Cake Number

The maximum number of regions that can be created by n cuts using space division by planes, cube division by planes, cylinder cutting, etc., is given by


(Yaglom and Yaglom 1987, pp. 102-106). For n=1, 2, ... planes, this gives the values 2, 4, 8, 15, 26, 42, ... (OEIS A000125), a sequence whose values are sometimes called the cake numbers.

See also

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

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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.

Cite this as:

Weisstein, Eric W. "Cake Number." From MathWorld--A Wolfram Web Resource.

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