{"id":5446,"date":"2022-04-02T21:14:02","date_gmt":"2022-04-02T13:14:02","guid":{"rendered":"https:\/\/egonlin.com\/?p=5446"},"modified":"2022-04-02T21:14:02","modified_gmt":"2022-04-02T13:14:02","slug":"04-06-%e5%ae%9e%e4%be%8b6-%e5%9c%86%e5%91%a8%e7%8e%87%e7%9a%84%e8%ae%a1%e7%ae%97","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=5446","title":{"rendered":"04-06 \u5b9e\u4f8b6-\u5706\u5468\u7387\u7684\u8ba1\u7b97"},"content":{"rendered":"

\u4e00\u3001"\u5706\u5468\u7387\u7684\u8ba1\u7b97"\u95ee\u9898\u5206\u6790<\/h1>\n

\u5706\u5468\u7387\u7684\u8fd1\u4f3c\u8ba1\u7b97\u516c\u5f0f
\n$$
\n?=\\sum\\limits_{k=0}^\u221e[\\frac {1}{16^?}(\\frac {4}{8k+1}\u2212\\frac {2}{8k+4}\u2212\\frac {1}{8k+5}\u2212\\frac {1}{8k+6})]
\n$$<\/p>\n

1.1 \u8499\u7279\u5361\u7f57\u65b9\u6cd5<\/h2>\n

\"\"<\/div><\/p>\n

\u4e8c\u3001"\u5706\u5468\u7387\u7684\u8ba1\u7b97"\u5b9e\u4f8b\u8bb2\u89e3<\/h1>\n

\u5706\u5468\u7387\u7684\u8fd1\u4f3c\u8ba1\u7b97\u516c\u5f0f
\n$$
\n?=\\sum\\limits_{k=0}^\u221e[\\frac {1}{16^?}(\\frac {4}{8k+1}\u2212\\frac {2}{8k+4}\u2212\\frac {1}{8k+5}\u2212\\frac {1}{8k+6})]
\n$$<\/p>\n

# CalPiV1.py\n\npi = 0\nN = 10\nfor k in range(N):\n    pi += 1 \/ pow(16, k) * (4 \/ (8 * k + 1) - 2 \/ (8 * k + 4) - 1 \/\n                            (8 * k + 5) - 1 \/ (8 * k + 6))\n    print("\u5706\u5468\u7387\u503c\u662f: {}".format(pi))\n\u5706\u5468\u7387\u503c\u662f: 3.1333333333333333\n\u5706\u5468\u7387\u503c\u662f: 3.1414224664224664\n\u5706\u5468\u7387\u503c\u662f: 3.1415873903465816\n\u5706\u5468\u7387\u503c\u662f: 3.1415924575674357\n\u5706\u5468\u7387\u503c\u662f: 3.1415926454603365\n\u5706\u5468\u7387\u503c\u662f: 3.141592653228088\n\u5706\u5468\u7387\u503c\u662f: 3.141592653572881\n\u5706\u5468\u7387\u503c\u662f: 3.141592653588973\n\u5706\u5468\u7387\u503c\u662f: 3.1415926535897523\n\u5706\u5468\u7387\u503c\u662f: 3.1415926535897913<\/code><\/pre>\n
2.1 \u8499\u7279\u5361\u7f57\u65b9\u6cd5<\/h2>\n
\"\"<\/div><\/p>\n
# CalPiV2.py\n\nfrom random import random\nfrom time import perf_counter\n\nDARTS = 1000 * 1000\nhits = 0.0\nstart = perf_counter()\n\nfor i in range(1, DARTS + 1):\n    x, y = random(), random()\n    dist = pow(x**2 + y**2, 0.5)\n    if dist <= 1.0:\n        hits = hits + 1\n\npi = 4 * (hits \/ DARTS)\nprint("\u5706\u5468\u7387\u503c\u662f: {}".format(pi))\nprint("\u8fd0\u884c\u65f6\u95f4\u662f: {:.5f}s".format(perf_counter() - start))\n\u5706\u5468\u7387\u503c\u662f: 3.141148\n\u8fd0\u884c\u65f6\u95f4\u662f: 0.77535s<\/code><\/pre>\n
\u4e09\u3001"\u5706\u5468\u7387\u7684\u8ba1\u7b97"\u4e3e\u4e00\u53cd\u4e09<\/h1>\n
\"\"<\/div><\/p>\n
3.1 \u7406\u89e3\u65b9\u6cd5\u601d\u7ef4<\/h2>\n
    \n
  • \u6570\u5b66\u601d\u7ef4\uff1a\u627e\u5230\u516c\u5f0f\uff0c\u5229\u7528\u516c\u5f0f\u6c42\u89e3<\/li>\n
  • \u8ba1\u7b97\u601d\u7ef4\uff1a\u62bd\u8c61\u4e00\u79cd\u8fc7\u7a0b\uff0c\u7528\u8ba1\u7b97\u673a\u81ea\u52a8\u5316\u6c42\u89e3<\/li>\n
  • \u8c01\u66f4\u51c6\u786e\uff1f \uff08\u4e0d\u597d\u8bf4\u2026\uff09<\/li>\n<\/ul>\n
    3.2 \u7a0b\u5e8f\u8fd0\u884c\u65f6\u95f4\u5206\u6790<\/h2>\n
      \n
    • \u4f7f\u7528time\u5e93\u7684\u8ba1\u65f6\u65b9\u6cd5\u83b7\u5f97\u7a0b\u5e8f\u8fd0\u884c\u65f6\u95f4<\/li>\n
    • \u6539\u53d8\u6492\u70b9\u6570\u91cf\uff0c\u7406\u89e3\u7a0b\u5e8f\u8fd0\u884c\u65f6\u95f4\u7684\u5206\u5e03<\/li>\n
    • \u521d\u6b65\u638c\u63e1\u7b80\u5355\u7684\u7a0b\u5e8f\u6027\u80fd\u5206\u6790\u65b9\u6cd5<\/li>\n<\/ul>\n
      3.3 \u8ba1\u7b97\u95ee\u9898\u7684\u6269\u5c55<\/h2>\n
      \"\"<\/div><\/p>\n
        \n
      • \u4e0d\u6c42\u89e3\u5706\u5468\u7387\uff0c\u800c\u662f\u67d0\u4e2a\u7279\u5b9a\u56fe\u5f62\u7684\u9762\u79ef<\/li>\n
      • \u5728\u5de5\u7a0b\u8ba1\u7b97\u4e2d\u5bfb\u627e\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u7684\u5e94\u7528\u573a\u666f<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"
        \u4e00\u3001"\u5706\u5468\u7387\u7684\u8ba1\u7b97"\u95ee\u9898\u5206\u6790 \u5706\u5468\u7387\u7684\u8fd1\u4f3c\u8ba1\u7b97\u516c\u5f0f $$ ?=\\sum\\limits_{k […]<\/p>\n","protected":false},"author":3,"featured_media":5449,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[371,375],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/5446"}],"collection":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5446"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/5446\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/media\/5449"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5446"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5446"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}