Search Results for ""

The constant ratio by which all distances are increased (or decreased) in a similarity. A similarity with ratio of magnification equal to 1 is called an isometry.

A function composed of a set of equally spaced jumps of equal length, such as the ceiling function f(x)=[x], floor function f(x)=|_x_|, or nearest integer function f(x)=[x].

An inequality is strict if replacing any "less than" and "greater than" signs with equal signs never gives a true expression. For example, a<=b is not strict, whereas a<b is.

For a subgroup H of a group G, the index of H, denoted (G:H), is the cardinal number of the set of left cosets of H in G (which is equal to the cardinal number of the set of ...

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 ...

A zero tensor is a tensor of any rank and with any pattern of covariant and contravariant indices all of whose components are equal to 0 (Weinberg 1972, p. 38).

A zero vector, denoted 0, is a vector of length 0, and thus has all components equal to zero. It is the additive identity of the additive group of vectors.

Given a unit disk, find the smallest radius r(n) required for n equal disks to completely cover the unit disk. The first few such values are r(1) = 1 (1) r(2) = 1 (2) r(3) = ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...