Pick's Theorem

Georg Alexander Pick

Quick Info

Born: 10 August 1859, Vienna, Austria-Hungary.

Died:  26 July 1942 (aged 82), Czechoslovakia.

Known for: Pick’s Theorem

Introduction

Pick’s Theorem provides a simple formula for the area of any lattice polygon. A lattice polygon is a simple polygon embedded on a grid, or lattice, whose vertices have integer coordinates, otherwise known as grid or lattice points. Given a lattice polygon P, the formula involves simply adding the number of lattice points on the boundary, b, dividing b by 2, and adding the number of lattice points in the interior of the polygon, i, and subtracting 1 from i. Then the area of P is:

\begin{equation} {\color{Blue} Area}={\color{Red} i}+\frac{{\color{Green} b}}{2}-1 \end{equation}

The theorem was first stated by Georg Alexander Pick, an Austrian mathematician, in 1899. However, it was not popularized until Polish mathematician Hugo Steinhaus published it in 1969, citing  Pick. Georg Pick was born in Vienna in 1859 and attended the University of Vienna when he was just 16, publishing his first mathematical paper at only 17.

References

1.  Kiradjiev, Kristian (October 2018). "Connecting the dots with Pick's theorem" (PDF). Mathematics Today.       pp. 212–214.