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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: D1(P)={Q:|P−Q|<1}.{\displaystyle D_{1}(P)=\{Q:\vert P-Q\vert <1\}.\,}The closed unit disk around P is the set of points whose distance from P is less than or equal to one: D¯1(P)={Q:|P−Q|≤1}.{\displaystyle {\bar {D}}_{1}(P)=\{Q:|P-Q|\leq 1\}.\,}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.

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