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The Simson line is the line containing the feet P_1, P_2, and P_3 of the perpendiculars from an arbitrary point P on the circumcircle of a triangle to the sides or their ...

Given a reference triangle DeltaABC, the trilinear coordinates of a point P with respect to DeltaABC are an ordered triple of numbers, each of which is proportional to the ...

A polynomial having random coefficients.

A stable isolated (i.e., solitary) traveling nonlinear wave solution to a set of equations that obeys a superposition-like principle (i.e., solitons passing through one ...

According to the novel The Hitchhiker's Guide to the Galaxy (Adams 1997), 42 is the ultimate answer to life, the universe, and everything. Unfortunately, it is left as an ...

An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements. For example, there are two distinct ...

A function representable as a generalized Fourier series. Let R be a metric space with metric rho(x,y). Following Bohr (1947), a continuous function x(t) for (-infty<t<infty) ...

Construct a chain C of 2n components in a solid torus V. Now thicken each component of C slightly to form a chain C_1 of 2n solid tori in V, where pi_1(V-C_1)=pi_1(V-C) via ...

Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, ...

First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of ...