python求pi的方法


            本文实例讲述了python求pi的方法，是一篇翻译自国外网站的文章，分享给大家供大家参考。

具体实现方法如下：





#_*_ coding=utf-8 *_*

## {{{ http://code.activestate.com/recipes/578130/ (r5)

def pi(places=10):

  """Computes pi to given number of decimal places

    参数places表示要返回的pi的小数点后位数  

    方法：先整体扩大10**8（10的八次方）倍，然后计算完成后再缩小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

  #这里的n 和d 分别为每一项的分子与分母 ,na 和 da 分别为分子和分分母后一项比前一项增加的数值

  #这里的//可不是C++中的注释,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:显示的半径

    aspect_ratio：调节显示的比率参数

  """

  #display_width为各行的显示长度

  display_width = int(radius * aspect_ratio + 10)

  pi_str = repr(pi(int(2 * radius ** 2 * aspect_ratio)))

  pos = 0

  #cols为每一行中要显示的数字个数

  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)) #将产生的pi数值生成的文本列表中相应的位数取出来显示在当前行

    pos += cols



if __name__ == '__main__':

  

  picirc(16)

## end of http://code.activestate.com/recipes/578130/ }}}







显示的结果为：





                  31415926535897932384                  

              6264338327950288419716939937510582              

            0974944592307816406286208998628034825342117            

          06798214808651328230664709384460955058223172535940          

         81284811174502841027019385211055596446229489549303819644         

        288109756659334461284756482337867831652712019091456485669234        

       6034861045432664821339360726024914127372458700660631558817488152       

      09209628292540917153643678925903600113305305488204665213841469519415      

     11609433057270365759591953092186117381932611793105118548074462379962749     

    5673518857527248912279381830119491298336733624406566430860213949463952247     

    371907021798609437027705392171762931767523846748184676694051320005681271452    

   63560827785771342757789609173637178721468440901224953430146549585371050792279    

   689258923542019956112129021960864034418159813629774771309960518707211349999998   

   3729780499510597317328160963185950244594553469083026425223082533446850352619311   

   88171010003137838752886587533208381420617177669147303598253490428755468731159562   

   86388235378759375195778185778053217122680661300192787661119590921642019893809525   

   72010654858632788659361533818279682303019520353018529689957736225994138912497217   

   75283479131515574857242454150695950829533116861727855889075098381754637464939319   

   2550604009277016711390098488240128583616035637076601047101819429555961989467678   

   374494482553797747268471040475346462080466842590694912933136770289891521047521   

   62056966024058038150193511253382430035587640247496473263914199272604269922796    

    782354781636009341721641219924586315030286182974555706749838505494588586926    

    9956909272107975093029553211653449872027559602364806654991198818347977535     

     66369807426542527862551818417574672890977772793800081647060016145249192     

      17321721477235014144197356854816136115735255213347574184946843852332      

       3907394143334547762416862518983569485562099219222184272550254256       

        887671790494601653466804988627232791786085784383827967976681        

         45410095388378636095068006422512520511739298489608412848         

          86269456042419652850222106611863067442786220391949          

            4504712371378696095636437191728746776465757            

              3962413890865832645995813390478027              

                  59009946576407895126                  







希望本文所述对大家的Python程序设计有所帮助。