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An algebra with no nontrivial nilpotent ideals. In the 1890s, Cartan, Frobenius, and Molien independently proved that any finite-dimensional semisimple algebra over the real ...

A transformation in which all points along a given line L remain fixed while other points are shifted parallel to L by a distance proportional to their perpendicular distance ...

The line segment connecting opposite polyhedron vertices (i.e., two polyhedron vertices which do not share a common face) in a parallelepiped or other similar solid. Also ...

A nickname for the one-sheeted hyperboloid due to Samuel (1988, p. 95).

The volume of a spherical wedge is V=2/3r^3theta. The surface area of the corresponding spherical lune is S=2r^2theta.

Let f(x) be a nonnegative and monotonic decreasing function in [a,b] and g(x) such that 0<=g(x)<=1 in [a,b], then int_(b-k)^bf(x)dx<=int_a^bf(x)g(x)dx<=int_a^(a+k)f(x)dx, ...

The Stolarsky mean of two numbers a and c is defined by S_p(a,c)=[(a^p-c^p)/(p(a-c))]^(1/(p-1)) (Havil 2003, p. 121).

Teichmüller's theorem asserts the existence and uniqueness of the extremal quasiconformal map between two compact Riemann surfaces of the same genus modulo an equivalence ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the third fundamental form is given by III(v_(p),w_(p))=S(v_(p))·S(w_(p)), where S is ...

A three-colorable graph G is a graph with chromatic number chi(G)<=3.