Lattice Polygons and the Number 12 [3 citations — 1 self]
by
Bjorn Poonen
,
Fernando Rodriguez-villegas
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@MISC{Poonen_latticepolygons,
author = {Bjorn Poonen and Fernando Rodriguez-villegas},
title = {Lattice Polygons and the Number 12},
year = {}
}
author = {Bjorn Poonen and Fernando Rodriguez-villegas},
title = {Lattice Polygons and the Number 12},
year = {}
}
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Abstract:
this article, we will discuss a theorem about polygons in the plane. Our reason for selecting this particular statement, besides the intriguing appearance of the number 12, is that its proofs display a surprisingly rich variety of methods, and at least some of them are symptomatic of connections between branches of mathematics that on the surface appear to have little to do with one another. The theorem (implicitly) and proofs 2 and 3 sketched below appear in Fulton's book [Fu] on toric varieties. We will give our new proof 4, which uses modular forms instead, in full. 2. The Theorem
