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

The logical axiom R(x,y)=!(!(x v y) v !(x v !y))=x, where !x denotes NOT and x v y denotes OR, that, when taken together with associativity and commutativity, is equivalent ...

For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

A pseudocylindrical map projection which distorts shape, area, scale, and distance to create attractive average projection properties.

dN^^+kappa_idr=0, where N^^ is the unit normal vector and kappa_i is one of the two principal curvatures.

The nonlinear three-dimensional map X^. = -(Y+Z) (1) Y^. = X+aY (2) Z^. = b+XZ-cZ (3) whose strange attractor is show above for a=0.2, b=0.2, and c=8.0.

|_n]={n for n!=0; 1 for n=0. (1)

If any of the roots of a polynomial are increased, then all of the critical points increase.

The operation of taking an nth root of a number.

The sum of the reciprocals of roots of an equation equals the negative coefficient of the linear term in the Maclaurin series.