Open Ball

An n-dimensional open ball of radius r is the collection of points of distance less than r from a fixed point in Euclidean n-space. Explicitly, the open ball with center x and radius r is defined by

The open ball for n=1 is called an open interval, and the term open disk is sometimes used for n=2 and sometimes as a synonym for open ball.

See also

Ball, Closed Disk, Hypersphere, Open Disk, Open Set, Sphere

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References

Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, p. 1, 1991.

Referenced on Wolfram|Alpha

Open Ball

Cite this as:

Weisstein, Eric W. "Open Ball." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OpenBall.html

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