\u4f30\u7b97<\/a>\u03c0\u3002<\/p>\n<\/p>\nimport random<\/p>\ndef monte_carlo_pi(num_samples: int) -> float:<\/p>\n
inside_circle = 0<\/p>\n
for _ in range(num_samples):<\/p>\n
x, y = random.random(), random.random()<\/p>\n
if x<strong>2 + y<\/strong>2 <= 1:<\/p>\n
inside_circle += 1<\/p>\n
return (inside_circle \/ num_samples) * 4<\/p>\n
\u8ba1\u7b97\u03c0\u503c<\/strong><\/h2>\npi_estimate = monte_carlo_pi(1000000)<\/p>\n
print(f"\u4f30\u7b97\u7684\u03c0\u503c\u4e3a: {pi_estimate}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
\n- \u8499\u7279\u5361\u7f57\u65b9\u6cd5\u7684\u4f18\u7f3a\u70b9<\/li>\n<\/ol>\n
\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u7b80\u5355\u6613\u4e8e\u5b9e\u73b0\uff0c\u5e76\u4e14\u53ef\u4ee5\u901a\u8fc7\u589e\u52a0\u6837\u672c\u6570\u6765\u63d0\u9ad8\u7cbe\u5ea6\uff0c\u4f46\u5176\u6536\u655b\u901f\u5ea6\u8f83\u6162\uff0c\u9700\u8981\u5927\u91cf\u7684\u6837\u672c\u6765\u83b7\u5f97\u8f83\u9ad8\u7684\u7cbe\u5ea6\u3002\u6b64\u5916\uff0c\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u7684\u968f\u673a\u6027\u4e5f\u53ef\u80fd\u5bfc\u81f4\u7ed3\u679c\u7684\u4e0d\u7a33\u5b9a\u3002<\/p>\n<\/p>\n
\u4e8c\u3001\u83b1\u5e03\u5c3c\u5179\u7ea7\u6570<\/p>\n<\/p>\n
\u83b1\u5e03\u5c3c\u5179\u7ea7\u6570\u662f\u4e00\u79cd\u57fa\u4e8e\u7ea7\u6570\u6c42\u548c\u7684\u65b9\u6cd5\uff0c\u5b83\u901a\u8fc7\u65e0\u7a77\u7ea7\u6570\u903c\u8fd1\u03c0\u3002\u5176\u516c\u5f0f\u4e3a\uff1a\u03c0 = 4 * (1 – 1\/3 + 1\/5 – 1\/7 + 1\/9 – …) \u3002<\/p>\n<\/p>\n
\n- \u83b1\u5e03\u5c3c\u5179\u7ea7\u6570\u5b9e\u73b0<\/li>\n<\/ol>\n
\u83b1\u5e03\u5c3c\u5179\u7ea7\u6570\u901a\u8fc7\u5faa\u73af\u8fed\u4ee3\u8ba1\u7b97\u7ea7\u6570\u7684\u524dn\u9879\uff0c\u7136\u540e\u5bf9\u7ed3\u679c\u8fdb\u884c\u4e58\u79ef\u8fd0\u7b97\u6765\u4f30\u7b97\u03c0\u503c\u3002<\/p>\n<\/p>\n
def leibniz_pi(n_terms: int) -> float:<\/p>\n pi_estimate = 0<\/p>\n
for i in range(n_terms):<\/p>\n
pi_estimate += ((-1) i) \/ (2 * i + 1)<\/p>\n
return pi_estimate * 4<\/p>\n
\u8ba1\u7b97\u03c0\u503c<\/strong><\/h2>\npi_estimate = leibniz_pi(1000000)<\/p>\n
print(f"\u4f30\u7b97\u7684\u03c0\u503c\u4e3a: {pi_estimate}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
\n- \u83b1\u5e03\u5c3c\u5179\u7ea7\u6570\u7684\u4f18\u7f3a\u70b9<\/li>\n<\/ol>\n
\u83b1\u5e03\u5c3c\u5179\u7ea7\u6570\u65b9\u6cd5\u7b80\u5355\u76f4\u89c2\uff0c\u6613\u4e8e\u5b9e\u73b0\uff0c\u4f46\u5176\u6536\u655b\u901f\u5ea6\u975e\u5e38\u6162\uff0c\u9700\u8981\u5927\u91cf\u7684\u8ba1\u7b97\u624d\u80fd\u83b7\u5f97\u8f83\u9ad8\u7684\u7cbe\u5ea6\u3002\u6b64\u5916\uff0c\u7531\u4e8e\u7ea7\u6570\u7684\u4ea4\u66ff\u6b63\u8d1f\u6c42\u548c\uff0c\u8ba1\u7b97\u65f6\u53ef\u80fd\u51fa\u73b0\u6570\u503c\u8bef\u5dee\u3002<\/p>\n<\/p>\n
\u4e09\u3001\u8d1d\u5229-\u6ce2\u5c14\u6e29-\u666e\u52b3\u65af\u7279\u516c\u5f0f\uff08BBP\u516c\u5f0f\uff09<\/p>\n<\/p>\n
