Pick's Theorem
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 numberof points in the interior of the Polygon. Then
The Formula has been generalized to 3-D and higher dimensions using Ehrhart Polynomials.See also Blichfeldt's Theorem, Ehrhart Polynomial, Lattice Point, Minkowski Convex Body Theorem
References
Diaz, R. and Robins, S. ``Pick's Formula via the Weierstraß 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.
-Function.'' Amer. Math. Monthly 102, 431-437, 1995.
- Discordant Permutation
- Discrepancy Theorem
- Discrete Distribution
- Discrete Fourier Transform
- Discrete Mathematics
- Discrete Set
- Discrete Uniform Distribution
- Discriminant
- Discriminant (Binary Quadratic Form)
- Discriminant (Elliptic Curve)
- Discriminant (Metric)
- Discriminant (Module)
- Discriminant (Polynomial)
- Discriminant (Quadratic Curve)
- Discriminant (Quadratic Form)
- Discriminant (Second Derivative Test)
- Disdyakis Dodecahedron
- Disdyakis Triacontahedron
- Disjoint
- Disjunction
- Disjunctive Game
- Disk
- Disk Covering Problem
- Disk Lattice Points
- Dispersion Numbers