Loci of Points Inspired by Viviani's Theorem

2017/01/24 by Abboud, Elias
#51F05 #FOS: Mathematics #History and Overview (math.HO)

paper · doi:10.48550/arxiv.1701.07339

Abstract

We consider loci of points such that their sum of distances or sum of squared distances to each of the sides of a given triangle is constant. These loci are inspired by Viviani's theorem and its extension. The former locus is a line segment or the whole triangle and the latter locus is an ellipse.

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