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A figurate number of the form 4n^2-3n. The first few are 1, 10, 27, 52, 85, ... (OEIS A001107). The generating function giving the decagonal numbers is ...

A delta sequence is a sequence of strongly peaked functions for which lim_(n->infty)int_(-infty)^inftydelta_n(x)f(x)dx=f(0) (1) so that in the limit as n->infty, the ...

Let s_b(n) be the sum of the base-b digits of n, and epsilon(n)=(-1)^(s_2(n)) the Thue-Morse sequence, then product_(n=0)^infty((2n+1)/(2n+2))^(epsilon(n))=1/2sqrt(2).

A binary relation associated with an instance of the stable marriage problem. Stable marriages correspond to vertices with outdegree 0 in the divorce digraph (Skiena 1990, p. ...

A number of attractive 10-compounds of the regular dodecahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

The equations are x = ((lambda-lambda_0)(1+costheta))/(sqrt(2+pi)) (1) y = (2theta)/(sqrt(2+pi)), (2) where theta is the solution to theta+sintheta=(1+1/2pi)sinphi. (3) This ...

A pentagonal rotunda adjoined to a decagonal prism which is Johnson solid J_(21).

To enumerate a set of objects satisfying some set of properties means to explicitly produce a listing of all such objects. The problem of determining or counting all such ...

An equilateral polygon is a polygon whose edges are all of equal length (Williams 1979, pp. 31-32). The most prominent examples of equilateral polygons are the regular ...

10^(18) bytes. Unfortunately, the term is sometimes also used to mean 2^(60)=1024^6 bytes. However, the latter usage is deprecated, and the term exbibyte is preferred for ...