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

• 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 more

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

• Unit disk graph
• Unit sphere
• De Branges's theorem See more