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A map defined by one or more polynomials. Given a field K, a polynomial map is a map f:K^n->K^m such that for all points (x_1,...,x_n) in K^n, ...

Let ad=bc, then (1) This can also be expressed by defining (2) (3) Then F_(2m)(a,b,c,d)=a^(2m)f_(2m)(x,y), (4) and identity (1) can then be written ...

By analogy with the squircle, a term first apparently used by Fernández Guasti et al. (2005), the term "rectellipse" (used here for the first time) is a natural ...

A surface which can be interpreted as a self-intersecting rectangle in three dimensions. The Whitney umbrella is the only stable singularity of mappings from R^2 to R^3. It ...

The Barth sextic is a sextic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 65. The surface was ...

The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...

A second-order algebraic surface given by the general equation (1) Quadratic surfaces are also called quadrics, and there are 17 standard-form types. A quadratic surface ...

The Ablowitz-Ramani-Segur conjecture states that a nonlinear partial differential equation is solvable by the inverse scattering method only if every nonlinear ordinary ...

A number which is simultaneously a nonagonal number N_m and pentagonal number P_n and therefore satisfies the Diophantine equation 1/2m(7m-5)=1/2n(3n-1). (1) Completing the ...

The lemniscate, also called the lemniscate of Bernoulli, is a polar curve defined as the locus of points such that the the product of distances from two fixed points (-a,0) ...