u4ee5\u628a ERM \u5730\u5716\u8f49\u63db\u6210 CP \u7684\u901a\u7528\u6f14\u7b97\u6cd5\u53ef\u4ee5\u7576\u4f5c\u6700\u5f8c\u4e00\u62db\uff0c\u8a72\u6f14\u7b97\u6cd5\u8ddf\u8218\u77e5\u5b8f\u63d0\u51fa\u7684 Origamizer \u6f14\u7b97\u6cd5\u975e\u5e38\u4e4b\u76f8\u4f3c\uff08\u518d\u52a0\u4e0a\u4e00\u4e9b\u984d\u5916\u7684\u6771\u897f\uff09\u3002<\/p>\n<p class=\" translation-block\">\u6211\u81ea\u5f9e 2014 \u5e74\u958b\u59cb\u5c31\u4f7f\u7528 ERM \u5728\u6211\u81ea\u5df1\u7684\u8a2d\u8a08\u4e4b\u4e0a\uff0c\u5f9e\u4e2d\u7b49\u8907\u96dc\u5ea6\u5230\u8d85\u8907\u96dc\u7cfb\u6a21\u578b\u90fd\u6709\u3002\u5176\u4e2d\u4e00\u500b ERM \u7528\u5f97\u6700\u51f6\u7684\u6a21\u578b\u662f\u6211\u7684<a href=\"https:\/\/origami.abstreamace.com\/zh\/2021\/05\/30\/cat\/\" target=\"_self\">\u99b4\u5316\u77ed\u6bdb\u8c93<\/a>\uff0c\u5176\u5730\u5716\u548c\u62bd\u8c61\u5f62\u5982\u5716\u4e8c\u5341\u4e03\u6240\u793a\u3002\u8a72\u6a21\u578b\u7528\u5230\u4e86\u6240\u6709\u6211\u5011\u76ee\u524d\u70ba\u6b62\u4ecb\u7d39\u5230\u7684\u6771\u897f\uff1a\u51f9\u9ede\u8655\u4f7f\u7528\u534a\u5cf6\uff08\u5176\u4e2d\u6709\u4e00\u4e9b\u662f\u5169\u55ae\u4f4d\u5bec\u7684\uff0c\u56e0\u70ba\u5176\u9644\u8fd1\u7684\u8936\u7247\u7528\u7684\u662f\u5169\u55ae\u4f4d\u5bec\u3001\u6216\u662f\u57fa\u65bc\u7b56\u7565\u6027\u7684\u7406\u7531\uff09\u3001\u80cc\u9762\u6e56\u8ddf\u6cbc\u6fa4\u3001\u91cd\u758a\u6cb3\u548c\u7011\u5e03\uff0c\u4ee5\u53ca\u8033\u6735\u8655\u4f7f\u7528\u4e86\u4e09\u7dad\u7d50\u69cb\u3002\u5404\u4f4d\u53ef\u4ee5\u5c07\u5b83\u548c\u5716\u4e8c\u5341\u516b\u7684 CP \u8207\u647a\u597d\u7684\u57fa\u672c\u5f62\u505a\u6bd4\u8f03\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639267924155.png\" class=\"lightbox\"><figcaption>\u5716\u4e8c\u5341\u4e03\uff1a\u99b4\u5316\u77ed\u6bdb\u8c93\u7684\u5730\u5716\u8207\u62bd\u8c61\u5f62\u3002<\/figcaption><\/figure>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/05\/CP-3d.png\" class=\"lightbox\"><figcaption>\u5716\u4e8c\u5341\u516b\uff1a\u99b4\u5316\u77ed\u6bdb\u8c93\u7684 CP \u8207\u647a\u597d\u7684\u57fa\u672c\u5f62\u3002<\/figcaption><\/figure>\n<p class=\" translation-block\">\u53e6\u4e00\u500b\u6211\u6700\u8fd1\u7684 ERM \u8a2d\u8a08\u662f<a