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

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

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

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