{"id":39441,"date":"2011-09-11T20:10:11","date_gmt":"2011-09-11T12:10:11","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=39441"},"modified":"2021-10-06T16:22:48","modified_gmt":"2021-10-06T08:22:48","slug":"%e8%aa%8d%e8%ad%98%e6%93%ba%e7%b7%9aon-the-cycloid","status":"publish","type":"post","link":"http:\/\/localhost\/%e8%aa%8d%e8%ad%98%e6%93%ba%e7%b7%9aon-the-cycloid\/","title":{"rendered":"\u8a8d\u8b58\u64fa\u7dda"},"content":{"rendered":"

\u8a8d\u8b58\u64fa\u7dda (On the Cycloid)<\/span>
\n\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u6578\u7cfb\u8d99\u6587\u654f\u6559\u6388<\/span><\/strong>\/\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u6578\u7cfb\u8d99\u6587\u654f\u6559\u6388<\/span><\/strong>\u8cac\u4efb\u7de8\u8f2f<\/span><\/strong><\/p>\n

\u6458\u8981\uff1a\u5728\u5713\u9310\u66f2\u7dda\u767c\u73fe\u4e4b\u5f8c\uff0c\u53d7\u5230\u79d1\u5b78\u5bb6\u5011\u6700\u591a\u95dc\u6ce8\u7684\u66f2\u7dda\u61c9\u8a72\u7b97\u662f\u64fa\u7dda\u4e86\uff0c\u5b83\u66fe\u7d93\u5f15\u8d77\u8a31\u591a\u79d1\u5b78\u5bb6\u7684\u7af6\u722d\u8207\u722d\u5435\uff0c\u6709\u4eba\u751a\u81f3\u628a\u5b83\u6bd4\u55bb\u6210\u53e4\u5e0c\u81d8\u6642\u4ee3\u7279\u6d1b\u4f9d\u6230\u722d\u4e2d\u7684\u6d77\u502b\uff0c\u672c\u6587\u4ecb\u7d39\u64fa\u7dda\u7684\u6b77\u53f2\u8207\u4e00\u4e9b\u6027\u8cea\u3002<\/strong><\/p>\n

\u4f55\u8b02\u64fa\u7dda<\/strong><\/span><\/p>\n

\u5728\u591c\u665a\u7684\u8def\u4e0a\uff0c\u7576\u4e00\u8f1b\u8173\u8e0f\u8eca\u5f9e\u4f60\u9762\u524d\u75be\u99b3\u800c\u904e\u6642\uff0c\u5982\u679c\u8eca\u8f2a\u4e0a\u639b\u8457\u4e00\u500b\u5c0f\u71c8\u6ce1\uff0c\u4f60\u53ef\u66fe\u6ce8\u610f\u5230\u5c0f\u71c8\u6ce1\u5728\u524d\u9032\u904e\u7a0b\u4e2d\u63cf\u7e6a\u51fa\u4ec0\u9ebc\u6a23\u7684\u7dda\u689d\uff1f<\/p>\n

\u8173\u8e0f\u8eca\u5728\u8def\u4e0a\u524d\u9032\uff0c\u8eca\u8f2a\u50cf\u4e00\u500b\u5713\uff0c\u524d\u9032\u7684\u8def\u5728\u4e00\u76f4\u7dda\u4e0a\uff0c\u6240\u4ee5\uff0c\u8173\u8e0f\u8eca\u7684\u524d\u9032\u53ef\u770b\u6210\u662f\u4e00\u500b\u5713\u5728\u4e00\u76f4\u7dda\u4e0a\u4f5c\u6c92\u6709\u6ed1\u52d5\u7684\u6efe\u52d5\u3002\u7576\u4e00\u5716\u5f62\u5728\u4e00\u66f2\u7dda\u4e0a\u4f5c\u6c92\u6709\u6ed1\u52d5\u7684\u6efe\u52d5\u6642\uff0c\u5716\u5f62\u4e0a\u7684\u6bcf\u4e00\u500b\u9ede\u5728\u6efe\u52d5\u904e\u7a0b\u4e2d\ufe50\u90fd\u6703\u63cf\u7e6a\u51fa\u4e00\u689d\u66f2\u7dda\uff0c\u9019\u7a2e\u66f2\u7dda\u7a31\u70ba\u300c\u65cb\u8f2a\u7dda\u300d(roulette)\u3002\u9078\u64c7\u4e0d\u540c\u7684\u5716\u5f62\u3001\u4e0d\u540c\u7684\u66f2\u7dda\u8207\u4e0d\u540c\u7684\u9ede\uff0c\u53ef\u4ee5\u5f97\u51fa\u8a31\u591a\u4e0d\u540c\u7684\u65cb\u8f2a\u7dda\uff0c\u6211\u5011\u8209\u51fa\u5e7e\u500b\u4f8b\u5b50\u5982\u4e0b\u3002<\/p>\n

