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S. M. Coxeter\u5c0d\u6578\u767e\u682a\u5411\u65e5\u8475\u9032\u884c\u4e86\u9a57\u8b49\uff0c\u767c\u73fe\u9019\u7a2e\u6a21\u5f0f\u5177\u6709\u9a5a\u4eba\u7684\u4e00\u81f4\u6027\u3002\u96a8\u8457\u5411\u65e5\u8475\u6578\u91cf\u7684\u589e\u5927\uff0c\u6bcf\u500b\u65b9\u5411\u4e0a\u87ba\u65cb\u7dda\u7684\u6578\u91cf\u4e4b\u6bd4\u63a5\u8fd1\u9ec3\u91d1\u5206\u5272\u7387\uff08\u7d041.618\uff09\uff0c\u9019\u662f\u6211\u5011\u5c07\u5728\u5f8c\u6587\u6df1\u5165\u63a2\u8a0e\u7684\u6578\u5b78\u5e38\u6578\u3002<\/p>\n\n\n\n<p>\u4f46\u70ba\u4ec0\u9ebc\u662f\u9019\u7a2e\u7279\u6b8a\u7684\u6392\u5217\u65b9\u5f0f\u5462\uff1f\u7b54\u6848\u662f\u70ba\u4e86\u5be6\u73fe\u6700\u4f73\u7684\u7a2e\u5b50\u5806\u7a4d\u6548\u7387\u3002\u96a8\u8457\u5411\u65e5\u8475\u7684\u751f\u9577\uff0c\u65b0\u7684\u7a2e\u5b50\u5f9e\u4e2d\u5fc3\u840c\u767c\u4e26\u5411\u5916\u4f38\u5c55\u3002\u6bcf\u7c92\u7a2e\u5b50\u90fd\u9700\u8981\u627e\u5230\u6700\u4f73\u4f4d\u7f6e\uff0c\u4ee5\u4fbf\u6700\u5927\u9650\u5ea6\u5730\u7372\u53d6\u990a\u5206\u3001\u6c34\u5206\uff0c\u6700\u7d42\u7372\u5f97\u5145\u8db3\u7684\u967d\u5149\u9032\u884c\u767c\u82bd\u3002\u6590\u6ce2\u90a3\u5951\u87ba\u65cb\u6392\u5217\u78ba\u4fdd\u7a2e\u5b50\u7dca\u5bc6\u6392\u5217\uff0c\u6700\u5927\u9650\u5ea6\u5730\u6e1b\u5c11\u7a7a\u9593\u6d6a\u8cbb\uff0c\u540c\u6642\u4fdd\u6301\u76f8\u5c0d\u5747\u52fb\u7684\u9593\u8ddd\u3002<\/p>\n\n\n\n<p>\u96fb\u8166\u6a21\u578b\u8b49\u5be6\u4e86\u81ea\u7136\u754c\u900f\u904e\u6f14\u5316\u767c\u73fe\u7684\u771f\u7406\uff1a\u6590\u6ce2\u90a3\u5951\u87ba\u65cb\u6a21\u5f0f\u662f\u6700\u6709\u6548\u7684\u6392\u5217\u65b9\u5f0f\u3002\u4efb\u4f55\u5176\u4ed6\u65cb\u8f49\u89d2\u5ea6\u90fd\u6703\u9020\u6210\u7a7a\u9699\u6216\u7c07\u72c0\u5206\u4f48\uff0c\u5f9e\u800c\u6e1b\u5c11\u82b1\u982d\u6240\u80fd\u5bb9\u7d0d\u7684\u7a2e\u5b50\u6578\u91cf\u3002\u5411\u65e5\u8475\u900f\u904e\u6f14\u5316\u300c\u89e3\u6c7a\u300d\u4e86\u4e00\u500b\u8907\u96dc\u7684\u6700\u4f73\u5316\u554f\u984c\uff0c\u800c\u6578\u5b78\u5bb6\u76f4\u5230\u4e8c\u5341\u4e16\u7d00\u624d\u5b8c\u5168\u7406\u89e3\u9019\u500b\u554f\u984c\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u5411\u65e5\u8475\u4e4b\u5916\uff1a\u6590\u6ce2\u90a3\u5951\u87ba\u65cb\u7121\u6240\u4e0d\u5728<\/strong><\/h3>\n\n\n\n<p>\u5411\u65e5\u8475\u4e26\u975e\u552f\u4e00\u904b\u7528\u6590