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The nine-point circle, also called Euler's circle or the Feuerbach circle, is the circle that passes through the perpendicular feet H_A, H_B, and H_C dropped from the ...

A Pisot number is a positive algebraic integer greater than 1 all of whose conjugate elements have absolute value less than 1. A real quadratic algebraic integer greater than ...

If there is an integer 0<x<p such that x^2=q (mod p), (1) i.e., the congruence (1) has a solution, then q is said to be a quadratic residue (mod p). Note that the trivial ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...

The Spencer-Brown form is a simple mathematical concept that formalizes what a mathematical object is formally identical to what it is not (Spencer-Brown 1997, pp. ix and ...

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 ...

Smarandache sequences are any of a number of simply generated integer sequences resembling those considered in published works by Smarandache such as the consecutive number ...

The arithmetic mean of a set of values is the quantity commonly called "the" mean or the average. Given a set of samples {x_i}, the arithmetic mean is x^_=1/Nsum_(i=1)^Nx_i. ...

Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...