<\/p>\n

\u7576\u4e00\u5713\u5728\u4e00\u76f4\u7dda\u4e0a\u4f5c\u4e0d\u6ed1\u7684\u6efe\u52d5\u6642\uff0c\u5728\u5713\u5468\u4e0a\u7684\u9ede\u6240\u63cf\u7e6a\u7684\u65cb\u8f2a\u7dda\u7a31\u70ba\u300c\u64fa\u7dda\u300d(cycloid)\uff1b\u5728\u5713\u5167\u90e8\u7684\u9ede\u6240\u63cf\u7e6a\u7684\u65cb\u8f2a\u7dda\u7a31\u70ba\u77ed\u64fa\u7dda(curtate cycloid)\uff1b\u5728\u5713\u5916\u90e8\u7684\u9ede\u6240\u63cf\u7e6a\u7684\u65cb\u8f2a\u7dda\u7a31\u70ba\u9577\u64fa\u7dda(prolate cycloid)\u3002\u77ed\u64fa\u7dda\u8207\u9577\u64fa\u7dda\u5408\u7a31\u70ba\u6b21\u64fa\u7dda(trochoid)\uff08\u53c3\u770b\u5716\u4e00\uff09\u3002\u5728\u4e0b\u6587\u4e2d\uff0c\u6211\u5011\u5c07\u5713\u7a31\u70ba\u6efe\u52d5\u5713\u3001\u76f4\u7dda\u7a31\u70ba\u5e95\u7dda\u3002\u64fa\u7dda\u8207\u5e95\u7dda\u76f8\u4ea4\u7684\u9ede\u662f\u64fa\u7dda\u7684\u5c16\u9ede(cusp)\uff0c\u5169\u76f8\u9130\u5c16\u9ede\u9593\u7684\u4e00\u6bb5\u5f27\u7a31\u70ba\u64fa\u7dda\u7684\u4e00\u62f1(arch)\u3002<\/p>\n

\"\"<\/a>

\u5716\u4e00<\/p><\/div>\n

\u64fa\u7dda\u7684\u7b49\u6642\u6027\u8cea <\/strong><\/span><\/p>\n

\u5728\u529b\u5b78\u4e0a\uff0c\u64fa\u7dda\u5177\u6709\u5f88\u91cd\u8981\u7684\u6027\u8cea\uff0c\u6211\u5011\u9996\u5148\u4ecb\u7d39\u5b83\u7684\u7b49\u6642\u6027\u8cea\uff08tautochrone\u00a0property\uff09\u3002<\/p>\n

\u5c07\u64fa\u7dda\u7684\u4e00\u62f1\u5012\u8f49\uff0c\u4ea6\u5373\uff1a\u5c0d\u5176\u5e95\u7dda\u4f5c\u93e1\u5c04\uff0c\u5247\u6b64\u6bb5\u64fa\u7dda\u7684\u6700\u9ad8\u9ede \\(C\\) \u8b8a\u6210\u6700\u4f4e\u9ede\u3002\u6b64\u6642\uff0c\u82e5\u4e00\u8cea\u9ede\u5f9e\u6b64\u6bb5\u64fa\u7dda\u4e0a\u4efb\u610f\u9ede\u51fa\u767c\uff0c\u5728\u91cd\u529b\u4f5c\u7528\u4e0b\u6cbf\u64fa\u7dda\u5411\u4e0b\u6ed1\uff0c\u5247\u6b64\u8cea\u9ede\u5230\u9054\u6700\u4f4e\u9ede \\(C\\) \u6240\u9700\u7684\u6642\u9593\u8207\u51fa\u767c\u9ede\u7684\u4f4d\u7f6e\u7121\u95dc\uff0c\u4ea6\u5373\uff1a\u5f9e\u4efb\u610f\u5169\u76f8\u7570\u9ede\u51fa\u767c\uff0c\u5b83\u5011\u5230\u9054 \\(C\\) \u9ede\u7684\u6642\u9593\u76f8\u540c\u3002\u9019\u5c31\u662f\u64fa\u7dda\u7684\u7b49\u6642\u6027\u8cea\u3002<\/p>\n

