Abstract
SummaryGiven a set of oriented hyperplanes ℘ = {p1, ‖, pk} in ℝn, define v : ℝn ⃯ ℝ by v(X) = the sum of the signed distances from X to p1, ‖, pk, for any point X ∈ Rℝn. We give a simple geometric characterization of ℘ for which v is constant, leading to a connection with the Fermat point of k points in ℝn. Finally, we discuss the full content of Viviani's theorem historically.
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