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 LinesExplore with Wolfram|Alpha
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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."Referenced on Wolfram|Alpha
Torus CuttingCite this as:
Weisstein, Eric W. "Torus Cutting." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TorusCutting.html