On the smallest area n-1-gon containing a convex n-gon

2021/07/31 by Hong, Elliot, Ismailescu, Dan, Kwak, Alex +1
#51N20 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2108.00326

Abstract

We prove that every unit area convex pentagon is contained in a convex quadrilateral of area no greater than 3/√(5), and that every unit area convex hexagon is contained in a convex pentagon of area no greater than 7/6. Both results are tight as the case of the regular pentagon (hexagon) shows. We conjecture that for every n≥ 6, every unit area convex n - gon is contained in a (n-1) - gon of area no greater than 1+tan(2π/n)\sec(π/n)/n.

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