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。