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A cylindrical segment, sometimes also called a truncated cylinder, is the solid cut from a circular cylinder by two (or more) planes. If there are two cutting planes, one ...

The space of immersions of a manifold in another manifold is homotopically equivalent to the space of bundle injections from the tangent space of the first to the tangent ...

The base manifold in a bundle is analogous to the domain for a set of functions. In fact, a bundle, by definition, comes with a map to the base manifold, often called pi or ...

Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...

Four circles c_1, c_2, c_3, and c_4 are tangent to a fifth circle or a straight line iff T_(12)T_(34)+/-T_(13)T_(42)+/-T_(14)T_(23)=0. (1) where T_(ij) is the length of a ...

The plane spanned by the tangent vector T and binormal vector B.

An even alternating permutation number, more commonly called a tangent number.

A small circle is a spheric section that does not contain a diameter of the sphere (Kern and Bland 1948, p. 87; Tietze 1965, p. 25).

The cotangent bundle of a manifold is similar to the tangent bundle, except that it is the set (x,f) where x in M and f is a dual vector in the tangent space to x in M. The ...

A tubular neighborhood of a submanifold N in M is an embedding of the normal bundle (nu_N) of N into M, i.e., f:nu_N->M, where the image of the zero section of the normal ...