Formalizing Pick's Theorem, efficiently

Michael Eisermann

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arXiv · 2603.23095

Formalizing Pick's Theorem, efficiently

Michael Eisermann

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Abstract

Pick's astonishing theorem explains how to obtain the area of any integer polygon by counting lattice points. It is a notoriously difficult challenge to translate the geometric statement and intuitive reasoning into a formal statement and rigorous proof. We transform the beautiful geometry into equally elegant algebra, and then implement the algebraic proof in Lean.

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Michael Eisermann. 2026-03-24. Formalizing Pick's Theorem, efficiently. https://arxiv.org/abs/2603.23095

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