Torus Cutting

With $n$ cuts of a Torus of Genus 1, the maximum number of pieces which can be obtained is

$$N(n)={\textstyle{1\over 6}}(n^3+3n^2+8n).$$

The first few terms are 2, 6, 13, 24, 40, 62, 91, 128, 174, 230, ... (Sloane's A003600).

See also Cake Cutting, Circle Cutting, Cylinder Cutting, Pancake Cutting, Plane Cutting, Pie Cutting, Square Cutting

References

Gardner, M. Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, pp. 149-150, 1978.

Sloane, N. J. A. Sequence A003600/M1594 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.