Khintchine's constant

Khintchine'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.