\u6ce2\u90a3\u5951\u87ba\u65cb\u7dda\u7684\u690d\u7269\u3002\u677e\u679c\u4e5f\u5448\u73fe\u51fa\u540c\u6a23\u7684\u6a21\u5f0f\uff0d\u6578\u4e00\u6578\u5305\u88f9\u677e\u679c\u7684\u9c57\u7247\u87ba\u65cb\u7dda\uff0c\u4f60\u6703\u767c\u73fe\u9023\u7e8c\u7684\u6590\u6ce2\u90a3\u5951\u6578\u5217\uff0c\u901a\u5e38\u662f5\u548c8\uff0c\u62168\u548c13\uff0c\u53d6\u6c7a\u65bc\u677e\u679c\u7684\u7a2e\u985e\u3002\u9cf3\u68a8\u5247\u5c55\u73fe\u51fa\u4e09\u7d44\u6590\u6ce2\u90a3\u5951\u87ba\u65cb\u7dda\uff1a5\u30018\u548c13\uff0c\u5b83\u5011\u4ee5\u516d\u89d2\u5f62\u82de\u7247\u7684\u5c0d\u89d2\u7dda\u5f62\u5f0f\u5448\u73fe\u3002<\/p>\n\n\n\n<p>\u96db\u83ca\u82b1\u7684\u4e2d\u5fc3\uff08\u7ba1\u72c0\u5c0f\u82b1\uff0c\u8207\u908a\u7de3\u7684\u820c\u72c0\u82b1\u74e3\u76f8\u5c0d\uff09\u6392\u5217\u6210\u6590\u6ce2\u90a3\u5951\u87ba\u65cb\u7dda\uff0c\u901a\u5e38\u662f 21 \u548c 34\uff0c\u6216 34 \u548c 55\u3002\u7f85\u99ac\u82b1\u6930\u83dc\u2014\u2014\u56b4\u683c\u4f86\u8aaa\u662f\u82b1\u857e\u2014\u2014\u5448\u73fe\u51fa\u81ea\u7136\u754c\u6700\u5f15\u4eba\u6ce8\u76ee\u7684\u6590\u6ce2\u90a3\u5951\u6392\u5217\u4e4b\u4e00\uff0c\u5728\u591a\u500b\u5c3a\u5ea6\u4e0a\u90fd\u53ef\u4ee5\u770b\u5230\u87ba\u65cb\u7dda\uff0c\u5448\u73fe\u51fa\u985e\u4f3c\u5206\u5f62\u7684\u5716\u6848\u3002<\/p>\n\n\n\n<p>\u751a\u81f3\u9023\u8449\u7247\u570d\u7e5e\u8396\u5e79\u7684\u6392\u5217\u65b9\u5f0f\uff08\u8449\u5e8f\uff09\u4e5f\u9075\u5faa\u6590\u6ce2\u90a3\u5951\u6578\u5217\u3002\u5f9e\u5e95\u90e8\u89c0\u5bdf\u73ab\u7470\u8396\u6216\u9b06\u679c\uff0c\u4f60\u6703\u767c\u73fe\u8449\u7247\u6216\u9c57\u7247\u4e26\u975e\u6392\u5217\u6210\u7b46\u76f4\u7684\u5782\u76f4\u7dda\uff0c\u800c\u662f\u87ba\u65cb\u72c0\u5730\u570d\u7e5e\u8396\u5e79\u3002\u6578\u4e00\u6578\u7e5e\u8396\u5e79\u65cb\u8f49\u4e86\u591a\u5c11\u5708\uff0c\u76f4\u5230\u5230\u9054\u6b63\u4e0a\u65b9\u7684\u4e00\u7247\u8449\u5b50\uff0c\u7136\u5f8c\u518d\u6578\u4e00\u6578\u7d93\u904e\u4e86\u591a\u5c11\u7247\u8449\u5b50\u3002\u9019\u5169\u500b\u6578\u5b57\u901a\u5e38\u90fd\u662f\u6590\u6ce2\u90a3\u5951\u6578\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u9ec3\u91d1\u6bd4\u4f8b\u8207\u9ec3\u91d1\u89d2\uff1a\u751f\u547d\u5f62\u614b\u4e2d\u7684\u6578\u5b78\u5e38\u6578<\/strong><\/h2>\n\n\n\n<p>\u6590\u6ce2\u90a3\u5951\u6578\u5217\u8207\u6578\u5b78\u4e2d\u6700\u8457\u540d\u7684\u5e38\u6578\u4e4b\u4e00