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A category modeled after the properties of the category of sets. A category E is a topos if E has finite limits and every object of E has a power object (Barr and Wells 1985, ...

Let m_1, m_2, ..., m_n be distinct primitive elements of a two-dimensional lattice M such that det(m_i,m_(i+1))>0 for i=1, ..., n-1. Each collection Gamma={m_1,m_2,...,m_n} ...

A torispherical dome is the surface obtained from the intersection of a spherical cap with a tangent torus, as illustrated above. The radius of the sphere R is called the ...

A system of curvilinear coordinates for which several different notations are commonly used. In this work (u,v,phi) is used, whereas Arfken (1970) uses (xi,eta,phi) and Moon ...

A divergenceless field can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics, and in particular in dynamo theory and ...

The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change of the curve's osculating plane. The torsion tau is ...

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.

With n cuts of a torus of genus 1, the maximum number of pieces which can be obtained is N(n)=1/6(n^3+3n^2+8n). The first few terms are 2, 6, 13, 24, 40, 62, 91, 128, 174, ...

The term "total curvature" is used in two different ways in differential geometry. The total curvature, also called the third curvature, of a space curve with line elements ...

There are at least two meanings of the term "total derivative" in mathematics. The first is as an alternate term for the convective derivative. The total derivative is the ...