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Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself. Without further specifications, the term unit disk is used for the open unit disk about the origin , D 1 ( 0 ) {\displaystyle D_{1}(0)} , with respect to the standard ...
In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one vertex for each disk in the family, and with an edge between two vertices whenever the corresponding vertices lie within a unit distance of each other.
This page was last edited on 17 May 2006, at 13:54 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply ...
The disk covering problem asks for the smallest real number such that disks of radius () can be arranged in such a way as to cover the unit disk.Dually, for a given radius ε, one wishes to find the smallest integer n such that n disks of radius ε can cover the unit disk.
A graph of the vertices of a pentagon, realized as an intersection graph of disks in the plane. This is an example of a graph with sphericity 2, also known as a unit disk graph . In graph theory , the sphericity of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required to realize the graph as an ...
Poincaré disk with hyperbolic parallel lines Poincaré disk model of the truncated triheptagonal tiling.. In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines are either circular arcs contained within the disk that are orthogonal to the unit circle or ...
In mathematics, the Littlewood subordination theorem, proved by J. E. Littlewood in 1925, is a theorem in operator theory and complex analysis.It states that any holomorphic univalent self-mapping of the unit disk in the complex numbers that fixes 0 induces a contractive composition operator on various function spaces of holomorphic functions on the disk.
(The spelling disk and disc are used interchangeably except where trademarks preclude one usage, e.g., the Compact Disc logo. The choice of a particular form is frequently historical, as in IBM's usage of the disk form beginning in 1956 with the " IBM 350 disk storage unit ".)