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Space Division by Planes

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The maximal number of regions into which space can be divided by n planes is

f(n)=1/6(n^3+5n+6)

(Yaglom and Yaglom 1987, pp. 102-106). For n=1, 2, ..., these give the values 2, 4, 8, 15, 26, 42, ... (OEIS A000125), a sequence whose values are sometimes called the "cake numbers" due to their relation to the cake cutting problem. This is the same solution as for cylinder cutting.

See also

Cake Cutting, Cake Number, Circle Division by Lines, Cube Division by Planes, Cylinder Cutting, Plane Division by Circles, Space Division by Spheres

Portions of this entry contributed by Christopher Stover

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References

Sloane, N. J. A. Sequence A000125/M1100 in "The On-Line Encyclopedia of Integer Sequences."Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 72, 1986.Yaglom, A. M. and Yaglom, I. M. Challenging Mathematical Problems with Elementary Solutions, Vol. 1. New York: Dover, 1987.

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Space Division by Planes

Cite this as:

Stover, Christopher and Weisstein, Eric W. "Space Division by Planes." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpaceDivisionbyPlanes.html

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