{"id":930770,"date":"2024-12-26T17:23:42","date_gmt":"2024-12-26T09:23:42","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/930770.html"},"modified":"2024-12-26T17:23:43","modified_gmt":"2024-12-26T09:23:43","slug":"python%e5%a6%82%e4%bd%95%e6%b1%82pi","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/930770.html","title":{"rendered":"python\u5982\u4f55\u6c42pi"},"content":{"rendered":"

\"python\u5982\u4f55\u6c42pi\"<\/p>\n

\u5728Python\u4e2d\u6c42pi\u7684\u65b9\u6cd5\u6709\uff1a\u4f7f\u7528\u6570\u5b66\u5e93\u3001\u501f\u52a9\u7b2c\u4e09\u65b9\u5e93\u3001\u901a\u8fc7\u6570\u503c\u65b9\u6cd5\u8ba1\u7b97\u3001\u5229\u7528\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u3002<\/strong>\u5728\u8fd9\u4e9b\u65b9\u6cd5\u4e2d\uff0c\u6700\u7b80\u5355\u7684\u65b9\u5f0f\u662f\u4f7f\u7528Python\u5185\u7f6e\u7684\u6570\u5b66\u5e93math\u63d0\u4f9b\u7684\u5e38\u91cfpi\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u5b66\u4e60\u548c\u7406\u89e3\u6570\u5b66\u8ba1\u7b97\u7684\u8fc7\u7a0b\u4ee5\u53ca\u63d0\u9ad8\u7f16\u7a0b\u6280\u80fd\uff0c\u6211\u4eec\u53ef\u4ee5\u63a2\u7d22\u5176\u4ed6\u8ba1\u7b97pi\u7684\u65b9\u6cd5\uff0c\u5982\u4f7f\u7528\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u6765\u901a\u8fc7\u6a21\u62df\u968f\u673a\u4e8b\u4ef6\u4f30\u8ba1pi\u7684\u503c\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u63a2\u8ba8\u8fd9\u4e9b\u65b9\u6cd5\u53ca\u5176\u5b9e\u73b0\u3002<\/p>\n<\/p>\n

\n

\u4e00\u3001\u4f7f\u7528\u6570\u5b66\u5e93<\/h2>\n<\/p>\n

Python\u7684math<\/code>\u5e93\u63d0\u4f9b\u4e86\u4e00\u4e2a\u7b80\u5355\u6613\u7528\u7684\u65b9\u5f0f\u6765\u83b7\u53d6pi\u7684\u503c\u3002\u8fd9\u4e2a\u5e93\u662fPython\u6807\u51c6\u5e93\u7684\u4e00\u90e8\u5206\uff0c\u4f7f\u7528\u65f6\u4e0d\u9700\u8981\u5b89\u88c5\u4efb\u4f55\u989d\u5916\u7684\u6a21\u5757\u3002<\/p>\n<\/p>\n

1\u3001\u83b7\u53d6pi\u503c<\/h3>\n<\/p>\n

math<\/code>\u5e93\u4e2d\u7684pi<\/code>\u662f\u4e00\u4e2a\u9884\u5b9a\u4e49\u7684\u5e38\u91cf\uff0c\u8868\u793a\u5706\u5468\u7387\u7684\u503c\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u83b7\u53d6\uff1a<\/p>\n<\/p>\n