href=\"https:\/\/origami.abstreamace.com\/zh\/2021\/12\/07\/angelfish-2021\/\" target=\"_self\">\u795e\u4ed9\u9b5a<\/a>\uff0c\u5982\u5716\u4e8c\u5341\u4e5d\u6240\u793a\u3002\u5728\u9019\u500b\u8a2d\u8a08\u7576\u4e2d\uff0c\u62bd\u8c61\u5f62\u6709\u8457\u66f4\u591a\u4e0d\u662f\u8ddf\u683c\u5b50\u6b63\u4ea4\u7684\u908a\uff0c\u9019\u4f7f\u5f97\u5b83\u9700\u8981\u66f4\u8907\u96dc\u5730\u898f\u5283\u80cc\u9762\u6e56\u624d\u80fd\u8b93\u5b83\u9069\u7528\u7bb1\u5f62\u8936\u7684\u6846\u67b6\u3002\u5e78\u597d\u6709 ERM \u7684\u5a01\u529b\uff0c\u6211\u5f97\u4ee5\u5728\u6700\u7d42\u7684\u6a21\u578b\u4e2d\u53d6\u5f97\u975e\u5e38\u4ee4\u4eba\u6eff\u610f\u7684\u6bd4\u4f8b\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639270662180.png\" class=\"lightbox\"><figcaption>\u5716\u4e8c\u5341\u4e5d\uff1a\u795e\u4ed9\u9b5a\u7684\u5730\u5716\u8207\u57fa\u672c\u5f62\u3002<\/figcaption><\/figure>\n<p>\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u5728\u5716\u4e8c\u5341\u4e03\u8207\u4e8c\u5341\u4e5d\u4e2d\uff0c\u6709\u8a31\u591a\u5730\u65b9\u90fd\u662f\u7528\u4e86\u7c21\u5316\u904e\u7684\u8868\u793a\u6cd5\u7684\u3002\u4f8b\u5982\uff0c\u9760\u8fd1\u5716\u4e8c\u5341\u4e5d\u7684\u5de6\u4e0a\u89d2\u8655\uff0c\u6280\u8853\u4e0a\u4f86\u8aaa\u90a3\u5176\u5be6\u61c9\u8a72\u662f\u5169\u689d\u91cd\u758a\u7684\u6cb3\uff0c\u5982\u5716\u4e09\u5341\u7684\u5de6\u908a\u6240\u793a\u3002\u5c0d\u6211\u4f86\u8aaa\u90a3\u6709\u9ede\u4e0d\u5fc5\u8981\u5730\u592a\u7cbe\u78ba\u4e86\uff0c\u6240\u4ee5\u6211\u5c07\u5b83\u5011\u5448\u73fe\u6210\u55ae\u4e00\u4e00\u689d\u6db5\u84cb\u4e86\u57fa\u672c\u5f62\u4e2d\u5169\u689d\u908a\u7684\u6cb3\u3002<\/p>\n<figure>\n    <img srcset=\"https:\/\/origami.abstreamace.com\/wp-content\/uploads\/2021\/12\/image-1639367554791.png 3x\" class=\"lightbox\"><figcaption>\u5716\u4e09\u5341\uff1a\u5716\u4e8c\u5341\u4e5d\u5de6\u4e0a\u89d2\u7684\u7cbe\u78ba\u5730\u5716\u4ee5\u53ca\u7c21\u5316\u5730\u5716\u3002<\/figcaption><\/figure>\n<h2>\u7d50\u8a9e<\/h2>\n<p>\u9019\u908a\u7c21\u4ecb\u5c31\u5230\u6b64\u70ba\u6b62\u3002\u6211\u60f3\u611f\u8b1d\u6240\u6709\u90a3\u4e9b\u5e6b\u52a9\u6211\u63d0\u7149 ERM \u7684\u60f3\u6cd5\u8207\u5448\u73fe\u7684\u670b\u53cb\u5011\uff0c\u5c24\u5176\u662f Drew Heskett \u548c Brandon Wong\u3002Drew \u4e5f\u5df2\u7d93\u5f88\u6210\u529f\u5730\u5c07 ERM \u5957\u7528\u81f3\u82e5\u5e72\u4ed6\u7684\u8a2d\u8a08\u4e4b\u4e0a\u3002\u6211\u5e0c\u671b ERM \u80fd\u555f\u767c\u66f4\u591a\u8a2d\u8a08\u8005\u4f86\u5275\u9020\u51fa\u904e\u53bb\u5728\u55ae\u8ef8\u7bc4\u5f0f\u4e4b\u4e0b\u96e3\u4ee5\u9054\u6210\u6216\u4e0d\u53ef\u80fd\u9054\u6210\u7684\u8a2d\u8a08\u3002<\/p>\n<div