Python - 数学 - 集合と確率を操作する(円の領域を推定する、πの値を推定する)

Pythonからはじめる数学入門
原著

開発環境

• OS X El Capitan - Apple (OS)
• Emacs (Text Editor)
• Python 3.5 (プログラミング言語)

Pythonからはじめる数学入門 (Amit Saha (著)、黒川 利明 (翻訳)、オライリージャパン)の5章(集合と確率を操作する)、5.4(プログラミングチャレンジ)、問題5-5(円の領域を推定する、πの値を推定する)を取り組んでみる。

問題5-5(円の領域を推定する、πの値を推定する)

コード(Emacs)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import random
import math


def distance(x, y):
    return math.sqrt(x**2 + y**2)


def estimate(radius, nums):
    n = 0
    m = 0
    for _ in range(nums):
        x0 = random.uniform(-radius, radius)
        y0 = random.uniform(-radius, radius)
        d = distance(x0, y0)
        if d <= radius:
            n += 1
        else:
            m += 1
    return n / (n + m)

if __name__ == '__main__':
    radius = float(input('Radius: '))
    area = math.pi * radius**2
    square_area = (2 * radius) ** 2
    nums = [10**3, 10**5, 10**6]
    for n in nums:
        estimated =  estimate(radius, n)
        print('Area: {0}, Estimated ({1} darts): {2}'.format(
            area, n, square_area * estimated))
    for n in nums:
        estimated = estimate(radius, n)
        print('pi (math.pi): {0}, Estimated ({1} darts): {2}'.format(
            math.pi, n, 4 * estimated))

入出力結果(Terminal, IPython)

$ ./sample5.py
Radius: 2
Area: 12.566370614359172, Estimated (1000 darts): 12.576
Area: 12.566370614359172, Estimated (100000 darts): 12.5728
Area: 12.566370614359172, Estimated (1000000 darts): 12.577136
pi (math.pi): 3.141592653589793, Estimated (1000 darts): 3.216
pi (math.pi): 3.141592653589793, Estimated (100000 darts): 3.1436
pi (math.pi): 3.141592653589793, Estimated (1000000 darts): 3.14434
$ ./sample5.py
Radius: 2
Area: 12.566370614359172, Estimated (1000 darts): 12.816
Area: 12.566370614359172, Estimated (100000 darts): 12.61504
Area: 12.566370614359172, Estimated (1000000 darts): 12.547936
pi (math.pi): 3.141592653589793, Estimated (1000 darts): 3.1
pi (math.pi): 3.141592653589793, Estimated (100000 darts): 3.13812
pi (math.pi): 3.141592653589793, Estimated (1000000 darts): 3.140856
$ ./sample5.py
Radius: 10
Area: 314.1592653589793, Estimated (1000 darts): 319.6
Area: 314.1592653589793, Estimated (100000 darts): 313.96000000000004
Area: 314.1592653589793, Estimated (1000000 darts): 314.2164
pi (math.pi): 3.141592653589793, Estimated (1000 darts): 3.208
pi (math.pi): 3.141592653589793, Estimated (100000 darts): 3.13492
pi (math.pi): 3.141592653589793, Estimated (1000000 darts): 3.140992
$ ./sample5.py
Radius: 10000
Area: 314159265.3589793, Estimated (1000 darts): 316800000.0
Area: 314159265.3589793, Estimated (100000 darts): 314296000.0
Area: 314159265.3589793, Estimated (1000000 darts): 314274800.0
pi (math.pi): 3.141592653589793, Estimated (1000 darts): 3.164
pi (math.pi): 3.141592653589793, Estimated (100000 darts): 3.13736
pi (math.pi): 3.141592653589793, Estimated (1000000 darts): 3.141904
$ ./sample5.py
Radius: 0.001
Area: 3.141592653589793e-06, Estimated (1000 darts): 3.128e-06
Area: 3.141592653589793e-06, Estimated (100000 darts): 3.14228e-06
Area: 3.141592653589793e-06, Estimated (1000000 darts): 3.1410319999999997e-06
pi (math.pi): 3.141592653589793, Estimated (1000 darts): 3.152
pi (math.pi): 3.141592653589793, Estimated (100000 darts): 3.1382
pi (math.pi): 3.141592653589793, Estimated (1000000 darts): 3.14366
$