On the geometric median of triangular domains and other median type points

Peter Panov; Alexei Savvateev

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arXiv · 1811.07306

On the geometric median of triangular domains and other median type points

Peter Panov·Alexei Savvateev

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Abstract

The geometric median of a domain is the point that minimises the average distance from itself to the points of the domain. We will give a gradient system of equations that defines the geometric median of a triangular domain and will prove a simple geometric property of the median. This property states that all three average distances from the median to the sides of the triangle are equal. Further we generalise these results to other types of domains and to other types of median like points.

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Peter Panov, Alexei Savvateev. 2018-11-18. On the geometric median of triangular domains and other median type points. https://arxiv.org/abs/1811.07306

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