{"id":1301,"date":"2015-07-24T09:12:36","date_gmt":"2015-07-24T01:12:36","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=1301"},"modified":"2022-01-20T13:28:37","modified_gmt":"2022-01-20T05:28:37","slug":"buffons-needle-problem-%e8%92%b2%e4%b8%b0%e6%8a%95%e9%92%88%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"http:\/\/www.jdcui.com\/?p=1301","title":{"rendered":"[\u6570\u5b66][\u6982\u7387] Buffon&#8217;s Needle problem [\u84b2\u4e30\u6295\u9488\u95ee\u9898]"},"content":{"rendered":"<p>\u8457\u540d\u7684\u51e0\u4f55\u6982\u7387\u95ee\u9898\u2014\u2014<strong>\u84b2\u4e30\u6295\u9488\u95ee\u9898<\/strong>\uff08<strong><span style=\"color: #0000ff;\">Buffon&#8217;s Needle problem<\/span><\/strong>\uff09\uff0c\u6700\u521d\u7531\u6570\u5b66\u5bb6<strong>Georges-Louis Leclerc, Comte de Buffon<\/strong>\u4e8e18\u4e16\u7eaa\u63d0\u51fa\u3002\u95ee\u9898\u53ef\u8868\u8ff0\u4e3a\uff1a\u5047\u5b9a\u957f\u5ea6\u4e3aL\u7684\u7684\u9488\uff0c\u968f\u673a\u6295\u5230\u753b\u6ee1\u95f4\u8ddd\u4e3aT\u7684\u5e73\u884c\u7ebf\u7684\u7eb8\u4e0a\uff0c\u6c42\u9488\u548c\u5e73\u884c\u7ebf\u76f8\u4ea4\u7684\u6982\u7387\u3002\u540c\u65f6\u6709\u8da3\u7684\u662f\uff0c\u8be5\u6982\u7387\u503c\u548c<strong>\u5706\u5468\u7387(PI)<\/strong>\u6709\u5173\u7cfb\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u6295\u9488\u8bd5\u9a8c\u6765\u8ba1\u7b97<strong>\u5706\u5468\u7387(PI)<\/strong>\u7684\u503c\u3002\u5b9e\u9645\u4e0a\uff0c\u8fd9\u4e2a\u8bd5\u9a8c\u66f4\u6709\u4ef7\u503c\u7684\u5730\u65b9\u5728\u4e8e:\u6211\u4eec\u53ef\u4ee5\u8bbe\u8ba1\u4e00\u4e2a\u8bd5\u9a8c\uff0c\u5b83\u7684\u6982\u7387\u4e0e\u6211\u4eec\u611f\u5174\u8da3\u7684\u4e00\u4e2a\u53d8\u91cf\u6709\u5173\uff0c\u7136\u540e\u901a\u8fc7\u5927\u91cf\u8bd5\u9a8c\u6765\u4f30\u7b97\u8fd9\u4e2a\u91cf\uff0c\u8fd9\u5176\u5b9e\u5c31\u662f\u76ee\u524d\u4f7f\u7528\u5f97\u5341\u5206\u5e7f\u6cdb\u7684\u8499\u5854\u5361\u7f57\u6cd5\uff08<strong>Monte Carlo method<\/strong>\uff09\u7684\u4e3b\u8981\u601d\u60f3\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\u6211\u4eec\u7528\u8ba1\u7b97\u673a\u6765\u6a21\u62df\u8fd9\u4e2a\u6295\u9488\u8fc7\u7a0b\uff0c\u5e76\u4f30\u7b97\u5706\u5468\u7387(PI)\u7684\u503c\u3002\u5047\u8bbe\u9488\u7684\u957f\u5ea6\u4e3aL\uff0c\u5e73\u884c\u7ebf\u7684\u957f\u5ea6\u4e3aL\uff0c\u9488\u7684\u4e2d\u70b9\u53ef\u4ee5\u57280~L\u4e2d\u968f\u673a\u51fa\u73b0\uff0c\u6295\u9488\u89d2\u5ea6\u4e3a0~PI\u968f\u673a\u503c\uff0c\u5219<strong>\u5706\u5468\u7387(PI)<\/strong>\u7684\u503c\u5219\u4e3a\u53ef\u4ee5\u901a\u8fc7\u516c\u5f0f\uff1a\uff08<strong>2<\/strong>*<strong>Total drops\/Num of Hits<\/strong>\uff09\u6765\u4f30\u7b97\u3002<strong>Total Drops<\/strong>\u4e3a\u6295\u9488\u6570\u91cf<strong>\u3002Num of Hits<\/strong>\u4e3a\u9488\u4e0e\u5e73\u884c\u7ebf\u76f8\u4ea4\u7684\u6b21\u6570\u3002<\/p>\n<p>\u6295\u9488\u6b21\u6570<strong>10<\/strong>\u7684\u6a21\u62df\u5b9e\u9a8c\uff1a<\/p>\n<p><center><br \/>\n<script src=\"wp-content\/uploads\/ProcessingData\/processing-1.4.8.min.js\" type=\"text\/javascript\"><\/script><canvas data-processing-sources=\"wp-content\/uploads\/ProcessingData\/Needle10.pde\"> <\/canvas><\/center><br \/>\n\u6295\u9488\u6b21\u6570<strong>100<\/strong>\u7684\u6a21\u62df\u5b9e\u9a8c\uff1a<\/p>\n<p><center><script src=\"wp-content\/uploads\/ProcessingData\/processing-1.4.8.min.js\" type=\"text\/javascript\"><\/script><canvas data-processing-sources=\"wp-content\/uploads\/ProcessingData\/Needle100.pde\"><\/canvas><\/center>\u6295\u9488\u6b21\u6570<strong>10000<\/strong>\u7684\u6a21\u62df\u5b9e\u9a8c\uff1a<\/p>\n<p><center><br \/>\n<script src=\"wp-content\/uploads\/ProcessingData\/processing-1.4.8.min.js\" type=\"text\/javascript\"><\/script><canvas data-processing-sources=\"wp-content\/uploads\/ProcessingData\/Needle10000.pde\"><\/canvas><\/center><strong>PS.