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Origami is the Japanese art of paper folding. In traditional origami, constructions are done using a single sheet of colored paper that is often, though not always, square. ...

The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for quaternions occurred to him while he was walking along ...

The resistance distance between vertices i and j of a graph G is defined as the effective resistance between the two vertices (as when a battery is attached across them) when ...

The Spencer-Brown form is a simple mathematical concept that formalizes what a mathematical object is formally identical to what it is not (Spencer-Brown 1997, pp. ix and ...

The mathematical study of the likelihood and probability of events occurring based on known information and inferred by taking a limited number of samples. Statistics plays ...

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...

Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...

An amicable pair (m,n) consists of two integers m,n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other. Amicable ...

A problem posed by L. Collatz in 1937, also called the 3x+1 mapping, 3n+1 problem, Hasse's algorithm, Kakutani's problem, Syracuse algorithm, Syracuse problem, Thwaites ...

A definite integral is an integral int_a^bf(x)dx (1) with upper and lower limits. If x is restricted to lie on the real line, the definite integral is known as a Riemann ...