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# Circle Division by Lines

Determining the maximum number of pieces in which it is possible to divide a circle for a given number of cuts is called the circle cutting or pancake cutting problem. The minimum number is always , where is the number of cuts, and it is always possible to obtain any number of pieces between the minimum and maximum. The first cut creates 2 regions, and the th cut creates new regions, so

 (1) (2) (3)

Therefore,

 (4) (5) (6) (7) (8)

Evaluating for , 2, ... gives 2, 4, 7, 11, 16, 22, ... (OEIS A000124). This is equivalent to the maximal number of regions into which a plane can be cut by lines.

Circle Division by Chords, Plane Division by Circles, Plane Division by Ellipses, Plane Division by Lines, Space Division by Planes, Space Division by Spheres, Square Division by Lines

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## References

Santaló, L. A. "Sobre la distrabucion de planos en el espacio." Rev. Unión Mat. Argentina 13, 120-124, 1948.Sloane, N. J. A. Sequence A000124/M1041 in "The On-Line Encyclopedia of Integer Sequences."Sloane, N. J. A. and Plouffe, S. Figure M1041 in The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.Trott, M. "Coloring Closed Curves." §1.6 in The Mathematica GuideBook for Graphics. New York: Springer-Verlag, pp. 393-430, 2004. http://www.mathematicaguidebooks.org/.Yaglom, A. M. and Yaglom, I. M. Challenging Mathematical Problems with Elementary Solutions, Vol. 1. New York: Dover, pp. 102-106, 1987.Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 31, 1986.

## Referenced on Wolfram|Alpha

Circle Division by Lines

## Cite this as:

Weisstein, Eric W. "Circle Division by Lines." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CircleDivisionbyLines.html