What is picks rule?

Picks' rule is a mathematical principle used in geometry, particularly in the context of counting lattice points within polygons. It states that the area ( A ) of a simple polygon whose vertices are lattice points (points with integer coordinates) can be calculated using the formula: ( A = I + \frac{B}{2} - 1 ), where ( I ) is the number of interior lattice points and ( B ) is the number of boundary lattice points. This rule provides a way to determine the area of polygons in a grid without needing to use traditional calculus or geometric methods.