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Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

Convergents of the pi continued fractions are the simplest approximants to pi. The first few are given by 3, 22/7, 333/106, 355/113, 103993/33102, 104348/33215, ... (OEIS ...

A prime constellation, also called a prime k-tuple, prime k-tuplet, or prime cluster, is a sequence of k consecutive numbers such that the difference between the first and ...

A quadrilateral, sometimes also known as a tetragon or quadrangle (Johnson 1929, p. 61) is a four-sided polygon. If not explicitly stated, all four polygon vertices are ...

The regular octahedron, often simply called "the" octahedron, is the Platonic solid with six polyhedron vertices, 12 polyhedron edges, and eight equivalent equilateral ...

The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century (Wolfram 2002, p. 43). It is also called the Sierpiński ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...