\u5728\u5716\u4e8c\u4e2d\uff0c\u5f27 \\(ACB\\) \u662f\u7531\u64fa\u7dda\u7684\u4e00\u62f1\u5012\u7f6e\u800c\u6210\u3001\u5f27 \\(AA’B\\) \u5247\u662f\u7531\u540c\u4e00\u64fa\u7dda\u76f8\u9130\u5169\u62f1\u7684\u4e2d\u9ede\u9593\u7684\u4e00\u6bb5\u5012\u7f6e\u800c\u6210\u3002\u82e5\u6211\u5011\u4ee5\u4e00\u689d\u9577\u5ea6\u70ba\u64fa\u7dda\u4e00\u62f1\u9577\u4e4b\u534a\u7684\u7dda\u7e6b\u4f4f\u4e00\u500b\u64fa\u9318\uff0c\u53e6\u4e00\u7aef\u56fa\u5b9a\u5728\u5f27 \\(AA’B\\) \u7684\u4e2d\u9ede \\(A’\\)\u3002\u7576\u64fa\u9318\u64fa\u52d5\u6642\uff0c\u7dda\u7684\u4e0a\u7aef\u56fa\u5b9a\u5728\u9ede \\(A’\\) \u4e0a\uff0c\u800c\u4e0b\u7aef\u6709\u4e00\u6bb5\u62c9\u76f4\u3002\u7531\u65bc\u7dda\u9577\u7b49\u65bc\u64fa\u7dda\u4e00\u62f1\u9577\u7684\u4e00\u534a\uff0c\u64fa\u9318\u64fa\u52d5\u7684\u8def\u7dda\u5c31\u662f\u5716\u4e8c\u4e2d\u7684\u64fa\u7dda\u5f27\u3002<\/p>\n

\u524d\u6bb5\u6240\u63d0\u7684\u7b49\u6642\u6027\uff0c\u5247\u662f\u8868\u793a\uff1a\u4e0d\u8ad6\u632f\u5e45\u70ba\u4f55\uff0c\u5176\u9031\u671f\u662f\u500b\u5b9a\u503c\uff0c\u6b64\u5b9a\u503c\u7b49\u65bc \\(2\\pi\\sqrt{(4a\/g)}\\)\uff0c\u5176\u4e2d \\(a\\) \u662f\u64fa\u7dda\u7684\u6efe\u52d5\u5713\u534a\u5f91\uff0c\\(g\\) \u662f\u91cd\u529b\u52a0\u901f\u5ea6\u3002<\/p>\n

\"\"<\/a>

\u5716\u4e8c<\/p><\/div>\n

\u524d\u6bb5\u6240\u63d0\u7684\u88dd\u7f6e\uff0c\u7a31\u70ba\u64fa\u7dda\u9418\uff08cycloidal pendulum\uff09\uff0c\u9019\u662f Christiaan Huygens\uff081629\uff5e1695\u5e74\uff0c\u8377\u862d\u4eba\uff09\u5728 1673 \u5e74\u6240\u767c\u660e\u7684\uff0c\u5b83\u662f\u5177\u6709\u771f\u6b63\u7b49\u6642\u6027\u7684\u9418\u64fa\u3002<\/p>\n

\u64fa\u7dda\u7684\u6700\u901f\u964d\u6027\u8cea <\/strong><\/span><\/p>\n

\u64fa\u7dda\u5728\u529b\u5b78\u4e0a\u7684\u53e6\u4e00\u9805\u91cd\u8981\u6027\u8cea\uff0c\u4e43\u662f\u6700\u901f\u964d\u6027\u8cea\uff08brachistochrone\u00a0property\uff09\uff0c\u6211\u5011\u8aaa\u660e\u5982\u4e0b\u3002<\/p>\n