BBP\u516c\u5f0f\u662f\u4e00\u79cd\u7528\u4e8e\u8ba1\u7b97\u03c0\u7684\u5c0f\u6570\u4f4d\u7684\u516c\u5f0f\uff0c\u5b83\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97\u51fa\u03c0\u7684\u4efb\u610f\u4f4d\u5c0f\u6570\uff0c\u8fd9\u662f\u5176\u4ed6\u65b9\u6cd5\u6240\u4e0d\u5177\u5907\u7684\u7279\u6027\u3002BBP\u516c\u5f0f\u662f\u7531\u8d1d\u5229\u3001\u6ce2\u5c14\u6e29\u548c\u666e\u52b3\u65af\u7279\u57281995\u5e74\u53d1\u73b0\u7684\u3002<\/p>\n<\/p>\n
\n- BBP\u516c\u5f0f\u5b9e\u73b0<\/li>\n<\/ol>\n
BBP\u516c\u5f0f\u7684\u5b9e\u73b0\u8f83\u4e3a\u590d\u6742\uff0c\u4f46\u5176\u8ba1\u7b97\u7cbe\u5ea6\u975e\u5e38\u9ad8\uff0c\u5e76\u4e14\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97\u51fa\u03c0\u7684\u4efb\u610f\u5c0f\u6570\u4f4d\u3002<\/p>\n<\/p>\n
def bbp_pi(n_terms: int) -> float:<\/p>\n pi_estimate = 0<\/p>\n
for k in range(n_terms):<\/p>\n
pi_estimate += (1 \/ (16 k)) * (<\/p>\n
4 \/ (8 * k + 1) -<\/p>\n
2 \/ (8 * k + 4) -<\/p>\n
1 \/ (8 * k + 5) -<\/p>\n
1 \/ (8 * k + 6)<\/p>\n
)<\/p>\n
return pi_estimate<\/p>\n
\u8ba1\u7b97\u03c0\u503c<\/strong><\/h2>\npi_estimate = bbp_pi(1000)<\/p>\n
print(f"\u4f30\u7b97\u7684\u03c0\u503c\u4e3a: {pi_estimate}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
\n- BBP\u516c\u5f0f\u7684\u4f18\u7f3a\u70b9<\/li>\n<\/ol>\n
BBP\u516c\u5f0f\u7684\u6700\u5927\u4f18\u70b9\u662f\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97\u03c0\u7684\u4efb\u610f\u4f4d\u5c0f\u6570\uff0c\u8ba1\u7b97\u7cbe\u5ea6\u975e\u5e38\u9ad8\u3002\u4f46\u5176\u5b9e\u73b0\u8f83\u4e3a\u590d\u6742\uff0c\u4e0d\u9002\u5408\u521d\u5b66\u8005\u3002\u6b64\u5916\uff0cBBP\u516c\u5f0f\u7684\u8ba1\u7b97\u901f\u5ea6\u8f83\u6162\uff0c\u5c24\u5176\u662f\u5728\u8ba1\u7b97\u5927\u91cf\u5c0f\u6570\u4f4d\u65f6\u3002<\/p>\n<\/p>\n
\u56db\u3001\u9ad8\u65af-\u83b1\u683c\u6717\u65e5\u7b97\u6cd5<\/p>\n<\/p>\n
\u9ad8\u65af-\u83b1\u683c\u6717\u65e5\u7b97\u6cd5\u662f\u4e00\u79cd\u5feb\u901f\u6536\u655b\u7684\u7b97\u6cd5\uff0c\u7528\u4e8e\u8ba1\u7b97\u03c0\u7684\u9ad8\u7cbe\u5ea6\u503c\u3002\u5b83\u57fa\u4e8e\u692d\u5706\u79ef\u5206\uff0c\u6536\u655b\u901f\u5ea6\u975e\u5e38\u5feb\u3002<\/p>\n<\/p>\n
\n- \u9ad8\u65af-\u83b1\u683c\u6717\u65e5\u7b97\u6cd5\u5b9e\u73b0<\/li>\n<\/ol>\n
\u9ad8\u65af-\u83b1\u683c\u6717\u65e5\u7b97\u6cd5\u7684\u5b9e\u73b0\u76f8\u5bf9\u590d\u6742\uff0c\u4f46\u5176\u8ba1\u7b97\u7cbe\u5ea6\u975e\u5e38\u9ad8\uff0c\u9002\u5408\u9700\u8981\u9ad8\u7cbe\u5ea6\u03c0\u503c\u7684\u573a\u5408\u3002<\/p>\n<\/p>\n
from decimal import Decimal, getcontext<\/p>\ndef gauss_legendre_pi(precision: int) -> Decimal:<\/p>\n
getcontext().prec = precision<\/p>\n
a, b, t, p = Decimal(1), Decimal(1) \/ Decimal(2).sqrt(), Decimal(0.25), Decimal(1)<\/p>\n
for _ in range(precision):<\/p>\n
