Cube Division by Planes

The average number of regions into which n randomly chosen planes divide a cube is


(Finch 2003, p. 482).

The maximum number of regions is presumably the same as for space division by planes, namely


(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" due to their relation to the cake cutting problem.

See also

Cake Number, Cake Cutting, Cylinder Cutting, Space Division by Planes, Square Division by Lines

Explore with Wolfram|Alpha


Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, 2003.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.

Referenced on Wolfram|Alpha

Cube Division by Planes

Cite this as:

Weisstein, Eric W. "Cube Division by Planes." From MathWorld--A Wolfram Web Resource.

Subject classifications