Pick's theorem
Teorema de Pick
- Date
- 1899 · confidence high
- Place
- Prague, Bohemia, Czechia
- Credited to
- Georg Alexander Pick
- Field
- Knowledge & symbols
What was discovered
Pick published an elegant formula for the area of a simple polygon whose vertices lie on an integer lattice: A = i + b/2 - 1, where i is the number of interior points and b the boundary points. It remained little known until Hugo Steinhaus popularised it in 1950.
There is no direct three-dimensional analogue of the theorem, as shown by Reeve tetrahedra.
What it led to
- Dot planimeters for estimating areas by counting
- Generalisations to polygons with holes and to graphs
- A boost to lattice geometry