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The contraction of a tensor is obtained by setting unlike indices equal and summing according to the Einstein summation convention. Contraction reduces the tensor rank by 2. ...

The Yiu triangle DeltaO_AO_BO_C is the triangle formed by the centers of the Yiu circles. It has area where f(a,b,c) is a 12th-order polynomial and Delta is the area of the ...

The total power of a triangle is defined by P=1/2(a_1^2+a_2^2+a_3^2), (1) where a_i are the side lengths, and the "partial power" is defined by p_1=1/2(a_2^2+a_3^2-a_1^2). ...

An extension field F subset= K is called finite if the dimension of K as a vector space over F (the so-called degree of K over F) is finite. A finite field extension is ...

In mathematics, a small positive infinitesimal quantity, usually denoted epsilon or epsilon, whose limit is usually taken as epsilon->0. The late mathematician P. Erdős also ...

A Laurent polynomial with coefficients in the field F is an algebraic object that is typically expressed in the form ...+a_(-n)t^(-n)+a_(-(n-1))t^(-(n-1))+... ...

A unique factorization domain, called UFD for short, is any integral domain in which every nonzero noninvertible element has a unique factorization, i.e., an essentially ...

The triangle with edge lengths 3, 4, and 5 is the right triangle with smallest possible integer lengths and corresponds to the Pythagorean triple (3,4,5) where the legs have ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

An interpolation formula, sometimes known as the Newton-Bessel formula, given by (1) for p in [0,1], where delta is the central difference and B_(2n) = 1/2G_(2n) (2) = ...