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Cylinder Cutting

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The maximum number of pieces into which a cylinder can be divided by n oblique cuts is given by

f(n)=(n+1; 3)+n+1
(1)
=1/6(n+1)(n^2-n+6)
(2)
=1/6(n^3+5n+6),
(3)

where (a; b) is a binomial coefficient.

This problem is sometimes also called cake cutting or pie cutting, and has the same solution as space division by planes. For n=1, 2, ... cuts, the maximum number of pieces is 2, 4, 8, 15, 26, 42, ... (OEIS A000125). Unsurprisingly, the numbers of this sequence are called cake numbers.

See also

Cake Number, Circle Division by Lines, Cube Division by Planes, Cylindrical Hoof, Cylindrical Wedge, Ham Sandwich Theorem, Pancake Theorem, Space Division by Planes, Torus Cutting

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References

Bogomolny, A. "Can You Cut a Cake into 8 Pieces with Three Movements." http://www.cut-the-knot.org/do_you_know/cake.shtml.Sloane, N. J. A. Sequence A000125/M1100 in "The On-Line Encyclopedia of Integer Sequences."

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Cylinder Cutting

Cite this as:

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

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