class=\"footnotes\">\n<hr \/>\n<ol>\n<li id=\"fn:p\">\n<p>\u5728\u67d0\u4e9b\u60c5\u6cc1\u4e2d\uff0c\u57fa\u65bc\u6211\u5011\u7b49\u4e00\u4e0b\u6703\u63d0\u5230\u7684\u3001\u7bb1\u5f62\u8936\u4e2d\u7684\u5947\u5076\u6027\u539f\u7406\uff0c\u6709\u53ef\u80fd\u6703\u9700\u8981\u7528\u4e0a\u5169\u55ae\u4f4d\u5bec\u7684\u534a\u5cf6\u3002<a href=\"#fnref1:p\" rev=\"footnote\" class=\"footnote-backref\">&#8617;<\/a><\/p>\n<\/li>\n<li id=\"fn:noroom\">\n<p>\u81f3\u5c11\uff0c\u6cbf\u8457\u683c\u5b50\u653e\u662f\u4e0d\u884c\u7684\u3002\u5728\u9019\u500b\u4f8b\u5b50\u4e2d\uff0c\u5176\u5be6\u662f\u6709\u8fa6\u6cd5\u5c07\u80cc\u9762\u6e56\u65cb\u8f49\u6210\u4e00\u500b\u6709\u9ede\u96a8\u6a5f\u7684\u89d2\u5ea6\u4f86\u8b93\u5b83\u653e\u5165\u7a7a\u9593\u4e4b\u4e2d\uff0c\u7136\u5f8c\u6211\u5011\u53ef\u4ee5\u7e7c\u7e8c\u7528\u901a\u7528\u6f14\u7b97\u6cd5\u4f86\u9020\u51fa CP\uff0c\u53ea\u662f\u9019\u6a23\u5c0e\u81f4\u7684 CP \u6703\u5f88\u96e3\u9810\u647a\u3002<a href=\"#fnref1:noroom\" rev=\"footnote\" class=\"footnote-backref\">&#8617;<\/a><\/p>\n<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u6700\u8fd1\u6211\u5728 Discord \u4e0a\u9762\u8ddf\u4e00\u4e9b\u647a\u7d19\u540c\u597d\u8a0e\u8ad6\u4e86\u6211\u7684\u908a\u6cb3\u6cd5\uff08ERM\uff09\u4e26\u5f97\u5230\u4e86\u4e00\u4e9b\u4e0d\u932f\u7684\u56de\u61c9\uff0c\u751a\u81f3\u958b\u59cb\u6709\u770b\u5230\u82e5\u5e72\u6210\u529f\u7684\u8a2d\u8a08\u5f9e\u4e2d\u6d6e\u51fa\uff0c\u56e0\u6b64\u6211\u60f3\u8a72\u662f\u6642\u5019\u4f86\u7c21\u55ae\u5beb\u4e00\u4e0b\u9019\u500b\u4e3b\u984c\u7684\u6587\u7ae0\u4e86\u3002\u6211\u5728\u9019\u908a\u7684\u76ee\u6a19\u662f\u8981\u5feb\u901f\u7d66\u500b\u6982\u5ff5\u95dc\u65bc ERM \u5230\u5e95\u662f\u5728\u8b1b\u4ec0\u9ebc [...]<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[32],"class_list":["post-755","post","type-post","status-publish","format-standard","hentry","category-essays","tag-erm"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Geography of Origami - A Brief Introduction to the Edge-River Method - Tsai Origami<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/origami.abstreamace.com\/zh\/2021\/12\/12\/geography-of-origami-a-brief-introduction-to-the-edge-river-method\/\" \/>\n<meta property=\"og:locale\" content=\"zh_TW\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Geography of Origami - 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