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Let x=[a_0;a_1,...]=a_0+1/(a_1+1/(a_2+1/(a_3+...))) (1) be the simple continued fraction of a "generic" real number x, where the numbers a_i are the partial denominator. ...

Given a Farey sequence with consecutive terms h/k and h^'/k^', then the mediant is defined as the reduced form of the fraction (h+h^')/(k+k^').

Every irrational number x has an approximation constant c(x) defined by c(x)=lim inf_(q->infty)q|qx-p|, where p=nint(qx) is the nearest integer to qx and lim inf is the ...

The Gauss-Kuzmin distribution is the distribution of occurrences of a positive integer k in the continued fraction of a random (or "generic") real number. Consider xi_n ...

Let p_n/q_n be the sequence of convergents of the continued fraction of a number alpha. Then a Brjuno number is an irrational number such that ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...

A set of real numbers x_1, ..., x_n is said to possess an integer relation if there exist integers a_i such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. For ...

If a fixed fraction x of a given amount of money P is lost, and then the same fraction x of the remaining amount is gained, the result is less than the original and equal to ...

Minkowski's question mark function is the function y=?(x) defined by Minkowski for the purpose of mapping the quadratic surds in the open interval (0,1) into the rational ...

G = int_0^infty(e^(-u))/(1+u)du (1) = -eEi(-1) (2) = 0.596347362... (3) (OEIS A073003), where Ei(x) is the exponential integral. Stieltjes showed it has the continued ...