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  2. 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_disk
    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.
    en.wikipedia.org/wiki/Unit_circle
     
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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 more

    The function
    $${\displaystyle f(z)={\frac {z}{1-|z|^{2}}}}$$
    is an example of a real analytic and bijective function from the open unit disk to the plane; its inverse … See more

    One 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

    Overview image

    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. … See more

     
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  11. 7. The Poincaré disk model for the hyperbolic plane

    WEBLearn how to construct and use the Poincaré disk model, a representation of the hyperbolic plane in the complex plane. Find out how to define hyperbolic lines, circles, polygons and distances, and see examples …

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