An easy way to a theorem of Kira Adaricheva and Madina Bolat on convexity and circles

2016/10/08 by Czédli, Gábor
#52A01 #52C99 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1610.02540

Abstract

Kira Adaricheva and Madina Bolat have recently proved that if U₀ and U₁ are circles in a triangle with vertices A₀,A₁,A₂, then there exist j∈ \0,1,2\ and k∈\0,1\ such that U_1-k is included in the convex hull of U_k∪(\A₀,A₁, A₂\∖\A_j\). We give a short new proof for this result, and we point out that a straightforward generalizaton for shperes fails.

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