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Torus Cutting


The torus cutting problem asks for the maximum number of pieces obtained by n planar cuts of a solid ring torus, without moving or rearranging the pieces. For a positive integer n, the maximum is

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

The first few terms for n=1, 2, ... are 2, 6, 13, 24, 40, 62, 91, 128, 174, 230, ... (OEIS A003600). With no cuts, there is one piece.


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 Resource. https://mathworld.wolfram.com/TorusCutting.html

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