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For a simple continued fraction x=[a_0,a_1,...] with convergents p_n/q_n, the fundamental recurrence relation is given by p_nq_(n-1)-p_(n-1)q_n=(-1)^(n+1).

The first few terms of the continued fraction of the Copeland-Erdős constant are [0; 4, 4, 8, 16, 18, 5, 1, ...] (OEIS A030168), illustrated above. Interestingly, while the ...

Euler's continued fraction is the name given by Borwein et al. (2004, p. 30) to Euler's formula for the inverse tangent, ...

The largest unit fraction, 1/2. 1/2 is a rational number with terminating decimal expansion 0.5.

The continued fraction ((x+1)^n-(x-1)^n)/((x+1)^n+(x-1)^n)=n/(x+)(n^2-1)/(3x+)(n^2-2^2)/(5x+...).

Every irrational number x can be expanded in a unique continued fraction expansion x=b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...)))=[b_0;e_1b_1,e_2b_2,e_3b_3,...] such that b_0 ...

The unit fraction 1/4, also called one-fourth. 1/4 is a rational number with terminating decimal expansion 0.25.

The simple continued fraction representations of e given by [2; 1, 2, 1, 1, 4, 1, 1, 6, ...] (OEIS A003417). This continued fraction is sometimes known as Euler's continued ...

An accumulation point is a point which is the limit of a sequence, also called a limit point. For some maps, periodic orbits give way to chaotic ones beyond a point known as ...

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...