\u2014\u2014\u9ec3\u91d1\u5206\u5272\u7387\u2014\u2014\u6709\u8457\u5bc6\u5207\u7684\u806f\u7e6b\u3002\u9ec3\u91d1\u5206\u5272\u7387\u4ee5\u5e0c\u81d8\u5b57\u6bcdphi\uff08\u03c6\uff09\u8868\u793a\uff0c\u7d04\u7b49\u65bc1.618033988749\u3002\u5169\u5343\u5e74\u4f86\uff0c\u9019\u500b\u6578\u5b57\u4e00\u76f4\u5438\u5f15\u8457\u6578\u5b78\u5bb6\u3001\u85dd\u8853\u5bb6\u548c\u54f2\u5b78\u5bb6\uff0c\u4e26\u4e14\u5b83\u4ee5\u9a5a\u4eba\u7684\u898f\u5f8b\u6027\u51fa\u73fe\u5728\u6574\u500b\u690d\u7269\u738b\u570b\u4e2d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u7406\u89e3\u9ec3\u91d1\u6bd4\u4f8b<\/strong><\/h3>\n\n\n\n<p>\u9ec3\u91d1\u5206\u5272\u662f\u6307\u5c07\u4e00\u689d\u7dda\u6bb5\u5206\u6210\u5169\u90e8\u5206\uff0c\u4f7f\u5f97\u6574\u689d\u7dda\u6bb5\u8207\u8f03\u9577\u90e8\u5206\u7684\u9577\u5ea6\u4e4b\u6bd4\u7b49\u65bc\u8f03\u9577\u90e8\u5206\u8207\u8f03\u77ed\u90e8\u5206\u7684\u9577\u5ea6\u4e4b\u6bd4\u3002\u6578\u5b78\u4e0a\uff0c\u82e5\u6574\u689d\u7dda\u6bb5\u7684\u9577\u5ea6\u70ba a+b\uff0c\u8f03\u9577\u90e8\u5206\u7684\u9577\u5ea6\u70ba a\uff0c\u8f03\u77ed\u90e8\u5206\u7684\u9577\u5ea6\u70ba b\uff0c\u5247\uff1a(a+b)\/a = a\/b = \u03c6 \u2248 1.618\u3002<\/p>\n\n\n\n<p>\u9019\u500b\u6bd4\u4f8b\u5177\u6709\u975e\u51e1\u7684\u6578\u5b78\u7279\u6027\u3002\u5b83\u662f\u6240\u6709\u7121\u7406\u6578\u4e2d\u6700\u7121\u7406\u7684\u2014\u2014\u9019\u610f\u5473\u8457\u5b83\u6700\u96e3\u7528\u5206\u6578\u8fd1\u4f3c\u8868\u793a\u3002\u5b83\u4e5f\u8207\u6590\u6ce2\u90a3\u5951\u6578\u5217\u5bc6\u5207\u76f8\u95dc\uff1a\u5982\u679c\u4f60\u7528\u6590\u6ce2\u90a3\u5951\u6578\u5217\u4e2d\u7684\u4efb\u4e00\u500b\u6578\u4f86\u9664\u4ee5\u524d\u4e00\u500b\u6578\uff0c\u7d50\u679c\u5c31\u6703\u8d8a\u4f86\u8d8a\u63a5\u8fd1\u9ec3\u91d1\u5206\u5272\u7387\u3002\u4f8b\u5982\uff0c5\/3 = 1.666\uff0c8\/5 = 1.6\uff0c13\/8 = 1.625\uff0c21\/13 = 1.615\uff0c34\/21 = 1.619\uff0c\u4f9d\u6b64\u985e\u63a8\uff0c\u87ba\u65cb\u5f0f\u5730\u4e0d\u65b7\u63a5\u8fd1 1.618\u3002<\/p>\n\n\n\n<h3 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class=\"wp-block-list\">\n<li><strong>\u6a5f\u68b0\u529b<\/strong>\u539f\u59cb\u9ad4\u5728\u5f62\u6210\u904e\u7a0b\u4e2d\u6703\u4e92\u76f8\u64e0\u58d3\u3002<\/li>\n\n\n\n<li><strong>\u5316\u5b78\u8a0a\u865f<\/strong>\u751f\u9577\u7d20\u7b49\u6fc0\u7d20\u6703\u5f62\u6210\u6fc3\u5ea6\u68af\u5ea6\uff0c\u9032\u800c\u6c7a\u