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In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

A theorem, also called a unicity theorem, stating the uniqueness of a mathematical object, which usually means that there is only one object fulfilling given properties, or ...

About Eric Weisstein's World of Mathematics

The divergence of a vector field F, denoted div(F) or del ·F (the notation used in this work), is defined by a limit of the surface integral del ·F=lim_(V->0)(∮_SF·da)/V (1) ...

A polyhedron is said to be canonical if all its polyhedron edges touch a sphere and the center of gravity of their contact points is the center of that sphere. In other ...

Let Delta denote an integral convex polytope of dimension n in a lattice M, and let l_Delta(k) denote the number of lattice points in Delta dilated by a factor of the integer ...

A collection of identities which hold on a Kähler manifold, also called the Hodge identities. Let omega be a Kähler form, d=partial+partial^_ be the exterior derivative, ...

A simplex, sometimes called a hypertetrahedron (Buekenhout and Parker 1998), is the generalization of a tetrahedral region of space to n dimensions. The boundary of a ...

"Stampacchia's theorem" is a name given to any number of related results in functional analysis, and while the body of the theorem often varies depending on the literature ...

Given a triangle DeltaABC and a point P not a vertex of DeltaABC, define the A^'-vertex of the circumcevian triangle as the point other than A in which the line AP meets the ...