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The unit of solid angle. The solid angle corresponding to all of space being subtended is 4pi steradians.

The exploration of three-dimensional space from two-dimensional sections of projections of solid bodies.

Maximize the amount of floor space which can be covered with a fixed tile (Hoffman 1998, p. 173).

A bundle or fiber bundle is trivial if it is isomorphic to the cross product of the base space and a fiber.

A "pointwise-bounded" family of continuous linear operators from a Banach space to a normed space is "uniformly bounded." Symbolically, if sup||T_i(x)|| is finite for each x ...

A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

An open three-manifold which is simply connected but is topologically distinct from Euclidean three-space.

The probability law on the space of continuous functions g with g(0)=0, induced by the Wiener process.

A curvature of a submanifold of a manifold which depends on its particular embedding. Examples of extrinsic curvature include the curvature and torsion of curves in ...

In the plane, there are 17 lattice groups, eight of which are pure translation. In R^3, there are 32 point groups and 230 space groups. In R^4, there are 4783 space lattice ...