Triangle inequalities in inner-product spaces

Martin  Lukarevski; Dan Stefan Marinescu

doi:10.55059/ijm.2022.1.2/29

Authors

Martin Lukarevski
Dan Stefan Marinescu

DOI:

https://doi.org/10.55059/ijm.2022.1.2/29

Keywords:

Inner-product space, Tereshin's inequality, Panaitopol's inequality

Abstract

Tereshin's and Panaitopol's are known inequalities involving the median, circumradius and sides of the triangle. In this short note we generalize the inequalities to inner-product spaces. As an application we derive inequality for the median and the radius of the circumscribed sphere of an $n$-dimensional simplex.

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