<\/strong><br \/>\n(1) \u968f\u7740\u6295\u9488\u6570\u91cf\u7684\u589e\u52a0\uff0c\u5706\u5468\u7387(PI)\u503c\u8d8b\u5411\u4e8e\u7cbe\u786e\u503c\u3002<br \/>\n(2) <strong><span style=\"color: #0000ff;\">\u70b9\u51fb\u56fe\u7247\u53ef\u4ee5\u91cd\u65b0\u8fdb\u884c\u8bd5\u9a8c\uff01\u4f53\u9a8c\u4e00\u4e0b\uff01<\/span><\/strong><\/p>\n<hr \/>\n<p><center><code><div  class=\"thumbs-rating-container\" id=\"thumbs-rating-1301\" data-content-id=\"1301\"><button class=\"thumbs-rating-up thumbs-rating-voted\" onclick=\"thumbs_rating_vote(1301, 1);\">Vote Up +78<\/button> <button class=\"thumbs-rating-down thumbs-rating-voted\" onclick=\"thumbs_rating_vote(1301, 2);\">Vote Down -15<\/button><span class=\"thumbs-rating-already-voted\">You already voted!<\/span><\/div><\/code><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8457\u540d\u7684\u51e0\u4f55\u6982\u7387\u95ee\u9898 \u2014\u2014 \u84b2\u4e30\u6295\u9488\u95ee\u9898\uff08Buffon&#8217;s Needle problem \uff09\uff0c\u6700\u521d\u7531\u6570\u5b66\u5bb6Georges-Louis Leclerc, Comte de Buffon\u4e8e18\u4e16\u7eaa\u63d0\u51fa\u3002\u95ee\u9898\u53ef\u8868\u8ff0\u4e3a\uff1a\u5047\u5b9a\u957f\u5ea6\u4e3aL\u7684\u7684\u9488\uff0c\u968f\u673a\u6295\u5230\u753b\u6ee1\u95f4\u8ddd\u4e3aT\u7684\u5e73\u884c\u7ebf\u7684\u7eb8\u4e0a\uff0c\u6c42\u9488\u548c\u5e73\u884c\u7ebf\u76f8\u4ea4\u7684\u6982\u7387\u3002\u540c\u65f6\u6709\u8da3\u7684\u662f\uff0c\u8be5\u6982\u7387\u503c\u548c\u5706\u5468\u7387(PI)\u6709\u5173\u7cfb\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u6295\u9488\u8bd5\u9a8c\u6765\u8ba1\u7b97\u5706\u5468\u7387(PI)\u7684\u503c\u3002\u5b9e\u9645\u4e0a\uff0c\u8fd9\u4e2a\u8bd5\u9a8c\u6709\u4ef7\u503c\u7684\u5730\u65b9\u5728\u4e8e\uff1a\u6211\u4eec\u53ef\u4ee5\u8bbe\u8ba1\u4e00\u4e2a\u8bd5\u9a8c\uff0c\u5b83\u7684\u6982\u7387\u4e0e\u6211\u4eec\u611f\u5174\u8da3\u7684\u4e00\u4e2a\u53d8\u91cf\u6709\u5173\uff0c\u7136\u540e\u901a\u8fc7\u5927\u91cf\u8bd5\u9a8c\u6765\u4f30\u7b97\u8fd9\u4e2a\u91cf\uff0c\u8fd9\u5176\u5b9e\u5c31\u662f\u76ee\u524d\u4f7f\u7528\u5f97\u5341\u5206\u5e7f\u6cdb\u7684\u8499\u5854\u5361\u7f57\u6cd5\uff08Monte Carlo method\uff09\u7684\u4e3b\u8981\u601d\u60f3\u3002<\/p>\n","protected":false},"author":1,"featured_media":7364,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[235,4,21],"tags":[202,233,203,206,204,135,234,205,201],"class_list":["post-1301","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-game-programming-","category-math-geometry","category-programming","tag-buffons-needle","tag-game","tag-geometrical-probability","tag-monte-carlo-method","tag-204","tag-135","tag-234","tag-205","tag-201"],"aioseo_notices":[],"views":6420,"_links":{"self":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts\/1301","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1301"}],"version-history":[{"count":0,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts\/1301\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/media\/7364"}],"wp:attachment":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1301"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}