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math.MG2004
The area of cyclic polygons: Recent progress on Robbins' Conjectures
Igor Pak
In his works [R1,R2] David Robbins proposed several interrelated conjectures on the area of the polygons inscribed in a circle as an algebraic function of its sides. Most recently,…
math.MG2003
Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings
Ezra Miller, Igor Pak
This paper is a study of the interaction between the combinatorics of boundaries of convex polytopes in arbitrary dimension and their metric geometry. Let S be the boundary of a co…