Viviani Polytopes and Fermat Points

2010/08/06 by Li Zhou, Zhou, Li
Mathematics · #FOS: Mathematics #History and Overview (math.HO) #Metric Geometry (math.MG) #math.HO #math.MG

paper · pdf · doi:10.48550/arxiv.1008.1236

4 pages, 2 figures

arxiv created 2010/11/29 · arxiv updated 2010/11/30

Abstract

Given a set of oriented hyperplanes P=\p₁, ..., p_k\ in ℝⁿ, define v(P) for any point P∈ℝⁿ as the sum of the signed distances from P to p₁,..., p_k. We give a simple geometric characterization of P so that v is a constant. The characterization leads to a connection with the Fermat point of k points in ℝⁿ. Finally, we discuss historically the full content of Viviani's theorem.

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