\u82e5\u4e00\u8cea\u9ede\u5728\u91cd\u529b\u4f5c\u7528\u4e0b\uff0c\u7531 \\(P\\) \u9ede\u6cbf\u8457\u67d0\u66f2\u7dda\u6ed1\u843d\u5230\u8f03\u4f4e\u7684 \\(Q\\) \u9ede\uff0c\u8a2d \\(P\\) \u8207 \\(Q\\) \u4e0d\u5728\u540c\u4e00\u925b\u5782\u76f4\u7dda\u4e0a\uff0c\u5247\u7576\u6ed1\u884c\u7684\u66f2\u7dda\u662f\u4ee5 \\(P\\) \u9ede\u70ba\u5c16\u9ede\u7684\u4e00\u6bb5\u5012\u8f49\u7684\u64fa\u7dda\u5f27\u6642\uff0c\u8cea\u9ede\u7531 \\(P\\) \u9ede\u6ed1\u843d\u5230 \\(Q\\) \u9ede\u6240\u9700\u7684\u6642\u9593\u70ba\u6700\u77ed\u3002\u9019\u5c31\u662f\u64fa\u7dda\u7684\u6700\u901f\u964d\u6027\u8cea\u3002<\/p>\n

\u8a2d \\(P\\) \u8207 \\(Q\\) \u7684\u5750\u6a19\u5206\u5225\u662f \\(P(x_1,y_1)\\) \u8207 \\(Q(x_2,y_2)\\)\uff0c\\(x_1<x_2\\)\u00a0\u4e14 \\(y_1>y_2\\)\uff0c\u800c \\(y=f(x)\\) \u662f\u6eff\u8db3 \\(y_1=f(x_1)\\) \u8207 \\(y_2=f(x_2)\\) \u7684\u4e00\u500b\u51fd\u6578\uff0c\u5247\u4e00\u8cea\u9ede\u6cbf\u8457\u66f2\u7dda \\(y=f(x)\\)\uff0c\u7531 \\(P\\) \u9ede\u6ed1\u843d\u5230 \\(Q\\) \u9ede\u6240\u9700\u7684\u6642\u9593\uff0c\u53ef\u4ee5\u8868\u793a\u6210\u67d0\u500b\u7531 \\(f(x)\\) \u8207 \\(f'(x)\\) \u7d44\u6210\u7684\u51fd\u6578\u7684\u5b9a\u7a4d\u5206\u3002<\/p>\n

\u5728\u6240\u6709\u6b64\u7a2e\u51fd\u6578 \\((y=f(x))\\)\u00a0\u4e2d\uff0c\u90a3\u4e00\u500b\u51fd\u6578\u80fd\u4f7f\u6b64\u5b9a\u7a4d\u5206\u7684\u503c\u6700\u5c0f\uff0c\u9019\u500b\u554f\u984c\u4e43\u662f\u300c\u4e00\u500b\u4ee5\u51fd\u6578\uff08\u6216\u66f2\u7dda\uff09\u70ba\u8b8a\u6578\u7684\u6975\u503c\u554f\u984c\u300d\u3002\u7814\u7a76\u9019\u985e\u554f\u984c\u7684\u65b9\u6cd5\u7a31\u70ba\u300c\u8b8a\u5206\u5b78\u300d\uff08calculus of variation\uff09\u3002\u5b83\u8207\u5fae\u7a4d\u5206\u4e2d\u8a0e\u8ad6\u6975\u503c\u7684\u65b9\u6cd5\u4e0d\u76f8\u540c\uff0c\u800c\u4e14\u4e5f\u56f0\u96e3\u5f97\u591a\u3002\u63a2\u8a0e\u6700\u901f\u964d\u66f2\u7dda\u7684\u554f\u984c\uff0c\u4e43\u662f\u8b8a\u5206\u5b78\u7684\u5148\u9a45\u554f\u984c\u4e4b\u4e00\uff0c\u4e00\u822c\u7684\u8b8a\u5206\u5b78\u66f8\u7c4d\u90fd\u6703\u8ac7\u5230\u9019\u500b\u4f8b\u5b50\u3002<\/p>\n

\u5728\u6700\u901f\u964d\u66f2\u7dda\u554f\u984c\u4e2d\uff0c\u6709\u4e00\u500b\u554f\u984c\u5fc5\u9808\u4ea4\u5f85\uff0c\u90a3\u5c31\u662f\uff1a\u5c0d\u4efb\u610f\u4e8c\u9ede \\(P(x_1,y_1)\\)\u00a0\u8207 \\(Q(x_2,y_2)\\)\uff0c\\(x_1<x_2\\) \u4e14 \\(y_1>y_2\\)\uff0c\u6709\u591a\u5c11\u64fa\u7dda\u4ee5 \\(P\\) \u9ede\u70ba\u4e00\u5c16\u9ede\u800c\u53c8\u901a\u904e \\(Q\\) \u5462\uff1f\u7b54\u6848\u662f\uff1a\u6070\u6709\u4e00\u689d\u3002<\/p>\n

