#_*_ coding=utf-8 *_*
## {{{ http://code.activestate.com/recipes/578130/ (r5)
def pi(places=10):
 """Computes pi to given number of decimal places
 參數places表示要返回的pi的小數點后位數 
 方法：先整體擴大10**8（10的八次方）倍，然后計算完成后再縮小10的八次方倍
 """
 
 # 3 + 3*(1/24) + 3*(1/24)*(9/80) + 3*(1/24)*(9/80)*(25/168)
 # The numerators 1, 9, 25, ... are given by (2x + 1) ^ 2
 # The denominators 24, 80, 168 are given by (16x^2 -24x + 8)
 extra = 8
 one = 10 ** (places+extra)
 t, c, n, na, d, da = 3*one, 3*one, 1, 0, 0, 24
 #這里的n 和d 分別為每一項的分子與分母 ,na 和 da 分別為分子和分分母后一項比前一項增加的數值
 #這里的//可不是C++中的注釋,而是除的意思
 while t > 1: 
 n, na, d, da = n+na, na+8, d+da, da+32
 t = t * n // d
 c += t
 return c // (10 ** extra)

def picirc(radius, aspect_ratio=5):
 """Display the digit of pi in a circle of given radius
 radius:顯示的半徑
 aspect_ratio：調節顯示的比率參數
 """
 #display_width為各行的顯示長度
 display_width = int(radius * aspect_ratio + 10)
 pi_str = repr(pi(int(2 * radius ** 2 * aspect_ratio)))
 pos = 0
 #cols為每一行中要顯示的數字個數
 for i in range(2 * radius):
 cols = int(0.5 + aspect_ratio * (radius**2 - (radius-(i+0.5))**2) ** 0.5)
 print(pi_str[pos:pos+cols].center(display_width)) #將產生的pi數值生成的文本列表中相應的位數取出來顯示在當前行
 pos += cols

if __name__ == '__main__':
 
 picirc(16)
## end of http://code.activestate.com/recipes/578130/ }}}

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