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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 algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...

The two-dimensional Euclidean space denoted R^2.

If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the ...

The largest area of intersection of a solid body by a plane parallel to a given plane, also called the "HA measurement."

Given a smooth manifold M with an open cover U_i, a partition of unity subject to the cover U_i is a collection of smooth, nonnegative functions psi_i, such that the support ...

Pre-Calculus

The plane through an edge of a trihedron drawn perpendicularly to the opposite face. The term was first used by J. Neuberg (Altshiller-Court 1979, p. 298).

A method for mapping three-dimensional figures onto the plane.

Let A_1, B_2, C_1, A_2, and B_1 be five points determining a conic. Then the conic is the locus of the point C_2=A_1(L·C_1A_2)·B_1(L·C_1B_2), where L is a line through the ...