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Martin Sleziak
Martin Sleziak
01:17
This question was recently mentioned on meta: Intuition behind Khinchin's constant
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Q: Intuition behind Khinchin's constant

easily_surprisedKhinchin proved that For almost all reals $r$ with continued fraction representation $[a_o; a_1, a_2, \dots ]$ the sequence $K_n = \left(\prod_{i=1}^{n} a_i\right)^{1/n}$ converges to a constant $K$ (Khinchin's constant) independent of $r$. This is quite surprising, and I was wonde...

number-theory continued-fractions
Khinchin's constant
In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers x, coefficients ai of the continued fraction expansion of x have a finite geometric mean that is independent of the value of x and is known as Khinchin's constant. That is, for x = a 0 + 1...

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