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A type of dimension which can be used to characterize fat fractals.

The kth exterior power of an element alpha in an exterior algebra LambdaV is given by the wedge product of alpha with itself k times. Note that if alpha has odd degree, then ...

The fractal illustrated above.

The term external direct product is used to refer to either the external direct sum of groups under the group operation of multiplication, or over infinitely many spaces in ...

The Cartesian product of a finite or infinite set of modules over a ring with only finitely many nonzero entries in each sequence.

An extreme point of a subset K of a vector space X is an extreme set S of K which consists of a single point x in K. The collection of all extreme points of K is sometimes ...

Consider a function f(x) in one dimension. If f(x) has a relative extremum at x_0, then either f^'(x_0)=0 or f is not differentiable at x_0. Either the first or second ...

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 ...

Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...

Generally, a face is a component polygon, polyhedron, or polytope. A two-dimensional face thus has vertices and edges, and can be used to make cells. More formally, a face is ...