python求pi的方法

#_*_ 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/ }}}

 314159265357932384 
 62338327950288419716939937510582 
 097494459230781062862098628034825342117 
 067982148086513282306709384460955058223172535940 
 81284811174502841027019385211055594622945493038194 
 28810975665933446128475823378678316527120190914585669234 
 60348610454326821339360726024914127372458700660631558817488152 
 0920962829254091715336725903600113305305488204665213841469519415 
 11609433057270365759591953092186117381932611793105118548074462379962749 
 567351885752724122793818301194912983367336244065630860213949463952247 
 371907021798609437027705392171762931767523846748184676694051320005681271452 
 635608277857713427577609173637178721468440901224953430146549585371050792279 
 625235420199561121290219608034418159813629774771309960518707211349999998 
 37297804995105973173281609631859502445945534690830225223082533446850352619311 
 88171010003137838752886587533208381420617177669147303598253490428755468731159562 
 8638823537875937519577818577805321712268066130019278766111959092120193809525 
 7201065485863278865936153381827968230301952035301852969577362259941312497217 
 7528347913151557485724245415069595082953311686172785580750983817546374939319 
 25506040092770167113900984882401285836160356370766010471018194295559619467678 
 374494482553797747268471040475346208046684259069491293313677021521047521 
 6205696602405803815019351125338243003558702474973263914199272604269922796 
 7823547816360093417211219924586315030286182974555706749838505494588586926 
 99569092721079750930295532116534498720275596023806654991198818347977535 
 6636980742654252786255181841757467209777727938000817060016145249192 
 17321721477235014144197356854816136115735255213347574184946843852332 
 39073941433345477624168625183569485562099219222184272550254256 
 887671790494601653466804988627232791786085784383827967976681 
 4541009538837863609506800225125205117392984608412848 
 86269456042419652850222106611863067442786220391949 
 450471237137869609563371917287467765757 
 396241308658325995813390478027 
 5900994657075126