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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)=1/6(n^3+3n^2+8n).

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

See also

Cake Cutting, Circle Division by Lines, Cylinder Cutting, Plane Division by Lines, Square Division by Lines

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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 "The On-Line Encyclopedia of Integer Sequences."

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Torus Cutting

Cite this as:

Weisstein, Eric W. "Torus Cutting." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TorusCutting.html

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