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A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...

There are a number of attractive polyhedron compounds involving four cubes, several of which are illustrated above. The first (left figures), also known as Bakos' compound, ...

C. Kimberling has extensively tabulated and enumerated the properties of triangle centers (Kimberling 1994, 1998, and online), denoting the nth center in his numbering scheme ...

The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

A triangle center (sometimes simply called a center) is a point whose trilinear coordinates are defined in terms of the side lengths and angles of a triangle and for which a ...

The associated Legendre differential equation is a generalization of the Legendre differential equation given by d/(dx)[(1-x^2)(dy)/(dx)]+[l(l+1)-(m^2)/(1-x^2)]y=0, (1) which ...

The first type of tensor-like object derived from a Riemannian metric g which is used to study the geometry of the metric. Christoffel symbols of the first kind are variously ...

A Fredholm integral equation of the first kind is an integral equation of the form f(x)=int_a^bK(x,t)phi(t)dt, (1) where K(x,t) is the kernel and phi(t) is an unknown ...

In two-dimensional polar coordinates, the Helmholtz differential equation is 1/rpartial/(partialr)(r(partialF)/(partialr))+1/(r^2)(partial^2F)/(partialtheta^2)+k^2F=0. (1) ...

The Lommel differential equation is a generalization of the Bessel differential equation given by z^2y^('')+zy^'+(z^2-nu^2)y=kz^(mu+1), (1) or, in the most general form, by ...