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Also known as the Serret-Frenet formulas, these vector differential equations relate inherent properties of a parametrized curve. In matrix form, they can be written [T^.; ...

Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define ...

This is sometimes knows as the "bars and stars" method. Suppose a recipe called for 5 pinches of spice, out of 9 spices. Each possibility is an arrangement of 5 spices ...

A global field is either a number field, a function field on an algebraic curve, or an extension of transcendence degree one over a finite field. From a modern point of view, ...

Let a Gram point g_n be called "good" if (-1)^nZ(g_n)>0, and "bad" otherwise (Rosser et al. 1969; Edwards 2001, p. 180). Then the interval between two consecutive good Gram ...

The Grassmann graph J_q(n,k) is defined such that the vertices are the k-dimensional subspaces of an n-dimensional finite field of order q and edges correspond to pairs of ...

For any positive integer k, there exists a prime arithmetic progression of length k. The proof is an extension of Szemerédi's theorem.

If 0<p<infty, then the Hardy space H^p(D) is the class of functions holomorphic on the disk D and satisfying the growth condition ...

A non-zero module which is not the direct sum of two of its proper submodules. The negation of indecomposable is, of course, decomposable. An abstract vector space is ...

The inner Napoleon circle, a term coined here for the first time, is the circumcircle of the inner Napoleon triangle. It has center at the triangle centroid G (and is thus ...