def pi(places=10):
"Computes pi to given number of decimal places"
# 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)
# They n / d ratio converges on 0.25
extra = 8
one = 10 ** (places+extra)
t, c, n, na, d, da = 3*one, 3*one, 1, 0, 0, 24
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"
display_width = int(radius * aspect_ratio + 10)
pi_str = repr(pi(int(2 * radius ** 2 * aspect_ratio)))
pos = 0
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))
pos += cols
if __name__ == '__main__':
picirc(16)
Diff to Previous Revision
--- revision 3 2012-05-12 20:59:10
+++ revision 4 2012-05-13 04:34:36
@@ -1,22 +1,26 @@
def pi(places=10):
"Computes pi to given number of decimal places"
- # 3 + 3*(1/24) + 3*(1/24)*(9/80) + 3*(1/24)*(9/80)*(25/168) + ...
+ # 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)
+ # They n / d ratio converges on 0.25
extra = 8
one = 10 ** (places+extra)
t, c, n, na, d, da = 3*one, 3*one, 1, 0, 0, 24
while t > 1:
- n, na, d, da = n+na, na+8, d+da, da+32
+ 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, screen_width=90, aspect_ratio=5):
+def picirc(radius, aspect_ratio=5):
"Display the digit of pi in a circle of given radius"
+ display_width = int(radius * aspect_ratio + 10)
pi_str = repr(pi(int(2 * radius ** 2 * aspect_ratio)))
pos = 0
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(screen_width))
+ print(pi_str[pos:pos+cols].center(display_width))
pos += cols
if __name__ == '__main__':
