Set of points at distance less than one from a given point
For other uses, see Disc (disambiguation).
An open Euclidean unit disk
In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1:
The closed unit disk around P is the set of points whose distance from P is less than or equal to one:
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. It is the interior of a circle of radius 1, centered at the origin. This set can be identified with the set of all complex numbers of absolute value less than one. When viewed as a subset of the complex plane (C), the unit disk is often denoted .
In mathematics, the open unitdisk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than...
magnetic disk storage devices from 1956 to 2003, when it sold its hard disk drive business to Hitachi. Both the hard disk drive (HDD) and floppy disk drive...
frequently historical, as in IBM's usage of the disk form beginning in 1956 with the "IBM 350 disk storage unit".) Audio information was originally recorded...
Hardy classes) Hp are certain spaces of holomorphic functions on the unitdisk or upper half plane. They were introduced by Frigyes Riesz (Riesz 1923)...
the Advanced Format (AF). The sector is the minimum storage unit of a hard drive. Most disk partitioning schemes are designed to have files occupy an integral...
explicitly. For example, the solution to the Dirichlet problem for the unitdisk in R2 is given by the Poisson integral formula. If f {\displaystyle f}...
cover the unitdisk. Dually, for a given radius ε, one wishes to find the smallest integer n such that n disks of radius ε can cover the unitdisk. The best...
two-dimensional Laplace equation, given Dirichlet boundary conditions on the unitdisk. The kernel can be understood as the derivative of the Green's function...
as the area of a circle in informal contexts, strictly speaking the term disk refers to the interior region of the circle, while circle is reserved for...
A hard disk drive (HDD), hard disk, hard drive, or fixed disk, is an electro-mechanical data storage device that stores and retrieves digital data using...
readily available. Unit production peaked in 2010 at about 650 million units, and has been in a slow decline since then. The IBM 350 Disk File was developed...
In mathematics, an infinite geometric series of the form ∑ n = 1 ∞ a r n − 1 = a + a r + a r 2 + a r 3 + ⋯ {\displaystyle \sum _{n=1}^{\infty }ar^{n-1...
the open unitdisk extends continuously to a homeomorphism between their closures, mapping the Jordan curve homeomorphically onto the unit circle. To...
whose inverse is also holomorphic) from U {\displaystyle U} onto the open unitdisk D = { z ∈ C : | z | < 1 } . {\displaystyle D=\{z\in \mathbb {C} :|z|<1\}...
spaces. A sequence of points ( a n ) {\displaystyle (a_{n})} inside the unitdisk is said to satisfy the Blaschke condition when ∑ n ( 1 − | a n | ) < ∞...
mainframe hard disk drives beginning with the 3333 in 1972. The 3333 was the first unit in a string of up to eight 3330 type hard disk drives; it contained...
to the unitdisk. In terms of the models of hyperbolic geometry, this Cayley transform relates the Poincaré half-plane model to the Poincaré disk model...
on compact sets as t tends to infinity. Let D {\displaystyle D} be the unitdisk in the complex plane with the Poincaré metric d s 2 = 4 | d z | 2 ( 1...
polynomials are a sequence of polynomials that are orthogonal on the unitdisk. Named after optical physicist Frits Zernike, laureate of the 1953 Nobel...
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