Point Distances

The maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of n points in three-dimensional space occurs more than cn^(5/3) times. The maximum distance can occur no more than |_1/4n^2_| times in four dimensions, where |_x_| is the floor function.

See also

Geometric Span, Line Line Picking, Point-Line Distance--2-Dimensional, Point-Line Distance--3-Dimensional, Point-Point Distance--2-Dimensional, Point-Point Distance--3-Dimensional,

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References

Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 122-123, 1976.

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Point Distances

Cite this as:

Weisstein, Eric W. "Point Distances." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PointDistances.html

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