import math<\/p>\n
pi_value = math.pi<\/p>\n
print(f"Pi value from math library: {pi_value}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u7cbe\u5ea6\u548c\u4f7f\u7528\u573a\u666f<\/h3>\n<\/p>\n
math.pi<\/code>\u63d0\u4f9b\u7684\u503c\u662f\u4e00\u4e2a\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\uff0c\u901a\u5e38\u53ef\u4ee5\u6ee1\u8db3\u5927\u90e8\u5206\u79d1\u5b66\u8ba1\u7b97\u7684\u9700\u6c42\u3002\u5bf9\u4e8e\u4e00\u822c\u7684\u5e94\u7528\u573a\u666f\uff0c\u5982\u51e0\u4f55\u8ba1\u7b97\u3001\u7269\u7406\u6a21\u62df\u7b49\uff0cmath.pi<\/code>\u63d0\u4f9b\u7684\u7cbe\u5ea6\u5df2\u7ecf\u8db3\u591f\u3002<\/p>\n<\/p>\n
\n
\u4e8c\u3001\u4f7f\u7528\u7b2c\u4e09\u65b9\u5e93<\/h2>\n<\/p>\n
\u9664\u4e86math<\/code>\u5e93\u4e4b\u5916\uff0c\u8fd8\u6709\u4e00\u4e9b\u7b2c\u4e09\u65b9\u5e93\u53ef\u4ee5\u7528\u6765\u83b7\u53d6pi\u7684\u503c\uff0c\u5e76\u4e14\u63d0\u4f9b\u66f4\u591a\u7684\u6570\u5b66\u529f\u80fd\uff0c\u5982numpy<\/code>\u548csympy<\/code>\u3002<\/p>\n<\/p>\n
1\u3001\u4f7f\u7528numpy<\/h3>\n<\/p>\n
numpy<\/code>\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u5b83\u4e5f\u63d0\u4f9b\u4e86pi\u7684\u5e38\u91cf\u3002\u5b89\u88c5numpy<\/code>\u53ef\u4ee5\u901a\u8fc7pip<\/code>\u547d\u4ee4\u5b8c\u6210\uff1a<\/p>\n<\/p>\n
pip install numpy<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4f7f\u7528numpy<\/code>\u83b7\u53d6pi\u7684\u503c\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
pi_value = np.pi<\/p>\n
print(f"Pi value from numpy library: {pi_value}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u4f7f\u7528sympy<\/h3>\n<\/p>\n
sympy<\/code>\u662f\u4e00\u4e2a\u7528\u4e8e\u7b26\u53f7\u8ba1\u7b97\u7684Python\u5e93\uff0c\u53ef\u4ee5\u7cbe\u786e\u5730\u5904\u7406pi\u7b49\u6570\u5b66\u5e38\u91cf\u3002\u5b89\u88c5sympy<\/code>\uff1a<\/p>\n<\/p>\n
pip install sympy<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4f7f\u7528sympy<\/code>\u83b7\u53d6pi\u7684\u503c\uff1a<\/p>\n<\/p>\n
from sympy import pi<\/p>\n
print(f"Pi value from sympy library: {pi.evalf()}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
sympy<\/code>\u7684\u4f18\u52bf\u5728\u4e8e\u5b83\u53ef\u4ee5\u8fdb\u884c\u7b26\u53f7\u8fd0\u7b97\uff0c\u5e76\u4e14\u53ef\u4ee5\u6839\u636e\u9700\u8981\u6307\u5b9a\u7cbe\u5ea6\u3002<\/p>\n<\/p>\n
\n
\u4e09\u3001\u6570\u503c\u65b9\u6cd5\u8ba1\u7b97pi<\/h2>\n<\/p>\n
\u6570\u503c\u65b9\u6cd5\u63d0\u4f9b\u4e86\u4e00\u79cd\u901a\u8fc7\u6570\u5b66\u516c\u5f0f\u8ba1\u7b97pi\u7684\u65b9\u5f0f\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5bf9\u4e8e\u5b66\u4e60\u548c\u7406\u89e3\u6570\u5b66\u8ba1\u7b97\u975e\u5e38\u6709\u5e2e\u52a9\u3002<\/p>\n<\/p>\n
1\u3001\u83b1\u5e03\u5c3c\u8328\u516c\u5f0f<\/h3>\n<\/p>\n
\u83b1\u5e03\u5c3c\u8328\u516c\u5f0f\u662f\u8ba1\u7b97pi\u7684\u4e00\u79cd\u7b80\u5355\u65b9\u6cd5\uff1a<\/p>\n<\/p>\n
[<\/p>\n
\\pi = 4 \\times (1 – \\frac{1}{3} + \\frac{1}{5} – \\frac{1}{7} + \\frac{1}{9} – \\ldots)<\/p>\n
]<\/p>\n<\/p>\n
\u5b9e\u73b0\u4ee3\u7801\uff1a<\/p>\n<\/p>\n
def leibniz_formula(n_terms):<\/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 4 * pi_estimate<\/p>\n
pi_value = leibniz_formula(1000000)<\/p>\n
print(f"Pi value from Leibniz formula: {pi_value}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u8d1d\u5229-\u6ce2\u5c14\u6e29-\u666e\u52b3\u8f9b\u65af\u5361\u516c\u5f0f<\/h3>\n<\/p>\n
