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A plane curve is a curve that lies in a single plane. A plane curve may be closed or open. Curves which are interesting for some reason and whose properties have therefore ...

The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...

A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...

The real projective plane is the closed topological manifold, denoted RP^2, that is obtained by projecting the points of a plane E from a fixed point P (not on the plane), ...

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

The Schröder number S_n is the number of lattice paths in the Cartesian plane that start at (0, 0), end at (n,n), contain no points above the line y=x, and are composed only ...

Smale's problems are a list of 18 challenging problems for the twenty-first century proposed by Field medalist Steven Smale. These problems were inspired in part by Hilbert's ...

Consider the consecutive number sequences formed by the concatenation of the first n positive integers: 1, 12, 123, 1234, ... (OEIS A007908; Smarandache 1993, Dumitrescu and ...

The Sobolev embedding theorem is a result in functional analysis which proves that certain Sobolev spaces W^(k,p)(Omega) can be embedded in various spaces including ...