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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 ...

Calculating the 13th root of a large number (that is a perfect 13th power) is a famous mental calculation challenge. However, because of difficulties in standardizing the ...

The coordinates representing any point of an n-dimensional affine space A by an n-tuple of real numbers, thus establishing a one-to-one correspondence between A and R^n. If V ...

An algebraic manifold is another name for a smooth algebraic variety. It can be covered by coordinate charts so that the transition functions are given by rational functions. ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

An Anosov diffeomorphism is a C^1 diffeomorphism phi of a manifold M to itself such that the tangent bundle of M is hyperbolic with respect to phi. Very few classes of Anosov ...

An antisymmetric matrix, also known as a skew-symmetric or antimetric matrix, is a square matrix that satisfies the identity A=-A^(T) (1) where A^(T) is the matrix transpose. ...

Consider the excircles J_A, J_B, and J_C of a triangle, and the external Apollonius circle Gamma tangent externally to all three. Denote the contact point of Gamma and J_A by ...

Given a ship with a known constant direction and speed v, what course should be taken by a chase ship in pursuit (traveling at speed V) in order to intercept the other ship ...

The Behrmann cylindrical equal-area projection is a cylindrical equal-area projection with a standard parallel of phi_s=30 degrees.