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An algebraic surface of degree eight. The maximum number of ordinary double points known to exist on an octic surface is 168 (the Endraß octics), although the rigorous upper ...

The class m, curve order n, number of ordinary double points delta, number of cusps kappa, number of inflection points (inflection points) iota, number of bitangents tau, and ...

A knot equivalent to a polygon in R^3, also called a tame knot. For a polygonal knot K, there exists a plane such that the orthogonal projection pi on it satisfies the ...

A smooth map f:S^1->R^3 whose image has singularities. In particular, in the theory of Vassiliev's knot invariants, singular knots with a finite number of ordinary double ...

A tensor defined in terms of the tensors which satisfy the double contraction relation.

A double point at which two (or more) osculating curves are tangent. The above plot shows the tacnode of the curve 2x^4-3x^2y+y^2-2y^3+y^4=0. The capricornoid and links curve ...

A triple integral is a three-fold multiple integral of the form intintintf(x,y,z)dxdydz. Triple integrals arise in evaluating quantities such as the mass, volume, moment, ...

Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not explicitly derive equations for such surfaces. Beauville ...

The Barth decic is a decic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 345. It is given by the ...

A generalization of the factorial and double factorial, n! = n(n-1)(n-2)...2·1 (1) n!! = n(n-2)(n-4)... (2) n!!! = n(n-3)(n-6)..., (3) etc., where the products run through ...