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Space Division by Spheres


SphereIntersections

The number of regions into which space can be divided by n mutually intersecting spheres is

 N=1/3n(n^2-3n+8),

giving 2, 4, 8, 16, 30, 52, 84, ... (OEIS A046127) for n=1, 2, ....


See also

Plane Division by Circles, Space Division by Planes, Sphere-Sphere Intersection

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References

Sloane, N. J. A. Sequence A046127 in "The On-Line Encyclopedia of Integer Sequences."Yaglom, A. M. and Yaglom, I. M. Challenging Mathematical Problems with Elementary Solutions, Vol. 1. New York: Dover, pp. 102-106, 1987.

Referenced on Wolfram|Alpha

Space Division by Spheres

Cite this as:

Weisstein, Eric W. "Space Division by Spheres." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpaceDivisionbySpheres.html

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