info prev up next book cdrom email home

Square Cutting

The average number of regions into which $N$ lines divide a Square is

\begin{displaymath}
{\textstyle{1\over 16}}N(N-1)\pi+N+1
\end{displaymath}

(Santaló 1976).

See also Circle Cutting


References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/geom/geom.html

Santaló, L. A. Integral Geometry and Geometric Probability. Reading, MA: Addison-Wesley, 1976.




© 1996-9 Eric W. Weisstein
1999-05-26