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A rounded rectangle is the shape obtained by taking the convex hull of four equal circles of radius r and placing their centers at the four corners of a rectangle with side ...

Two square matrices A and B that are related by B=X^(-1)AX, (1) where X is a square nonsingular matrix are said to be similar. A transformation of the form X^(-1)AX is called ...

A flexagon made with square faces. Gardner (1961) shows how to construct a tri-tetraflexagon, tetra-tetraflexagon, and hexa-tetraflexagon.

The number M_2(n) = 1/nsum_(k=1)^(n^2)k (1) = 1/2n(n^2+1) (2) to which the n numbers in any horizontal, vertical, or main diagonal line must sum in a magic square. The first ...

Clean tile is a game investigated by Buffon (1777) in which players bet on the number of different tiles a thrown coin will partially cover on a floor that is regularly ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

Probability and Statistics

The eight Gell-Mann matrices lambda_i, i=1,...,8, are an example of the set of generators of the Lie algebra associated to the special unitary group SU(3). Explicitly, these ...

Fermat's 4n+1 theorem, sometimes called Fermat's two-square theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique ...

There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...