一、公式法:
pi = 0
N = 100
for k in range(N):
pi += 1/pow(16,k)*(\
4/(8*k+1) - 2/(8*k+4) -\
1/(8*k+5) - 1/(8*k+6))
print("圓周率是:{}".format(pi))
pi = 0
N = 100
for k in range(N):
pi += 1/pow(16,k)*(4/(8*k+1) - 2/(8*k+4) - 1/(8*k+5) - 1/(8*k+6))
print("圓周率是:{}".format(pi))
圓周率是:3.141592653589793
二、蒙特卡羅方法:
from random import random
from time import perf_counter
DARTS =1000*1000
hits = 0.0
start = perf_counter()
for i in range(1,DARTS+1):
x, y = random(), random()
dist = pow(x ** 2 + y ** 2, 0.5)
if dist <= 1.0:
hits = hits +1
pi = 4* (hits/DARTS)
print("圓周率值是:{}".format(pi))
print("運行時間是:{:.5f}".format(perf_counter()-start))
圓周率值是:3.14018
運行時間是:1.09499
【MOOC嵩天Python語言程序設計】4.5 實例6:圓周率的計算
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