\u7d66\u4e86 \\(P\\)\u3001\\(Q\\) \u5169\u9ede\uff0c\u6211\u5011\u600e\u9ebc\u4f5c\u51fa\u9019\u6a23\u7684\u64fa\u7dda\u5462\uff1f\u4efb\u53d6\u4e00\u5713\uff0c\u4f7f\u5b83\u8207\u904e\u9ede \\(P\\) \u7684\u6c34\u5e73\u76f4\u7dda\u5207\u65bc \\(P\\) \u9ede\u4e14\u5713\u5728\u6c34\u5e73\u76f4\u7dda\u4e0b\u65b9\u3002\u8b93\u5713\u5728\u6c34\u5e73\u76f4\u7dda\u4e0b\u6efe\u52d5\uff0c\u8a2d\u5b9a\u9ede \\(P\\) \u7684\u8ecc\u8de1\u8207\u76f4\u7dda \\(PQ\\) \u4ea4\u65bc \\(Q’\\) \u9ede\u3002\u53e6\u53d6\u4e00\u5713\uff0c\u5176\u534a\u5f91\u7b49\u65bc\u524d\u4e00\u5713\u7684\u534a\u5f91\u4e58\u4ee5 \\(\\frac{\\overline{pq}}{\\overline{PQ’}}\\)\uff0c\u5247\u5c07\u5f8c\u4e00\u5713\u5728\u904e \\(P\\) \u9ede\u7684\u6c34\u5e73\u76f4\u7dda\u4e0b\u6efe\u52d5\u6642\uff0c\u5b9a\u9ede \\(P\\) \u6240\u63cf\u7e6a\u7684\u8ecc\u8de1\uff0c\u5c31\u662f\u4ee5 \\(P\\) \u70ba\u4e00\u5c16\u9ede\u4e14\u901a\u904e \\(Q\\) \u7684\u64fa\u7dda\u3002<\/p>\n

\u524d\u6bb5\u6240\u63d0\u7684\u4f5c\u6cd5\uff0c\u4e8b\u5be6\u4e0a\u8207\u64fa\u7dda\u7684\u4e00\u9805\u6027\u8cea\u6709\u95dc\u3002\u82e5\u5169\u64fa\u7dda\u7684\u5e95\u7dda\u91cd\u5408\uff0c\u4e14\u6709\u4e00\u5c16\u9ede\u91cd\u5408\uff0c\u5247\u5176\u4e2d\u4efb\u4e00\u64fa\u7dda\u90fd\u53ef\u7531\u53e6\u4e00\u64fa\u7dda\u4ee5\u91cd\u5408\u5c16\u9ede\u70ba\u4e2d\u5fc3\uff0c\u653e\u5927\u6216\u7e2e\u5c0f\u800c\u5f97\u3002\u63db\u8a00\u4e4b\uff0c\u4efb\u610f\u4e8c\u64fa\u7dda\u90fd\u662f\u76f8\u4f3c\u7684\u66f2\u7dda\u3002<\/p>\n

\u64fa\u7dda\u53f2\u8a71<\/strong><\/span><\/p>\n

\u5728\u5713\u9310\u66f2\u7dda\u767c\u73fe\u4e4b\u5f8c\uff0c\u53d7\u5230\u79d1\u5b78\u5bb6\u5011\u6700\u591a\u95dc\u6ce8\u7684\u66f2\u7dda\u61c9\u8a72\u7b97\u662f\u64fa\u7dda\u4e86\uff0c\u5b83\u66fe\u7d93\u5f15\u8d77\u8a31\u591a\u79d1\u5b78\u5bb6\u7684\u7af6\u722d\u8207\u722d\u5435\uff0c\u6709\u4eba\u751a\u81f3\u628a\u5b83\u6bd4\u55bb\u6210\u53e4\u5e0c\u81d8\u6642\u4ee3\u7279\u6d1b\u4f9d\u6230\u722d\u4e2d\u7684\u6d77\u502b\uff0c\u800c\u7a31\u4e4b\u70ba\u300cthe Helen of geometry\u300d\u3002<\/p>\n

