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The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...

A two-dimensional grid graph, also known as a rectangular grid graph or two-dimensional lattice graph (e.g., Acharya and Gill 1981), is an m×n lattice graph that is the graph ...

The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

The Möbius strip, also called the twisted cylinder (Henle 1994, p. 110), is a one-sided nonorientable surface obtained by cutting a closed band into a single strip, giving ...

A quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...

The small stellated dodecahedron is the Kepler-Poinsot polyhedra whose dual polyhedron is the great dodecahedron. It is also uniform polyhedron with Maeder index 34 (Maeder ...

Every planar graph (i.e., graph with graph genus 0) has an embedding on a torus. In contrast, toroidal graphs are embeddable on the torus, but not in the plane, i.e., they ...

An additive cellular automaton is a cellular automaton whose rule is compatible with an addition of states. Typically, this addition is derived from modular arithmetic. ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

Archimedes' cattle problem, also called the bovinum problema, or Archimedes' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...