Cylinder Cutting

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

$$f(n)={n+1\choose 3}+n+1={\textstyle{1\over 6}}(n+2)(n+3),$$

where ${a\choose b}$ is a Binomial Coefficient. This problem is sometimes also called Cake Cutting or Pie Cutting. For $n=1$, 2, ... cuts, the maximum number of pieces is 2, 4, 8, 15, 26, 42, ... (Sloane's A000125).

See also Circle Cutting, Ham Sandwich Theorem, Pancake Theorem, Torus Cutting

References

Bogomolny, A. ``Can You Cut a Cake into 8 Pieces with Three Movements.'' http://www.cut-the-knot.com/do_you_know/cake.html.

Sloane, N. J. A. Sequence A000125/M1100 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.