\u4f3d\u5229\u7565\uff08Galileo\uff0c1564\uff5e1642\u5e74\uff0c\u7fa9\u5927\u5229\u4eba\uff09\u662f\u6700\u65e9\u6ce8\u610f\u5230\u64fa\u7dda\u7684\u79d1\u5b78\u5bb6\u4e4b\u4e00\uff0c\u4ed6\u5728 1599 \u5e74\u66fe\u7d93\u5617\u8a66\u4ee5\u64cd\u4f5c\u7684\u65b9\u6cd5\uff0c\u4f86\u8a08\u7b97\u64fa\u7dda\u7684\u4e00\u62f1\u8207\u5176\u5e95\u7dda\u9593\u7684\u9762\u7a4d\u3002\u4ed6\u5c07\u8f2a\u5b50\u5728\u4e00\u76f4\u7dda\u4e0a\u6efe\u52d5\uff0c\u5be6\u5730\u63cf\u7e6a\u51fa\u64fa\u7dda\u7684\u4e00\u62f1\uff0c\u7136\u5f8c\u5229\u7528\u76f8\u540c\u7684\u6750\u6599\u505a\u6210\u64fa\u7dda\u7684\u4e00\u62f1\u4ee5\u53ca\u6efe\u52d5\u5713\uff0c\u5728\u5929\u5e73\u4e0a\u79e4\u7684\u7d50\u679c\u767c\u73fe\u64fa\u7dda\u7684\u4e00\u62f1\u8207\u4e09\u500b\u6efe\u52d5\u5713\u76e4\u5927\u81f4\u5e73\u8861\u3002\u6240\u4ee5\uff0c\u64fa\u7dda\u4e00\u62f1\u7684\u9762\u7a4d\u5927\u7d04\u662f\u6efe\u52d5\u5713\u9762\u7a4d\u7684\u4e09\u500d\uff0c\u9019\u662f\u6b63\u78ba\u7684\u3002\u4e0d\u904e\uff0c\u4f3d\u5229\u7565\u537b\u89ba\u5f97\u6bd4\u503c\u61c9\u8a72\u662f\u7121\u7406\u6578\uff0c\u6240\u4ee5\uff0c\u4ed6\u731c\u6e2c\u64fa\u7dda\u4e00\u62f1\u7684\u9762\u7a4d\u662f\u6efe\u52d5\u5713\u9762\u7a4d\u7684 \\(\\pi\\)\u00a0\u500d\u3002<\/p>\n

\u64fa\u7dda\u4e00\u62f1\u7684\u9762\u7a4d\uff0c\u662f Gilles Persone de Roberval (1602\uff5e1675\u5e74\uff0c\u6cd5\u570b\u4eba\uff09\u5728 1634 \u5e74\u6700\u5148\u6c42\u5f97\u7684\u3002\u4ed6\u5728 1638 \u5e74\u9084\u627e\u5230\u64fa\u7dda\u4e4b\u5207\u7dda\u7684\u4f5c\u6cd5\u3002\u7d04\u5728\u540c\u4e00\u6642\u671f\uff0c\u7b1b\u5361\u5152\uff08Descartes\uff0c1596\uff5e1650\u5e74\uff0c\u6cd5\u570b\u4eba\uff09\u8207\u8cbb\u746a\uff08Fermat\uff0c1601\uff5e1665\u5e74\uff0c\u6cd5\u570b\u4eba\uff09\u4e5f\u627e\u5230\u5207\u7dda\u7684\u4f5c\u6cd5\u3002\u53e6\u5916\uff0cRoberval \u4e5f\u8a0e\u8ad6\u904e\u64fa\u7dda\u7684\u4e00\u62f1\u7e5e\u5176\u5e95\u7dda\u65cb\u8f49\u6240\u5f97\u65cb\u8f49\u9ad4\u7684\u9ad4\u7a4d\u3002<\/p>\n

