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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


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.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein