Python - Math - Playing with Sets and Probability(Estimating the Area of a Circle, π)

Doing Math with Python

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)

Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More! (Amit Saha (著)、No Starch Press)のChapter 5.(Playing with Sets and Probability)、Programming Challenges #5: Estimating the Area of a Circle, π(No. 3664)を解いてみる。

#5: Estimating the Area of a Circle, π(No. 3664)

コード(Emacs)

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

import random
import math

RADIUS = 2


def area_of_circle(num):
    n = 0
    for _ in range(num):
        x = random.uniform(0, 2 * RADIUS)
        y = random.uniform(0, 2 * RADIUS)
        if abs((RADIUS - x)**2 + (RADIUS - y)**2) <= RADIUS**2:
            n += 1
    return (2 * RADIUS) ** 2 * n / num

# estimating the value of pi


def pi(radius, num):
    n = 0
    for _ in range(num):
        x = random.uniform(0, 2 * radius)
        y = random.uniform(0, 2 * radius)
        if abs((radius - x)**2 + (radius - y)**2) <= radius**2:
            n += 1
    return 4 * n / num

if __name__ == '__main__':
    print('Radius: {0}'.format(RADIUS))
    AREA = RADIUS**2 * math.pi
    nums = [10**3, 10**5, 10**6]
    for n in nums:
        print('Area: {0}, Estimated ({1} darts): {2})'.format(
            AREA, n, area_of_circle(n)))

    print('π: {0}'.format(math.pi))
    for r in range(1, 6):
        print('Radius: {0}'.format(r))
        for n in nums:
            print('Estimated ({0}): {1}'.format(n, pi(r, n)))

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): 12.60672)
Area: 12.566370614359172, Estimated (1000000 darts): 12.573664)
π: 3.141592653589793
Radius: 1
Estimated (1000): 3.12
Estimated (100000): 3.14028
Estimated (1000000): 3.143084
Radius: 2
Estimated (1000): 3.212
Estimated (100000): 3.14244
Estimated (1000000): 3.141948
Radius: 3
Estimated (1000): 3.068
Estimated (100000): 3.15572
Estimated (1000000): 3.141496
Radius: 4
Estimated (1000): 3.216
Estimated (100000): 3.13848
Estimated (1000000): 3.140504
Radius: 5
Estimated (1000): 3.136
Estimated (100000): 3.14436
Estimated (1000000): 3.142588
$