5b9a\u65b0\u539f\u57fa\u7684\u5f62\u6210\u4f4d\u7f6e\u3002<\/li>\n\n\n\n<li><strong>\u5e7e\u4f55\u7d04\u675f<\/strong>\u5206\u751f\u7d44\u7e54\u8868\u9762\u7684\u53ef\u7528\u7a7a\u9593\u9650\u5236\u4e86\u53ef\u80fd\u7684\u6392\u5217\u65b9\u5f0f<\/li>\n\n\n\n<li><strong>\u512a\u5316\u539f\u5247<\/strong>\u81ea\u7136\u9078\u64c7\u504f\u611b\u90a3\u4e9b\u80fd\u6700\u5927\u9650\u5ea6\u63d0\u9ad8\u6548\u7387\u7684\u5b89\u6392\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5229\u7528\u9019\u4e9b\u539f\u7406\u9032\u884c\u7684\u96fb\u8166\u6a21\u64ec\u53ef\u4ee5\u7522\u751f\u975e\u5e38\u903c\u771f\u7684\u690d\u7269\u7d50\u69cb\uff0c\u9019\u8868\u660e\u8907\u96dc\u7684\u6590\u6ce2\u90a3\u5951\u6a21\u5f0f\u53ef\u4ee5\u5f9e\u7c21\u55ae\u7684\u5c40\u90e8\u898f\u5247\u4e2d\u81ea\u7136\u7522\u751f\uff0c\u800c\u7121\u9700\u5168\u5c40\u5354\u8abf\u6216\u7279\u5b9a\u89d2\u5ea6\u6216\u6578\u5b57\u7684\u57fa\u56e0\u7de8\u78bc\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u9ec3\u91d1\u87ba\u65cb\u8207\u5c0d\u6578\u6210\u9577<\/strong><\/h2>\n\n\n\n<p>\u8a31\u591a\u82b1\u5349\u548c\u690d\u7269\u7d50\u69cb\u90fd\u9075\u5faa\u5c0d\u6578\u87ba\u65cb\u7dda\u2014\u2014\u6bcf\u65cb\u8f49\u4e00\u5468\uff0c\u66f2\u7dda\u90fd\u6703\u4ee5\u6046\u5b9a\u7684\u500d\u6578\u589e\u52a0\u3002\u6700\u8457\u540d\u7684\u5c0d\u6578\u87ba\u65cb\u7dda\u662f\u9ec3\u91d1\u87ba\u65cb\u7dda\uff0c\u5b83\u6bcf\u65cb\u8f49\u56db\u5206\u4e4b\u4e00\u9031\uff0c\u9577\u5ea6\u5c31\u6703\u589e\u52a0\u9ec3\u91d1\u5206\u5272\u7387\uff08\u03c6 \u2248 1.618\uff09\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u5c0d\u6578\u87ba\u65cb\u7dda\u7684\u7279\u6b8a\u4e4b\u8655\u662f\u4ec0\u9ebc\uff1f<\/strong><\/h3>\n\n\n\n<p>\u8207\u963f\u57fa\u7c73\u5fb7\u87ba\u65cb\u7dda\uff08\u4f8b\u5982\u624b\u9336\u767c\u689d\uff0c\u5176\u5708\u8ddd\u4fdd\u6301\u4e0d\u8b8a\uff09\u4e0d\u540c\uff0c\u5c0d\u6578\u87ba\u65cb\u7dda\u5728\u751f\u9577\u904e\u7a0b\u4e2d\u4fdd\u6301\u5f62\u72c0\u4e0d\u8b8a\uff0c\u53ea\u662f\u5c3a\u5ea6\u4e0d\u540c\u3002\u9019\u7a2e\u7279\u6027\u7a31\u70ba\u81ea\u76f8\u4f3c\u6027\uff0c\u4f7f\u5176\u6210\u70ba\u751f\u7269\u751f\u9577\u7684\u7406\u60f3\u5f62\u72c0\u3002\u9e1a\u9d61\u87ba\u7684\u6bbc\u5c31\u9075\u5faa\u5c0d\u6578\u87ba\u65cb\u7dda\uff0c\u4e0d\u65b7\u589e\u5927\uff0c\u540c\u6642\u4fdd\u6301\u76f8\u540c\u7684\u6bd4\u4f8b\u3002<\/p>\n\n\n\n<p>\u82b1\u6735