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December 2, 2017 13:57
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Decimals to fractions, and some other stuff i was playing with and forgot about.
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# https://www.quora.com/How-do-you-determine-sum-limits_-n-1-infty-frac-n+1-4-n-by-hand/answer/Job-Bouwman | |
from __future__ import division, print_function # Fix Python 2. | |
def dec2frac(f): | |
"From scratch, 7dec15. Handles negative input since 9apr17." | |
of = f | |
f = abs(f) | |
n = 1 | |
d = 2 | |
while 1: | |
diff = n/d - f | |
#print(n, d, diff, f) | |
if abs(diff) < 0.00001: break | |
if diff > 0: | |
n -= 1 | |
d += 1 | |
else: n += 1 | |
return (-n if of < 0 else n, d) | |
print(dec2frac(0.235)) # => 47/200 | |
print(dec2frac(0.3333333333333)) # => 1/3 | |
print(dec2frac(0.35)) # => 7/20 | |
print(dec2frac(0.13)) # => 13/100 | |
print(dec2frac(0.37)) # => 37/100 | |
print(dec2frac(7/8)) # => 7/8 | |
1/0 # lazy exit | |
def gcd(a, b): | |
"https://en.wikipedia.org/wiki/Greatest_common_divisor" | |
gcd = int(a) | |
while gcd > 1: | |
if a%gcd == 0 and b%gcd == 0: break | |
gcd -= 1 | |
return gcd | |
def dec_to_frac(f): | |
"http://www.purplemath.com/modules/percents2.htm" | |
if f == 0: return 0 | |
sf = str(f%1)[2:] | |
lf = len(sf) | |
repeating = False | |
for i, c in enumerate(sf): | |
if sf.find(c) < i: | |
lf = i | |
repeating = True | |
break | |
x = 10**(lf) | |
print("f:%s len:%s x:%s"%(str(f), lf, x)) | |
a = int(x*f)#-f) | |
if repeating: | |
a = int(x*f-f) | |
b = x -1 | |
else: | |
a = int(x*f) | |
b = x | |
print("gcd(x*f, x)", x*f) | |
d = gcd(a, x) | |
#print(a, b, d) | |
return (a//d, b//d) | |
sum = 0 | |
for i in range(5): | |
n = i+1 | |
sum += (n+1)/(4**n) | |
print(i, sum) | |
print(7/9) | |
for i in range(10): | |
print("{}/{}={}, {}".format(i, i+1, i/(i+1), dec2frac(i/(i+1)))) |
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Python can do this since 4 months ago: