Open AccessTriangle inequalities in inner-product spaces
Author(s) -
Martin Lukarevski,
Dan Ştefan Marinescu
Publication year - 2022
Publication title -
innovative journal of mathematics
Language(s) - English
Resource type - Journals
eISSN - 2790-3389
pISSN - 2790-3370
DOI - 10.55059/ijm.2022.1.2/29
Subject(s) - inequality , mathematics , inner product space , triangle inequality , simplex , product (mathematics) , radius , pure mathematics , combinatorics , mathematical analysis , geometry , computer science , computer security
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.