\u7684\u751f\u9577\u6a21\u5f0f\u9075\u5faa\u5c0d\u6578\u87ba\u65cb\u7dda\uff0c\u56e0\u70ba\u9019\u7a2e\u66f2\u7dda\u5141\u8a31\u82b1\u6735\u5728\u4e0d\u6539\u8b8a\u5176\u57fa\u672c\u5e7e\u4f55\u5f62\u72c0\u7684\u524d\u63d0\u4e0b\u6301\u7e8c\u4f38\u5c55\u3002\u73ab\u7470\u6cbf\u8457\u5c0d\u6578\u87ba\u65cb\u7dda\u7dbb\u653e\uff0c\u6bcf\u4e00\u7247\u82b1\u74e3\u90fd\u6839\u64da\u9019\u689d\u66f2\u7dda\u4e0a\u7684\u9ec3\u91d1\u89d2\u4f86\u5b9a\u4f4d\u3002\u6700\u7d42\uff0c\u73ab\u7470\u5f9e\u82b1\u82de\u5230\u76db\u958b\u90fd\u80fd\u4fdd\u6301\u5176\u6bd4\u4f8b\u548c\u7f8e\u9e97\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u8cbb\u99ac\u87ba\u65cb\u6a21\u578b<\/strong><\/h3>\n\n\n\n<p>\u6cd5\u570b\u6578\u5b78\u5bb6\u76ae\u57c3\u723e\u00b7\u8cbb\u99ac\u63cf\u8ff0\u4e86\u4e00\u7a2e\u7279\u6b8a\u7684\u5c0d\u6578\u87ba\u65cb\u7dda\uff0c\u5b83\u80fd\u7cbe\u78ba\u5730\u6a21\u64ec\u5411\u65e5\u8475\u548c\u5176\u4ed6\u8907\u5408\u82b1\u5349\u7684\u7a2e\u5b50\u6392\u5217\u3002\u5728\u8cbb\u99ac\u87ba\u65cb\u6a21\u578b\u4e2d\uff0c\u6bcf\u7c92\u7a2e\u5b50\u5230\u87ba\u65cb\u4e2d\u5fc3\u7684\u8ddd\u96e2\u8207\u5176\u5e8f\u865f\u7684\u5e73\u65b9\u6839\u6210\u6b63\u6bd4\uff0c\u4e26\u4e14\u8207\u87ba\u65cb\u4e2d\u5fc3\u7684\u593e\u89d2\u7b49\u65bc\u8a72\u5e8f\u865f\u4e58\u4ee5\u9ec3\u91d1\u5206\u5272\u7387\u3002<\/p>\n\n\n\n<p>\u5f9e\u6578\u5b78\u89d2\u5ea6\u4f86\u8aaa\uff1a\u5c0d\u65bc\u7b2c n \u500b\u7a2e\u5b50\uff0c\u5176\u6975\u5ea7\u6a19\u70ba\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u534a\u5f91\uff1ar = c\u221an<\/li>\n\n\n\n<li>\u89d2\u5ea6\uff1a\u03b8 = n \u00d7 137.5\u00b0<\/li>\n<\/ul>\n\n\n\n<p>\u5176\u4e2d c \u662f\u6c7a\u5b9a\u6574\u9ad4\u898f\u6a21\u7684\u5e38\u6578\u3002<\/p>\n\n\n\n<p>\u9019\u500b\u7cbe\u5999\u800c\u7c21\u55ae\u7684\u516c\u5f0f\u9020\u5c31\u4e86\u5411\u65e5\u8475\u7a2e\u5b50\u7279\u6709\u7684\u6392\u5217\u6a21\u5f0f\u3002\u79d1\u5b78\u5bb6\u53ef\u4ee5\u5728\u96fb\u8166\u6a21\u578b\u4e2d\u7565\u5fae\u8abf\u6574\u89d2\u5ea6\uff0c\u89c0\u5bdf\u5176\u8b8a\u5316\uff1a\u5982\u679c\u89d2\u5ea6\u504f\u96e2\u9ec3\u91d1\u89d2\uff0c\u6392\u5217\u6a21\u5f0f\u7684\u6548\u7387\u5c31\u6703\u964d\u4f4e\uff0c\u51fa\u73fe\u660e\u986f\u7684\u7a7a\u9699\u6216\u64c1\u64e0\u3002\u9ec3\u91d1\u89d2\u7684\u78ba\u662f\u6700\u4f73\u89d2\u5ea6\u3002<\/p>\n\n\n\n<h3 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