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The primes nearest to the nonnegative integers n=0, 1, 2, ..., assigning ties to the smaller prime, are 2, 2, 2, 3, 3, 5, 5, 7, 7, 7, 11, 11, 11, 13, ... (OEIS A051697). If ...

The pentagrammic prism is the self-intersecting uniform polyhedron with Maeder index 78 (Maeder 1997), Coxeter index 33 (Coxeter et al. 1954), and Har'El index 3 (Har'El ...

If a cyclic quadrilateral ABCD is inscribed in a circle c_1 of a coaxal system such that one pair AC of connectors touches another circle c_2 of the system at P, then each ...

The principal branch of an analytic multivalued function, also called a principal sheet, is a single-valued "slice" (i.e., branch) of the function chosen that is for ...

A curve alpha on a regular surface M is a principal curve iff the velocity alpha^' always points in a principal direction, i.e., S(alpha^')=kappa_ialpha^', where S is the ...

Let sigma(m) be the divisor function of m. Then two numbers m and n are a quasiamicable pair if sigma(m)=sigma(n)=m+n+1. The first few are (48, 75), (140, 195), (1050, 1925), ...

A Gaussian quadrature-like formula for numerical estimation of integrals. It requires m+1 points and fits all polynomials to degree 2m, so it effectively fits exactly all ...

Regular expressions define formal languages as sets of strings over a finite alphabet. Let sigma denote a selected alphabet. Then emptyset is a regular expression that ...

A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...