\u5c31\u5728 Roberval \u7814\u7a76\u64fa\u7dda\u6709\u6240\u6210\u5c31\u7684\u6642\u5019\uff0c\u4f3d\u5229\u7565\u7684\u4e00\u4f4d\u5b78\u751f Torricelli\uff081608\uff5e1647 \u5e74\uff0c\u7fa9\u5927\u5229\u4eba\uff09\u4e5f\u5c0d\u64fa\u7dda\u5927\u611f\u8208\u8da3\u30021643 \u5e74\uff0cTorricelli \u51fa\u7248\u4e00\u7bc7\u540d\u70ba\u3008De\u00a0parabole\u3009\u7684\u4f5c\u54c1\uff0c\u5176\u4e2d\u9644\u5e36\u63d0\u5230\u64fa\u7dda\u7684\u6c42\u7a4d\u6cd5\u8207\u5207\u7dda\u7684\u4f5c\u6cd5\uff0c\u4f46\u537b\u6c92\u6709\u63d0\u5230 Roberval \u5728\u4ed6\u4e4b\u524d\u5df2\u7d93\u5f97\u51fa\u9019\u5169\u500b\u7d50\u679c\u3002\u7531\u65bc\u9019\u500b\u7de3\u6545\uff0cRoberval \u66fe\u5728 1646 \u5e74\u5beb\u4fe1\u8b74\u8cac Torricelli \u7aca\u53d6\u4ed6\u4eba\u7684\u7814\u7a76\u6210\u679c\u3002\u5c0d\u65bc\u9019\u4ef6\u4e8b\uff0c\u5f8c\u4e16\u6578\u5b78\u53f2\u5bb6\u8a8d\u70ba Torricelli \u662f\u53d7\u51a4\u6789\u4e86\uff0c\u56e0\u70ba Roberval \u7684\u6210\u679c\u76f4\u5230 1693\u5e74\u624d\u767c\u8868\u3002<\/p>\n

1658 \u5e74\uff0c\u66fe\u7d93\u5728\u56db\u5e74\u524d\u5c31\u653e\u68c4\u6578\u5b78\u8f49\u653b\u795e\u5b78\u7684\u5929\u624d\u6578\u5b78\u5bb6\u5df4\u65af\u5361\uff08Pascal\uff0c\u00a01623\uff5e1662 \u5e74\uff0c\u6cd5\u570b\u4eba\uff09\u767c\u751f\u4e00\u4ef6\u8da3\u4e8b\u3002\u6709\u5929\u665a\u4e0a\uff0c\u5df4\u65af\u5361\u56e0\u7259\u75db\u800c\u7761\u4e0d\u8457\u89ba\uff0c\u70ba\u4e86\u60f3\u5fd8\u6389\u75bc\u75db\uff0c\u5c31\u5c08\u5fc3\u601d\u8003\u64fa\u7dda\u7684\u6027\u8cea\u3002\u60f3\u8457\u60f3\u8457\uff0c\u7259\u9f52\u7adf\u7136\u4e0d\u75db\u4e86\uff0c\u5df4\u65af\u5361\u8a8d\u70ba\u9019\u662f\u4e0a\u5e1d\u5728\u7d66\u4ed6\u63d0\u793a\uff0c\u8868\u793a\u4ed6\u7814\u7a76\u6578\u5b78\u4e26\u6c92\u6709\u60f9\u4e0a\u5e1d\u4e0d\u9ad8\u8208\u3002<\/p>\n

