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math.MG2018
Barycenters of points in polytope skeleta
Michael Gene Dobbins, Florian Frick
The first author showed that for a given point in an -polytope there are points in the -faces of , whose barycenter is . We show that we can increase the d…
math.MG2018
Splitting loops and necklaces: Variants of the square peg problem
Jai Aslam, Shujian Chen, Florian Frick +3
Toeplitz conjectured that any simple planar loop inscribes a square. Here we prove variants of Toeplitz' square peg problem. We prove Hadwiger's 1971 conjecture that any simple loo…