Search Results for ""

A number of the form Tt_n=((n+2; 2); 2)=1/8n(n+1)(n+2)(n+3) (Comtet 1974, Stanley 1999), where (n; k) is a binomial coefficient. The first few values are 3, 15, 45, 105, 210, ...

The twin composites may be defined by analogy with the twin primes as pairs of composite numbers (n,n+2). Since all even number are trivially twin composites, it is natural ...

A walk is a sequence v_0, e_1, v_1, ..., v_k of graph vertices v_i and graph edges e_i such that for 1<=i<=k, the edge e_i has endpoints v_(i-1) and v_i (West 2000, p. 20). ...

Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

The geometric centroid of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as x^_ = ...

Ballantine's series is the series for pi given by pi=864sum_(n=0)^infty((n!)^24^n)/((2n+1)!325^(n+1)) +1824sum_(n=0)^infty((n!)^24^n)/((2n+1)!3250^(n+1))-20cot^(-1)239 ...

The chromatic number of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color (Skiena 1990, p. ...

(1) for p in [-1/2,1/2], where delta is the central difference and S_(2n+1) = 1/2(p+n; 2n+1) (2) S_(2n+2) = p/(2n+2)(p+n; 2n+1), (3) with (n; k) a binomial coefficient.

The "binary" Champernowne constant is obtained by concatenating the binary representations of the integers C_2 = 0.(1)(10)(11)(100)(101)(110)(111)..._2 (1) = ...