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The direction from an object A to another object B can be specified as a vector v=AB^-> with tail at A and head at B. However, since this vector has length equal to the ...

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

Let a, b, and c be the lengths of the legs of a triangle opposite angles A, B, and C. Then the law of cosines states a^2 = b^2+c^2-2bccosA (1) b^2 = a^2+c^2-2accosB (2) c^2 = ...

An asymptotic direction at a point p of a regular surface M in R^3 is a direction in which the normal curvature of M vanishes. 1. There are no asymptotic directions at an ...

The directions in which the principal curvatures occur.

Each of the sets forming a direct product is said to be a direct factor. A group G is said to be a direct factor of the group G^' if G^' is isomorphic to the group direct ...

A compositeness certificate is a piece of information which guarantees that a given number p is composite. Possible certificates consist of a factor of a number (which, in ...

The inverse limit of a family of R-modules is the dual notion of a direct limit and is characterized by the following mapping property. For a directed set I and a family of ...

The direct sum of modules A and B is the module A direct sum B={a direct sum b|a in A,b in B}, (1) where all algebraic operations are defined componentwise. In particular, ...

The differential forms on C^n decompose into forms of type (p,q), sometimes called (p,q)-forms. For example, on C, the exterior algebra decomposes into four types: ^ C = ^ ^0 ...