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One of the three standard tori given by the parametric equations x = (c+acosv)cosu (1) y = (c+acosv)sinu (2) z = asinv (3) with c>a. This is the torus which is generally ...

One of the three standard tori given by the parametric equations x = (c+acosv)cosu (1) y = (c+acosv)sinu (2) z = asinv (3) with c<a. The exterior surface is called an apple ...

A space which is isomorphic to a Borel subset B of a Polish space equipped with its sigma-algebra of Borel sets.

One of the three standard tori given by the parametric equations x = a(1+cosv)cosu (1) y = a(1+cosv)sinu (2) z = asinv, (3) corresponding to the torus with a=c. It has ...

A cyclide is a pair of focal conics which are the envelopes of two one-parameter families of spheres, sometimes also called a cyclid. The cyclide is a quartic surface, and ...

A cyclide formed by inversion of a standard torus when inversion sphere is tangent to the torus.

Irreducible orientable compact 3-manifolds have a canonical (up to isotopy) minimal collection of disjointly embedded incompressible tori such that each component of the ...

Construct a chain C of 2n components in a solid torus V. Now thicken each component of C slightly to form a chain C_1 of 2n solid tori in V, where pi_1(V-C_1)=pi_1(V-C) via ...

The Reeb foliation of the hypersphere S^3 is a foliation constructed as the union of two solid tori with common boundary.

A torus with a hole that can eat another torus. The transformation is continuous, and so can be achieved by stretching only without tearing or making new holes in the tori.