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Using disk point picking, x = sqrt(r)costheta (1) y = sqrt(r)sintheta (2) for r in [0,1], theta in [0,2pi), choose two points at random in a unit disk and find the ...

In one dimension, the Gaussian function is the probability density function of the normal distribution, f(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)), (1) sometimes also ...

In 1757, V. Riccati first recorded the generalizations of the hyperbolic functions defined by F_(n,r)^alpha(x)=sum_(k=0)^infty(alpha^k)/((nk+r)!)x^(nk+r), (1) for r=0, ..., ...

Let E be a compact connected subset of d-dimensional Euclidean space. Gross (1964) and Stadje (1981) proved that there is a unique real number a(E) such that for all x_1, ...

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

The m×n rook graph (confusingly called the m×n grid by Brouwer et al. 1989, p. 440) and also sometimes known as a lattice graph (e.g., Brouwer) is the graph Cartesian product ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...

A matrix whose elements may contain complex numbers. The matrix product of two 2×2 complex matrices is given by (1) where R_(11) = ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

A cylindrical wedge, also called a cylindrical hoof or cylindrical ungula, is a wedge cut from a cylinder by slicing with a plane that intersects the base of the cylinder. ...