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Cake Number


The cake number for a nonnegative integer n is the maximum number of regions into which n planes can divide a three-dimensional convex body. It is given by

 N_(max)=1/6(n^3+5n+6)

(Yaglom and Yaglom 1987, pp. 102-106). For n=1, 2, ... planes, this gives the values 2, 4, 8, 15, 26, 42, ... (OEIS A000125).


See also

Cake Cutting, Cube Division by Planes, Cylinder Cutting, Rascal Triangle, Space Division by Planes, Square Division by Lines

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References

Sloane, N. J. A. Sequence A000125/M1100 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, 1987.

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Cake Number

Cite this as:

Weisstein, Eric W. "Cake Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CakeNumber.html

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