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The volume of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as V=1/6sum_(i=1)^Na_i·n_i, where the normal n_i ...

An elementary theorem in geometry whose name means "asses' bridge," perhaps in reference to the fact that fools would be unable to pass this point in their geometric studies. ...

A positive semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonnegative. A matrix m may be tested to determine if it is positive semidefinite in the ...

Triangle centers with triangle center functions of the form alpha=a^n are called nth power points. These points lie along the trilinear curve a^n:b^n:c^n that passes through ...

The Prosthaphaeresis formulas, also known as Simpson's formulas, are trigonometry formulas that convert a product of functions into a sum or difference. They are given by ...

A radial function is a function phi:R^+->R satisfying phi(x,c)=phi(|x-c|) for points c in some subset Xi subset R^n. Here, |·| denotes the standard Euclidean norm in R^n and ...

A positive number k such that a lamina or solid body with moment of inertia about an axis I and mass m is given by I=mk^2. Pickover (1995) defines a generalization of k as a ...

The regular dodecagon, illustrated above, is the constructible 12-sided regular polygon that can be denoted using the Schläfli symbol {12}. The Australian 50-cent piece is ...

Isolated resonances in a dynamical system can cause considerable distortion of preserved tori in their neighborhood, but they do not introduce any chaos into a system. ...

If A is a class of recursively enumerable sets, then the set of Gödel numbers of functions whose domains belong to A is called its index set. If the index set of A is a ...