\u65bc\u662f\uff0c\u4ed6\u5168\u5fc3\u6295\u5165\u4f86\u63a2\u8a0e\u64fa\u7dda\u7684\u6027\u8cea\uff0c\u6578\u5929\u5f8c\uff0c\u4ed6\u5c31\u7372\u5f97\u4e00\u4e9b\u8207\u64fa\u7dda\u6709\u95dc\u7684\u9762\u7a4d\u3001\u9ad4\u7a4d\u8207\u91cd\u5fc3\u7b49\u65b9\u9762\u7684\u7d50\u679c\u3002\u4ed6\u5c07\u7814\u7a76\u6240\u5f97\u5beb\u6210\u554f\u984c\u5411\u7576\u4ee3\u6578\u5b78\u5bb6\u63d0\u51fa\u6311\u6230\uff0c\u4e26\u4e14\u8a2d\u7f6e\u5169\u500b\u734e\uff0c\u9084\u8acb Roberval \u64d4\u4efb\u5176\u4e2d\u7684\u4e00\u4f4d\u8a55\u5be9\u4eba\u3002\u4e5f\u8a31\u56e0\u70ba\u6c92\u80fd\u516c\u544a\u7d66\u591a\u6578\u4eba\u77e5\u9053\uff0c\u6216\u662f\u56e0\u70ba\u6642\u9593\u592a\u7dca\u8feb\u4e86\uff0c\u9019\u6b21\u61f8\u8cde\u884c\u52d5\u53ea\u6536\u5230 Antoine de Lalouvire(1600\uff5e1664\u5e74\uff0c\u6cd5\u570b\u4eba)\u8207 Wallis(1616\uff5e1703\u5e74\uff0c\u82f1\u570b\u4eba\uff09\u7684\u56de\u61c9\uff0c\u800c\u4e14\u6240\u9001\u7684\u89e3\u7b54\u4e2d\u9084\u6709\u4e00\u4e9b\u8a08\u7b97\u4e0a\u7684\u932f\u8aa4\uff0c\u6240\u4ee5\uff0c\u5df4\u65af\u5361\u6c92\u6709\u9812\u734e\uff0c\u53ea\u5c07\u4ed6\u81ea\u5df1\u7684\u7814\u7a76\u6210\u679c\u5beb\u6210\u3008Histoire\u00a0de la roulette\u3009\u4e00\u6587\u4e88\u4ee5\u767c\u8868\u3002\uff08\u7576\u6642\u7684\u6cd5\u570b\u4eba\u5c07\u64fa\u7dda\u7a31\u70ba roulette\u3002\uff09\u7d50\u679c\u5462\uff1f\u00a0\u8207\u8cfd\u7684\u5169\u4eba\u56e0\u70ba\u6c92\u6709\u9812\u734e\u800c\u4e0d\u9ad8\u8208\uff0c\u800c\u7fa9\u5927\u5229\u7684\u6578\u5b78\u5bb6\u5011\u5247\u70ba\u5df4\u65af\u5361\u5728\u3008\u64fa\u7dda\u7684\u6b77\u53f2\u3009\u4e00\u6587\u4e2d\u6c92\u6709\u63d0\u5230 Torricelli \u800c\u4e0d\u75db\u5feb\u3002<\/p>\n

\u5c31\u5728 Wallis \u53c3\u52a0\u5df4\u65af\u5361\u7684\u6311\u6230\u7684\u540c\u6642\uff0c\u53e6\u4e00\u4f4d\u82f1\u570b\u4eba Wren \uff081632\uff5e1723\u5e74\uff09\ufe50\u5c07\u4ed6\u6240\u5f97\u7684\u64fa\u7dda\u5f27\u9577\u7684\u6c42\u6cd5\u5bc4\u7d66\u5df4\u65af\u5361\uff0c\u9019\u662f\u5df4\u65af\u5361\u4e0d\u66fe\u5f97\u5230\u7684\u7d50\u679c\u3002Wren \u5f8c\u4f86\u8f49\u884c\u53bb\u7814\u7a76\u7269\u7406\u8207\u5efa\u7bc9\uff0c1666 \u5e74\u502b\u6566\u5927\u706b\u5f8c\uff0cWren \u5c31\u56e0\u70ba\u8a2d\u8a08\u502b\u6566\u7684\u8056\u4fdd\u7f85\u6559\u5802\u800c\u805e\u540d\u3002<\/p>\n

\u64fa\u7dda\u5728\u529b\u5b78\u65b9\u9762\u7684\u6027\u8cea\uff0c\u7b49\u6642\u6027\u4fc2 Huygens \u6240\u767c\u73fe\u7684\uff0c\u800c\u6700\u901f\u964d\u6027\u8cea\u5247\u662f\u767d\u52aa\u5229\uff08J.Bernoulli, 1654\uff5e1705\u5e74\uff0c\u745e\u58eb\u4eba\uff09\u5728 1690 \u5e74\u767c\u73fe\u7684\u3002<\/p>\n

\n

\u5ef6\u4f38\u95b1\u8b80<\/strong><\/p>\n

    \n
  1. http:\/\/episte.math.ntu.edu.tw\/cgi\/mathfield.pl?aut=%BB%AF%A4%E5%B1%D3 <\/a><\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u8a8d\u8b58\u64fa\u7dda (On the Cycloid) \u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u6578\u7cfb\u8d99\u6587\u654f\u6559\u6388\/\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u6578\u7cfb\u8d99\u6587\u654f\u6559\u6388\u8cac\u4efb…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[224,111],"tags":[4350,4352,4351],"class_list":["post-39441","post","type-post","status-publish","format-standard","hentry","category-math04","category-mathematics00","tag-4350","tag-4352","tag-4351","loop-entry","cat-224","cat-111","no-thumbnail"],"views":10621,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/39441","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=39441"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/39441\/revisions"}],"predecessor-version":[{"id":87845,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/39441\/revisions\/87845"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=39441"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=39441"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=39441"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}