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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 ...

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 ...

Consider n strings, each oriented vertically from a lower to an upper "bar." If this is the least number of strings needed to make a closed braid representation of a link, n ...

The exponent is the component of a finite floating-point representation that signifies the integer power to which the radix is raised in determining the value of that ...

The Game of Logic, described by Lewis Carroll--author of Alice in Wonderland--in 1887 (Carroll 1972) consists of discussing the meaning of propositions like "Some fresh cakes ...

The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...

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 ...