Re: [math-fun] Khinchin & Geometric Means

Dan Asimov:

It's amazing that Khinchin found that for almost all positive reals x, the GM of the convergents of its CF expansion are independent of x.

Is there a simple reason why this should be true?

It's not simple to me but here is Khinchin's translated 1935 argument: http://chesswanks.com/txt/Khinchin.pdf