What is the best numerator and denominator couple to get the value of $\pi$?

Question

I need to express the value of $\pi$ as numerator/denominator. What is the best pair considering that the numerator should be less than or equal to $2^{62}$? Or how to get this pair?

See http://en.wikipedia.org/wiki/Continued_fraction#Continued_fraction_expansions_of_.CF.80 . — Qiaochu Yuan, Feb 21 '11 at 12:04
See also http://demonstrations.wolfram.com/ApproximatingPiWithContinuedFractions/ — lhf, Feb 21 '11 at 12:18
See http://stackoverflow.com/questions/4637967/algorithm-challenge-generate-continued-fractions-for-a-float — Shai Covo, Feb 21 '11 at 13:37

score 3 · Answer 1 · answered Jan 20 '15 at 18:23

3

I think $\frac{129988029236677443584}{41376474791582048256}$ is the closest fraction to $\pi$ with a numerator less than $2^{62}$.

Edit: I just realized that this question is four years old.

answered Jan 20 '15 at 18:23

KSFT

133

What is the best numerator and denominator couple to get the value of $\pi$?

1 Answers1