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Pick's theorem

Let \(P\) be a polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points. Let \(I\) be the number of lattice points in the interior of \(P\). Let \(B\) be the number of lattice points on the boundary of \(P\). Prove that the area \(A\) of the polygon \(P\) is given by

\(A = I + B/2 - 1\)

Source: folklore

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