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A formal proof of Pick's Theorem

Published online by Cambridge University Press:  01 July 2011

JOHN HARRISON
JOHN HARRISON*
Affiliation:
Intel Corporation, JF1-13, 2111 NE 25th Avenue, Hillsboro OR 97124, U.S.A. Email: johnh@ichips.intel.com
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Abstract

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Pick's Theorem relates the area of a simple polygon with vertices at integer lattice points to the number of lattice points in its inside and boundary. We describe a formal proof of this theorem using the HOL Light theorem prover. As sometimes happens for highly geometrical proofs, the formalisation turned out to be more work than initially expected. The difficulties arose mostly from formalising the triangulation process for an arbitrary polygon.

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