python - Pi 使用 Python

Question

我是 Python 初学者。我尝试用 Python 语言评估 pi。我在这里使用 Archimedes method .

我的代码是:

import math
from decimal import *
getcontext().prec = 50

pi = 0
PolySides = 6
SideLen = 1
Perim = 6
Dia = 2

while PolySides < 10000000000:
    SideLen2 = Decimal(SideLen) / Decimal(2)
    radius_a = Decimal(math.sqrt(1 - SideLen2**2))
    radius_b = Decimal(1) - Decimal(radius_a)
    SideLenNew = Decimal(math.sqrt(SideLen2**2 + radius_b**2))
    PolyCircum = Decimal(PolySides * SideLen)
    pi = PolyCircum / Dia
    print('Polygon Sides:', PolySides, 'Pi = ', pi)
    SideLen = SideLenNew
    PolySides = 2 * PolySides

但出于某种原因，此代码将 pi 打印到小数点后 14 位。我不明白我在哪里失去了精度。谢谢。

Answer 1

您在 float 和 decimal 之间穿梭。 math.sqrt 接受一个float 并返回一个float，因此会进行转换，将精度截断为float的。

这些改变就足够了:

while PolySides < 10000000000000000000:
    SideLen2 = Decimal(SideLen) / 2
    radius_a = (1 - SideLen2**2).sqrt()
    radius_b = 1 - radius_a
    SideLenNew = (SideLen2**2 + radius_b**2).sqrt()
    PolyCircum = Decimal(PolySides * SideLen)
    pi = PolyCircum / Dia
    print('Polygon Sides:', PolySides, 'Pi = ', pi)
    SideLen = SideLenNew
    PolySides = 2 * PolySides