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Let t, u, and v be the lengths of the tangents to a circle C from the vertices of a triangle with sides of lengths a, b, and c. Then the condition that C is tangent to the ...

Let j, r, and s be distinct integers (mod n), and let W_i be the point of intersection of the side or diagonal V_iV_(i+j) of the n-gon P=[V_1,...,V_n] with the transversal ...

A condition used in the definition of a mathematical object, commonly denoted : or |. For example, the rationals Q can be defined by Q={p/q:q!=0,p,q in Z}, read as "the set ...

The series sum_(j=1)^(infty)f_j(z) is said to be uniformly Cauchy on compact sets if, for each compact K subset= U and each epsilon>0, there exists an N>0 such that for all ...

A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies det(A)=+/-1. A necessary and sufficient condition that a linear transformation transform a ...

The set of n quantities v_j are components of an n-dimensional vector v iff, under rotation, v_i^'=a_(ij)v_j (1) for i=1, 2, ..., n. The direction cosines between x_i^' and ...

A weighted graph is a graph in which each branch is given a numerical weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers ...

A lattice path from one point to another is p-good if it lies completely below the line y=(p-1)x. (1) Hilton and Pederson (1991) show that the number of p-good paths from (1, ...

A set in R^n which can be reduced to one of its points, say P, by a continuous deformation, is said to be contractible. The transformation is such that each point of the set ...

A second-order ordinary differential equation arising in the study of stellar interiors, also called the polytropic differential equations. It is given by ...