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
 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/ }}}

 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