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The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is ...

A noncayley graph is a graph which is not a Cayley graph. All graphs that are not vertex-transitive are noncayley graphs. However, some vertex-transitive graph are noncayley. ...

An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A ...

The pentagram, also called the five-point star, pentacle, pentalpha, or pentangle, is the star polygon {5/2}. It is a pagan religious symbol that is one of the oldest symbols ...

pi has decimal expansion given by pi=3.141592653589793238462643383279502884197... (1) (OEIS A000796). The following table summarizes some record computations of the digits of ...

Define a valid "coloring" to occur when no two faces with a common edge share the same color. Given two colors, there is a single way to color an octahedron (Ball and Coxeter ...

A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...

Propositional calculus is the formal basis of logic dealing with the notion and usage of words such as "NOT," "OR," "AND," and "implies." Many systems of propositional ...

If there is no integer 0<x<p such that x^2=q (mod p), i.e., if the congruence (35) has no solution, then q is said to be a quadratic nonresidue (mod p). If the congruence ...

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...