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Lattice Polygons and the Number 12

2000/03/01 by Bjorn Poonen, Fernando Rodriguez-Villegas · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Mathematics and Applications #Geometric and Algebraic Topology #Combinatorics #Mathematics #Lattice (music) #Physics

paper · doi:10.1080/00029890.2000.12005186

openalex publication_date 2000/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

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

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