Mathematical Sciences Department Seminar
Jane Coons, Max Planck Institute
Tuesday, January 28th
4-5pm
Stratton 202
Title: Pick’s Theorem
In this talk, I will present a proof of Pick’s Theorem, which
gives a beautiful formula for the area of an integer polygon in
terms of the number of integer points in contains. In
particular, it says that $A = i + b/2 -1$ where $i$ is the number
of integer points on the interior of the polygon and $b$ is the
number of integer points on its boundary. There are many
proofs of Pick’s Theorem, but this one uses almost entirely
elementary techniques, requiring only simple geometry and
some clever counting arguments.