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A Riemann surface is a surface-like configuration that covers the complex plane with several, and in general infinitely many, "sheets." These sheets can have very complicated ...

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 surface parameterized in variables u and v is called smooth if the tangent vectors in the u and v directions satisfy T_uxT_v!=0, where AxB is a cross product.

The inversion of a spindle torus. If the inversion center lies on the torus, then the spindle cyclide degenerates to a parabolic spindle cyclide.

A smooth two-dimensional surface given by embedding the projective plane into projective 5-space by the homogeneous parametric equations v(x,y,z)=(x^2,y^2,z^2,xy,xz,yz). The ...

The singleton set {0}, with respect to the trivial group structure defined by the addition 0+0=0. The element 0 is the additive identity element of the group, and also the ...

In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

Given a square n×n nonsingular integer matrix A, there exists an n×n unimodular matrix U and an n×n matrix H (known as the Hermite normal form of A) such that AU=H. ...

There are a number of tilings of various shapes by all the 12 order n=6 polyiamonds, summarized in the following table. Several of these (starred in the table below) are also ...