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A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

A ternary diagram is a triangular diagram which displays the proportion of three variables that sum to a constant and which does so using barycentric coordinates. The ...

The tesseract is the hypercube in R^4, also called the 8-cell or octachoron. It has the Schläfli symbol {4,3,3}, and vertices (+/-1,+/-1,+/-1,+/-1). The figure above shows a ...

A complete oriented graph (Skiena 1990, p. 175), i.e., a graph in which every pair of nodes is connected by a single uniquely directed edge. The first and second 3-node ...

A universal cellular automaton is a cellular automaton which, like a Turing machine, exhibits universality. von Neumann proved that an automaton consisting of cells with four ...

Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, configuration spaces, etc.) that ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...

An array is a "list of lists" with the length of each level of list the same. The size (sometimes called the "shape") of a d-dimensional array is then indicated as ...

A number k such that nk^2 has its last digit(s) equal to k is called n-automorphic. For example, 1·5__^2=25__ (Wells 1986, pp. 58-59) and 1·6__^2=36__ (Wells 1986, p. 68), so ...

One of the Zermelo-Fraenkel axioms, also known as the axiom of regularity (Rubin 1967, Suppes 1972). In the formal language of set theory, it states that x!=emptyset=> exists ...