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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, (), with respect to the standard Euclidean metric.
Every induced subgraph of a unit disk graph is also a unit disk graph. An example of a graph that is not a unit disk graph is the star K 1 , 6 {\displaystyle K_{1,6}} with one central node connected to six leaves: if each of six unit disks touches a common unit disk, some two of the six disks must touch each other.
In geometry, a disk (also spelled disc) [1] is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not. [2] For a radius, , an open disk is usually denoted as and a closed disk is ¯.
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 ...
The interior of the unit circle is called the open unit disk, while the interior of the unit circle combined with the unit circle itself is called the closed unit disk. One may also use other notions of "distance" to define other "unit circles", such as the Riemannian circle; see the article on mathematical norms for additional examples.
There are several equivalent definitions of a Riemann surface. A Riemann surface X is a connected complex manifold of complex dimension one. This means that X is a connected Hausdorff space that is endowed with an atlas of charts to the open unit disk of the complex plane: for every point x ∈ X there is a neighbourhood of x that is homeomorphic to the open unit disk of the complex plane, and ...
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 ...
Disk storage (also sometimes called drive storage) is a data storage mechanism based on a rotating disk. The recording employs various electronic, magnetic, optical, or mechanical changes to the disk's surface layer. A disk drive is a device implementing such a storage mechanism.