## Khintchine's constantKhintchine's constant is one of the most remarkable yet poorly understand constants in mathematics, which captures in a fascinating way the behavior of almost all real numbers. Pick a real number at
random and write it down as a continued
fraction. Almost certainly, the geometric
mean of the terms in this continued fraction will be Khintchine's constant,
which has the value 2.685452... It is important to say "almost certainly"
because there are some real numbers including all rational
numbers, roots of third order polynomials,
and certain other classes of number, whose continued fractions would give
a different result. These exceptions, however, form a tiny minority of all
real numbers. ## Related category• NOTABLE NUMBERS | |||||

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