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The triangle DeltaM_AM_BM_C formed by joining the midpoints of the sides of a triangle DeltaABC. The medial triangle is sometimes also called the auxiliary triangle (Dixon ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...

The moment of inertia with respect to a given axis of a solid body with density rho(r) is defined by the volume integral I=intrho(r)r__|_^2dV, (1) where r__|_ is the ...

The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for quaternions occurred to him while he was walking along ...

Symmetry operations include the improper rotation, inversion operation, mirror plane, and rotation. Together, these operations create 32 crystal classes corresponding to the ...

The graph sum of graphs G and H is the graph with adjacency matrix given by the sum of adjacency matrices of G and H. A graph sum is defined when the orders of G and H are ...

An area-preserving affine transformation. Equiaffinities include the crossed hyperbolic rotation, elliptic rotation, hyperbolic rotation, and parabolic rotation.

If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f degreesg is differentiable at x. Furthermore, let y=f(g(x)) and u=g(x), then ...

A plane partition whose solid Ferrers diagram is invariant under the rotation which cyclically permutes the x-, y-, and z-axes. Macdonald's plane partition conjecture gives a ...

The word "degree" has many meanings in mathematics. The most common meaning is the unit of angle measure defined such that an entire rotation is 360 degrees. This unit harks ...