a_next = (a + b) \/ 2<\/p>\n
b = (a * b).sqrt()<\/p>\n
t -= p * (a - a_next) 2<\/p>\n
a = a_next<\/p>\n
p *= 2<\/p>\n
return (a + b) 2 \/ (4 * t)<\/p>\n
\u8ba1\u7b97\u03c0\u503c<\/strong><\/h2>\npi_estimate = gauss_legendre_pi(1000)<\/p>\n
print(f"\u4f30\u7b97\u7684\u03c0\u503c\u4e3a: {pi_estimate}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
\n- \u9ad8\u65af-\u83b1\u683c\u6717\u65e5\u7b97\u6cd5\u7684\u4f18\u7f3a\u70b9<\/li>\n<\/ol>\n
\u9ad8\u65af-\u83b1\u683c\u6717\u65e5\u7b97\u6cd5\u7684\u4e3b\u8981\u4f18\u70b9\u662f\u6536\u655b\u901f\u5ea6\u5feb\uff0c\u53ef\u4ee5\u5728\u8f83\u5c11\u7684\u8fed\u4ee3\u4e2d\u83b7\u5f97\u9ad8\u7cbe\u5ea6\u7684\u03c0\u503c\u3002\u7136\u800c\uff0c\u5b83\u7684\u5b9e\u73b0\u6bd4\u8f83\u590d\u6742\uff0c\u6d89\u53ca\u5230\u9ad8\u7cbe\u5ea6\u8ba1\u7b97\u548c\u5e73\u65b9\u6839\u7684\u8ba1\u7b97\uff0c\u56e0\u6b64\u5bf9\u4e8e\u521d\u5b66\u8005\u6765\u8bf4\u53ef\u80fd\u8f83\u96be\u7406\u89e3\u3002<\/p>\n<\/p>\n
\u603b\u7ed3<\/p>\n<\/p>\n
Python\u4e2d\u6709\u591a\u79cd\u65b9\u6cd5\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97\u03c0\uff0c\u6bcf\u79cd\u65b9\u6cd5\u90fd\u6709\u5176\u72ec\u7279\u7684\u4f18\u70b9\u548c\u9002\u7528\u573a\u5408\u3002\u5bf9\u4e8e\u521d\u5b66\u8005\u6765\u8bf4\uff0c\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u548c\u83b1\u5e03\u5c3c\u5179\u7ea7\u6570\u662f\u4e0d\u9519\u7684\u9009\u62e9\uff0c\u56e0\u4e3a\u5b83\u4eec\u5b9e\u73b0\u7b80\u5355\u4e14\u6613\u4e8e\u7406\u89e3\u3002\u5982\u679c\u9700\u8981\u8ba1\u7b97\u66f4\u9ad8\u7cbe\u5ea6\u7684\u03c0\u503c\uff0c\u53ef\u4ee5\u8003\u8651\u4f7f\u7528BBP\u516c\u5f0f\u548c\u9ad8\u65af-\u83b1\u683c\u6717\u65e5\u7b97\u6cd5\u3002\u6839\u636e\u5177\u4f53\u9700\u6c42\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5728\u8ba1\u7b97\u7cbe\u5ea6\u548c\u5b9e\u73b0\u590d\u6742\u5ea6\u4e4b\u95f4\u627e\u5230\u5e73\u8861\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n \u5982\u4f55\u7528Python\u8ba1\u7b97\u03c0\u7684\u4e0d\u540c\u65b9\u6cd5\u6709\u54ea\u4e9b\uff1f<\/strong>
Python\u63d0\u4f9b\u4e86\u591a\u79cd\u8ba1\u7b97\u03c0\u7684\u65b9\u5f0f\u3002\u5176\u4e2d\u4e00\u79cd\u5e38\u89c1\u7684\u65b9\u6cd5\u662f\u4f7f\u7528\u6570\u5b66\u5e93\u4e2d\u7684\u5e38\u6570\uff0c\u4f8b\u5982math.pi<\/code>\u3002\u6b64\u5916\uff0c\u4f7f\u7528\u8499\u7279\u5361\u6d1b\u65b9\u6cd5\u4e5f\u662f\u4e00\u4e2a\u6709\u8da3\u7684\u9009\u62e9\uff0c\u901a\u8fc7\u968f\u673a\u751f\u6210\u70b9\u6765\u4f30\u7b97\u5706\u7684\u9762\u79ef\uff0c\u4ece\u800c\u8ba1\u7b97\u03c0\u7684\u503c\u3002\u8fd8\u6709\u4f7f\u7528\u7ea7\u6570\u5c55\u5f00\uff08\u5982\u83b1\u5e03\u5c3c\u8328\u7ea7\u6570\u6216\u9ad8\u65af-\u52d2\u8ba9\u5fb7\u7b97\u6cd5\uff09\u6765\u8fed\u4ee3\u8ba1\u7b97\u03c0\u7684\u503c\uff0c\u8fd9\u4e9b\u90fd\u662f\u6709\u6548\u7684\u6280\u672f\u3002<\/p>\n\u5728\u8ba1\u7b97\u03c0\u65f6\uff0cPython\u7684\u8ba1\u7b97\u7cbe\u5ea6\u5982\u4f55\u8bbe\u7f6e\uff1f<\/strong>
