Convert Pi to an approximate rational value on the various denominatorΒΆ
Convert a floating point number (pi) to an approximate rational value on the various denominator.
Note: max_denominator = 1000000
Expected output:
PI = 3.141592653589793
No limit = 3141592653589793/1000000000000000
1 = 3
5 = 16/5
50 = 22/7
90 = 267/85
100 = 311/99
500 = 355/113
1000000 = 3126535/995207
import fractions
import math
print('PI =', math.pi)
f_pi = fractions.Fraction(str(math.pi))
print('No limit =', f_pi)
for d in [1, 5, 50, 90, 100, 500, 1000000]:
limited = f_pi.limit_denominator(d)
print('{0:8} = {1}'.format(d, limited))
Output:
PI = 3.141592653589793
No limit = 3141592653589793/1000000000000000
1 = 3
5 = 16/5
50 = 22/7
90 = 267/85
100 = 311/99
500 = 355/113
1000000 = 3126535/995207