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Given a triangle DeltaABC with inner and outer Soddy centers S and S^', respectively, the inner Soddy triangle DeltaPQR (respectively, outer Soddy triangle DeltaP^'Q^'R^') is ...

A sparse matrix is a matrix that allows special techniques to take advantage of the large number of "background" (commonly zero) elements. The number of zeros a matrix needs ...

A recursive function devised by I. Takeuchi in 1978 (Knuth 1998). For integers x, y, and z, it is defined by (1) This can be described more simply by t(x,y,z)={y if x<=y; {z ...

Given 2n-1 numbers a_k, where k=-n+1, ..., -1, 0, 1, ..., n-1, a Toeplitz matrix is a matrix which has constant values along negative-sloping diagonals, i.e., a matrix of the ...

A topological space M satisfying some separability (i.e., it is a T2-space) and countability (i.e., it is a paracompact space) conditions such that every point p in M has a ...

Let L denote the n×n triangular lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L ...

A k-coloring of a graph G is a vertex coloring that is an assignment of one of k possible colors to each vertex of G (i.e., a vertex coloring) such that no two adjacent ...

Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

There are a number of meanings for the word "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. ...

Clebsch-Gordan coefficients are mathematical symbol used to integrate products of three spherical harmonics. Clebsch-Gordan coefficients commonly arise in applications ...