Python\u7684\u5185\u7f6e\u6d6e\u70b9\u6570\u7c7b\u578b\u901a\u5e38\u63d0\u4f9b\u8db3\u591f\u7684\u7cbe\u5ea6\u7528\u4e8e\u4e00\u822c\u8ba1\u7b97\uff0c\u4f46\u5982\u679c\u9700\u8981\u66f4\u9ad8\u7684\u7cbe\u5ea6\uff0c\u53ef\u4ee5\u4f7f\u7528decimal<\/code>\u6a21\u5757\u6216mpmath<\/code>\u5e93\u3002\u8fd9\u4e9b\u5de5\u5177\u5141\u8bb8\u7528\u6237\u6307\u5b9a\u6240\u9700\u7684\u5c0f\u6570\u4f4d\u6570\uff0c\u4ece\u800c\u63d0\u9ad8\u8ba1\u7b97\u7684\u51c6\u786e\u6027\uff0c\u7279\u522b\u662f\u5728\u8fdb\u884c\u590d\u6742\u7684\u6570\u5b66\u8fd0\u7b97\u65f6\u3002<\/p>\n\u4f7f\u7528\u8499\u7279\u5361\u6d1b\u65b9\u6cd5\u8ba1\u7b97\u03c0\u7684\u8fc7\u7a0b\u662f\u600e\u6837\u7684\uff1f<\/strong>
\u8499\u7279\u5361\u6d1b\u65b9\u6cd5\u901a\u8fc7\u5728\u4e00\u4e2a\u5355\u4f4d\u6b63\u65b9\u5f62\u5185\u968f\u673a\u751f\u6210\u70b9\uff0c\u5e76\u8ba1\u7b97\u843d\u5728\u5185\u5207\u5706\u5185\u7684\u70b9\u7684\u6bd4\u4f8b\u6765\u4f30\u7b97\u03c0\u3002\u5177\u4f53\u6b65\u9aa4\u5305\u62ec\uff1a\u751f\u6210\u968f\u673a\u70b9\u7684\u5750\u6807\uff0c\u68c0\u67e5\u8fd9\u4e9b\u70b9\u662f\u5426\u5728\u5706\u5185\uff0c\u8ba1\u7b97\u5706\u5185\u70b9\u7684\u6570\u91cf\u4e0e\u603b\u70b9\u6570\u7684\u6bd4\u4f8b\uff0c\u6700\u540e\u7528\u8be5\u6bd4\u4f8b\u4e58\u4ee54\u6765\u5f97\u5230\u03c0\u7684\u8fd1\u4f3c\u503c\u3002\u8fd9\u79cd\u65b9\u6cd5\u7b80\u5355\u6613\u61c2\uff0c\u4e14\u901a\u8fc7\u589e\u52a0\u968f\u673a\u70b9\u7684\u6570\u91cf\u53ef\u4ee5\u63d0\u9ad8\u8ba1\u7b97\u7684\u7cbe\u5ea6\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u4f7f\u7528Python\u8ba1\u7b97\u03c0\uff08pi\uff09\u53ef\u4ee5\u901a\u8fc7\u591a\u79cd\u65b9\u6cd5\u5b9e\u73b0\uff0c\u5305\u62ec\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u3001\u83b1\u5e03\u5c3c\u5179\u7ea7\u6570\u3001\u8d1d\u5229-\u6ce2\u5c14\u6e29-\u666e\u52b3\u65af\u7279\u516c\u5f0f […]","protected":false},"author":3,"featured_media":992254,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/992248"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=992248"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/992248\/revisions"}],"predecessor-version":[{"id":992255,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/992248\/revisions\/992255"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/992254"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=992248"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=992248"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=992248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
![\"\u5982\u4f55\u7528python\u8ba1\u7b97pi\"](\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25070150\/93fccab9-73d4-4955-a7d9-86c721793b0b.webp\")
<\/p>\n