A point $(x,y)$ in the plane is called a lattice point if both coordinates $x$ and $y$ are integers.
Let $P$ be a polygon whose vertices are lattice points. Then the area of $P$ is $I + \frac{1}{2}B - 1$, where $I$ denotes the number of lattice points inside the polygon and $B$ denots the number on the boundary.
How to establish this formula using induction on the number of edges (or otherwise)?