Continued fractions

[@prwchan]

@3:20 The continued fraction for sqrt(3) is wrong. It is [1; 1, 2, ...]

[@hamdaniyusuf_dani]

pi can be represented in regular patterns using generalized continued fraction. en.wikipedia.org/wiki/Generalized_continued_fraction#%CF%80

[@miraculix666]

[3;7,15,1]=355/113

[@GeoffryGifari]

oh, and since we know a series expansion of a number (like pi) and also its continued fraction, maybe we can figure out a relationship between both? maybe there is an entire set of theorems relating series and continued fractions

[@GeoffryGifari]

how do you get the continued fraction of π, knowing π first?

[@martinepstein9826]

You find a rational approximation for pi (there are some very good formulas you can use), then convert that approximation into a continued fraction.

[@wyattstevens8574]

If you found a sufficiently accurate approximation, run the numerator and denominator through the Euclidean algorithm and you have the continued fraction as the series of quotients!

[@GeoffryGifari]

maybe the coefficients of continued fractions of irrationals mentioned here are small because the those numbers themselves are small? what if we expand something like √15555401097000167000011

[@martinepstein9826]

Making the number itself large only makes the a_0 term large. To see why the terms are generally small look up Khinchin's constant.