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Python example of how to calculate the value of pi to any digit
Python example of how to calculate the value of pi to any digit
This article mainly introduces Python's method of calculating the value of pi to any position, briefly analyzes the calculation principle of pi, and analyzes the relevant operating skills of Python's calculation of pi in the form of examples. Friends in need can refer to the following
The example in this article describes the method of calculating the value of pi to any digit in Python. Share it with everyone for your reference, the details are as follows:
1. Requirements analysis
Enter the number of digits you want to calculate to the decimal point Number, calculate the value of pi.
2. Algorithm: Ma Qing formula
π/4=4arctan1/5-arctan1/239
This formula was discovered by the British astronomy professor John Mathing in 1706. He used this formula to calculate pi to 100 digits. Ma Qing's formula can obtain 1.4 decimal digits of precision for each calculated item. Because the multiplicand and dividend during its calculation are neither larger than a long integer, it can be easily programmed on a computer.
3. Write a program in python language to find the pi to any position as follows:
# -*- coding: utf-8 -*- from __future__ import pision ####################导入时间模块 import time ###############计算当前时间 time1=time.time() ################算法根据马青公式计算圆周率#################### number = int(raw_input('请输入想要计算到小数点后的位数n:')) # 多计算10位，防止尾数取舍的影响 number1 = number+10 # 算到小数点后number1位 b = 10**number1 # 求含4/5的首项 x1 = b*4//5 # 求含1/239的首项 x2 = b// -239 # 求第一大项 he = x1+x2 #设置下面循环的终点，即共计算n项 number *= 2 #循环初值=3，末值2n,步长=2 for i in xrange(3,number,2): # 求每个含1/5的项及符号 x1 //= -25 # 求每个含1/239的项及符号 x2 //= -57121 # 求两项之和 x = (x1+x2) // i # 求总和 he += x # 求出π pai = he*4 #舍掉后十位 pai //= 10**10 ############ 输出圆周率π的值 paistring=str(pai) result=paistring[0]+str('.')+paistring[1:len(paistring)] print result time2=time.time() print u'总共耗时：' + str(time2 - time1) + 's'
Run result:
Please enter the number of digits you want to calculate to the decimal point n:20
3.14159265358979323846
Total time spent: 9.77699995041s
Please enter the number of digits you want to calculate to the decimal point n:50
3.14159265358979323846264338327950288419716939937510
Total time spent: 2.30099987984s
The running screenshot is as follows:
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