significant_pi_digits.py

#! /usr/bin/env python3

# http://www.wolframalpha.com/input/?i=1000+digits+of+pi
pi_str = '3.1415926535897932384626'\
'433832795028841971693993751058209'\
'749445923078164062862089986280348'\
'253421170679821480865132823066470'\
'938446095505822317253594081284811'\
'174502841027019385211055596446229'\
'489549303819644288109756659334461'\
'284756482337867831652712019091456'\
'485669234603486104543266482133936'\
'072602491412737245870066063155881'\
'748815209209628292540917153643678'\
'925903600113305305488204665213841'\
'469519415116094330572703657595919'\
'530921861173819326117931051185480'\
'744623799627495673518857527248912'\
'279381830119491298336733624406566'\
'430860213949463952247371907021798'\
'609437027705392171762931767523846'\
'748184676694051320005681271452635'\
'608277857713427577896091736371787'\
'214684409012249534301465495853710'\
'507922796892589235420199561121290'\
'219608640344181598136297747713099'\
'605187072113499999983729780499510'\
'597317328160963185950244594553469'\
'083026425223082533446850352619311'\
'881710100031378387528865875332083'\
'814206171776691473035982534904287'\
'554687311595628638823537875937519'\
'577818577805321712268066130019278'\
'76611195909216420199'

def decimal_places(s):
	return len(s) - s.find('.') - 1

def shifted_integer(s):
	return int(s.replace('.',''))

def rebuild_decimal_string(i,d):
	s = str(i)
	return s[0]+'.'+s[1:]

# diameter of the observable universe
# http://www.wolframalpha.com/input/?i=880000000000000000000000000m
diameter_str = '88'+''.join(['0' for x in range(25)]) # m

# diameter of the earth
# http://www.wolframalpha.com/input/?i=diameter+of+the+earth+in+m
#diameter_str = '12734889'

# just a test
#diameter_str = '1000'

diameter = int(diameter_str)

significant_digits = 2
while significant_digits <= len(pi_str)-1:
	truncated_pi_str = pi_str[0:1+significant_digits]
	truncated_pi_decimal_places = decimal_places(truncated_pi_str)
	truncated_pi_integer = shifted_integer(truncated_pi_str)
	truncated_pi_integer_plus = truncated_pi_integer + 1
	truncated_pi_str_plus = rebuild_decimal_string(truncated_pi_integer_plus, truncated_pi_decimal_places) 
	
	circumference_str = str(truncated_pi_integer * diameter)[0:-truncated_pi_decimal_places]
	circumference_str_plus = str(truncated_pi_integer_plus * diameter)[0:-truncated_pi_decimal_places]
	difference = int(circumference_str_plus) - int(circumference_str)
	
	print('{}m * {} = {}m'.format(diameter, truncated_pi_str, circumference_str))
	print('{}m * {} = {}m'.format(diameter, truncated_pi_str_plus, circumference_str_plus))
	print('{}m - {}m = {}m, ({}%)'.format(circumference_str_plus, circumference_str, difference,100*difference/int(circumference_str)))
	print()
	if difference == 0:
		print('significant digits: {}'.format(significant_digits))
		print(truncated_pi_str)
		break
	significant_digits = significant_digits + 1