Let be the Area of a simply closed Polygon whose Vertices are lattice points.
Let denote the number of Lattice Points on the Edges and the number
of points in the interior of the Polygon. Then

The Formula has been generalized to 3-D and higher dimensions using Ehrhart Polynomials.

**References**

Diaz, R. and Robins, S. ``Pick's Formula via the Weierstraß -Function.'' *Amer. Math. Monthly* **102**, 431-437, 1995.

Ewald, G. *Combinatorial Convexity and Algebraic Geometry.* New York: Springer-Verlag, 1996.

Hammer, J. *Unsolved Problems Concerning Lattice Points.* London: Pitman, 1977.

Morelli, R. ``Pick's Theorem and the Todd Class of a Toric Variety.'' *Adv. Math.* **100**, 183-231, 1993.

Pick, G. ``Geometrisches zur Zahlentheorie.'' *Sitzenber. Lotos (Prague)* **19**, 311-319, 1899.

Steinhaus, H. *Mathematical Snapshots, 3rd American ed.* New York: Oxford University Press, pp. 97-98, 1983.

© 1996-9

1999-05-25