\u8d1d\u5229-\u6ce2\u5c14\u6e29-\u666e\u52b3\u8f9b\u65af\u5361(BAI<\/a>ley-Borwein-Plouffe)\u516c\u5f0f\u4ee5\u5176\u5feb\u901f\u6536\u655b\u6027\u800c\u95fb\u540d\uff1a<\/p>\n<\/p>\n
[<\/p>\n
\\pi = \\sum_{k=0}^{\\infty} \\frac{1}{16^k} (\\frac{4}{8k+1} – \\frac{2}{8k+4} – \\frac{1}{8k+5} – \\frac{1}{8k+6})<\/p>\n
]<\/p>\n<\/p>\n
\u5b9e\u73b0\u4ee3\u7801\uff1a<\/p>\n<\/p>\n
def bbp_formula(n_terms):<\/p>\n
    pi_estimate = 0<\/p>\n
    for k in range(n_terms):<\/p>\n
        pi_estimate += (1 \/ (16  k)) * (4 \/ (8 * k + 1) - 2 \/ (8 * k + 4) - 1 \/ (8 * k + 5) - 1 \/ (8 * k + 6))<\/p>\n
    return pi_estimate<\/p>\n
pi_value = bbp_formula(100)<\/p>\n
print(f"Pi value from BBP formula: {pi_value}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
\n
\u56db\u3001\u5229\u7528\u8499\u7279\u5361\u7f57\u65b9\u6cd5<\/h2>\n<\/p>\n
\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u662f\u4e00\u79cd\u57fa\u4e8e\u968f\u673a\u6570\u6a21\u62df\u7684\u6570\u503c\u8ba1\u7b97\u65b9\u6cd5\uff0c\u901a\u8fc7\u6a21\u62df\u5927\u91cf\u968f\u673a\u4e8b\u4ef6\u6765\u4f30\u8ba1\u7ed3\u679c\u3002<\/p>\n<\/p>\n
1\u3001\u57fa\u672c\u539f\u7406<\/h3>\n<\/p>\n
\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u7684\u57fa\u672c\u539f\u7406\u662f\u5c06pi\u7684\u8ba1\u7b97\u95ee\u9898\u8f6c\u5316\u4e3a\u5728\u4e00\u4e2a\u5355\u4f4d\u6b63\u65b9\u5f62\u4e2d\u968f\u673a\u6295\u63b7\u70b9\uff0c\u7136\u540e\u901a\u8fc7\u7edf\u8ba1\u843d\u5728\u5355\u4f4d\u5706\u5185\u7684\u70b9\u7684\u6bd4\u4f8b\u6765\u4f30\u8ba1pi\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5982\u679c\u5728\u6b63\u65b9\u5f62\u4e2d\u6295\u63b7n\u4e2a\u70b9\uff0c\u5176\u4e2d\u6709m\u4e2a\u70b9\u843d\u5728\u5706\u5185\uff0c\u90a3\u4e48pi\u53ef\u4ee5\u8fd1\u4f3c\u4e3a\uff1a<\/p>\n<\/p>\n
[<\/p>\n
\\pi \\approx 4 \\times \\frac{m}{n}<\/p>\n
]<\/p>\n<\/p>\n
2\u3001\u5b9e\u73b0\u4ee3\u7801<\/h3>\n<\/p>\n
import random<\/p>\n
def monte_carlo_pi(n_samples):<\/p>\n
    inside_circle = 0<\/p>\n
    for _ in range(n_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 4 * inside_circle \/ n_samples<\/p>\n
pi_value = monte_carlo_pi(1000000)<\/p>\n
print(f"Pi value from Monte Carlo method: {pi_value}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
3\u3001\u4f18\u7f3a\u70b9\u5206\u6790<\/h3>\n<\/p>\n
\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u7684\u4f18\u70b9\u5728\u4e8e\u5176\u7b80\u5355\u6027\u548c\u6613\u4e8e\u5b9e\u73b0\u7684\u7279\u6027\uff0c\u5e76\u4e14\u9002\u7528\u4e8e\u9ad8\u7ef4\u7a7a\u95f4\u7684\u79ef\u5206\u95ee\u9898\u3002\u4f46\u5176\u7f3a\u70b9\u662f\u6536\u655b\u901f\u5ea6\u8f83\u6162\uff0c\u9700\u8981\u5927\u91cf\u7684\u6837\u672c\u624d\u80fd\u5f97\u5230\u8f83\u9ad8\u7684\u7cbe\u5ea6\u3002<\/p>\n<\/p>\n
\n
\u901a\u8fc7\u4ee5\u4e0a\u51e0\u79cd\u65b9\u6cd5\uff0cPython\u80fd\u591f\u4ee5\u4e0d\u540c\u7684\u65b9\u5f0f\u8ba1\u7b97\u548c\u4f7f\u7528pi\u7684\u503c\u3002\u5bf9\u4e8e\u521d\u5b66\u8005\u6765\u8bf4\uff0c\u4f7f\u7528\u5185\u7f6e\u7684math.pi<\/code>\u662f\u6700\u7b80\u5355\u7684\u9009\u62e9\uff0c\u800c\u5bf9\u4e8e\u5e0c\u671b\u6df1\u5165\u7406\u89e3\u6570\u5b66\u8ba1\u7b97\u548c\u7f16\u7a0b\u6280\u5de7\u7684\u5b66\u4e60\u8005\uff0c\u53ef\u4ee5\u5c1d\u8bd5\u6570\u503c\u65b9\u6cd5\u548c\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u7b49\u66f4\u590d\u6742\u7684\u8ba1\u7b97\u65b9\u5f0f\u3002\u65e0\u8bba\u9009\u62e9\u54ea\u79cd\u65b9\u6cd5\uff0c\u4e86\u89e3\u5176\u539f\u7406\u548c\u9002\u7528\u573a\u666f\u90fd\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u5982\u4f55\u5728Python\u4e2d\u4f7f\u7528\u6570\u503c\u65b9\u6cd5\u8ba1\u7b97\u03c0\u7684\u503c\uff1f<\/strong>
