Pick's theorem

For a simple polygon whose vertices are lattice points in

Z^{2}

, its area is

A = I + B /2 - 1

, where

I

counts interior lattice points and

B

counts boundary lattice points.

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Pick's theorem by

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Pick's Theorem provides a formula for determining the area of a simple lattice polygon (a polygon whose vertices are points with integer coordinates) based on the number of lattice points inside the polygon and on its boundary.

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