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- The unit disk and unit circle are different mathematical concepts12.
- The open unit disk is the set of points for the Poincaré disk model of the hyperbolic plane. Circular arcs perpendicular to the unit circle form the "lines" in this model. The unit circle is the Cayley absolute that determines a metric on the disk through use of cross-ratio in the style of the Cayley–Klein metric1.
- 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 disk2.
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.The open unit disk forms the set of points for the Poincaré disk model of the hyperbolic plane. Circular arcs perpendicular to the unit circle form the "lines" in this model. The unit circle is the Cayley absolute that determines a metric on the disk through use of cross-ratio in the style of the Cayley–Klein metric.en.wikipedia.org/wiki/Unit_diskThe 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.en.wikipedia.org/wiki/Unit_circle - People also ask
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Unit disk - Wikipedia
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 ... See more
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:
$${\displaystyle D_{1}(P)=\{Q:\vert P-Q\vert <1\}.\,}$$ See moreOne also considers unit disks with respect to other metrics. For instance, with the taxicab metric and the Chebyshev metric disks look like squares (even though the underlying See more
• Weisstein, Eric W. "Unit disk". MathWorld.
• On the Perimeter and Area of the Unit Disc, by J.C. Álvarez Pavia and A.C. Thompson See moreThe open unit disk forms the set of points for the Poincaré disk model of the hyperbolic plane. Circular arcs perpendicular to the unit circle form the "lines" in this model. … See more
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7. The Poincaré disk model for the hyperbolic plane
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