\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u6570\u503c\u65b9\u6cd5\u5982\u83b1\u5e03\u5c3c\u8328\u516c\u5f0f\u3001\u8499\u7279\u5361\u6d1b\u65b9\u6cd5\u7b49\u6765\u8ba1\u7b97\u03c0\u7684\u503c\u3002\u4f8b\u5982\uff0c\u83b1\u5e03\u5c3c\u8328\u516c\u5f0f\u8868\u793a\u4e3a\u03c0\/4 = 1 – 1\/3 + 1\/5 – 1\/7 + …\uff0c\u53ef\u4ee5\u901a\u8fc7\u7f16\u5199\u7b80\u5355\u7684\u5faa\u73af\u6765\u5b9e\u73b0\u3002\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u8499\u7279\u5361\u6d1b\u65b9\u6cd5\uff0c\u901a\u8fc7\u968f\u673a\u751f\u6210\u70b9\u5e76\u8ba1\u7b97\u843d\u5728\u5355\u4f4d\u5706\u5185\u7684\u6bd4\u4f8b\u6765\u4f30\u7b97<\/a>\u03c0\u7684\u503c\u3002<\/p>\n
\u6709\u6ca1\u6709Python\u5e93\u4e13\u95e8\u7528\u4e8e\u8ba1\u7b97\u03c0\uff1f<\/strong>
\u662f\u7684\uff0cPython\u6709\u591a\u4e2a\u5e93\u53ef\u4ee5\u9ad8\u6548\u5730\u8ba1\u7b97\u03c0\u7684\u503c\u3002\u6bd4\u5982math<\/code>\u5e93\u63d0\u4f9b\u4e86math.pi<\/code>\u5e38\u91cf\uff0c\u53ef\u4ee5\u76f4\u63a5\u83b7\u53d6\u03c0\u7684\u503c\u3002\u6b64\u5916\uff0cmpmath<\/code>\u5e93\u5219\u53ef\u4ee5\u8ba1\u7b97\u9ad8\u7cbe\u5ea6\u7684\u03c0\uff0c\u9002\u5408\u9700\u8981\u8d85\u9ad8\u7cbe\u5ea6\u8ba1\u7b97\u7684\u573a\u666f\u3002<\/p>\n
\u5728Python\u4e2d\uff0c\u5982\u4f55\u63d0\u9ad8\u8ba1\u7b97\u03c0\u7684\u7cbe\u5ea6\uff1f<\/strong>
\u8981\u63d0\u9ad8\u8ba1\u7b97\u03c0\u7684\u7cbe\u5ea6\uff0c\u53ef\u4ee5\u4f7f\u7528\u9ad8\u7cbe\u5ea6\u8ba1\u7b97\u5e93\u5982mpmath<\/code>\uff0c\u901a\u8fc7\u8bbe\u7f6e\u7cbe\u5ea6\u6765\u83b7\u5f97\u66f4\u51c6\u786e\u7684\u7ed3\u679c\u3002\u4f7f\u7528mp.dps<\/code>\u5c5e\u6027\u53ef\u4ee5\u8bbe\u7f6e\u5c0f\u6570\u70b9\u540e\u7684\u4f4d\u6570\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u901a\u8fc7mp.dps = 50<\/code>\u6765\u8bbe\u7f6e\u8ba1\u7b9750\u4f4d\u5c0f\u6570\u7684\u03c0\u503c\u3002\u8fd9\u6837\u80fd\u591f\u6ee1\u8db3\u79d1\u5b66\u8ba1\u7b97\u548c\u5de5\u7a0b\u5e94\u7528\u4e2d\u7684\u9ad8\u7cbe\u5ea6\u9700\u6c42\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\u6c42pi\u7684\u65b9\u6cd5\u6709\uff1a\u4f7f\u7528\u6570\u5b66\u5e93\u3001\u501f\u52a9\u7b2c\u4e09\u65b9\u5e93\u3001\u901a\u8fc7\u6570\u503c\u65b9\u6cd5\u8ba1\u7b97\u3001\u5229\u7528\u8499\u7279\u5361\u7f57\u65b9\u6cd5\u3002\u5728\u8fd9\u4e9b\u65b9\u6cd5\u4e2d\uff0c\u6700 […]","protected":false},"author":3,"featured_media":930773,"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\/930770"}],"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=930770"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/930770\/revisions"}],"predecessor-version":[{"id":930774,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/930770\/revisions\/930774"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/930773"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=930770"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=930770"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=930770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}