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arXiv · 1805.11442

Generalizations of Triangle Inequalities to Spherical and Hyperbolic Geometry

Karina Cho·Jacob Naranjo
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Abstract

Certain triangle inequalities involving the circumradius, inradius, and side lengths of a triangle are generalized to spherical and hyperbolic geometry. Examples include strengthenings of Euler's inequality, $R\geq2r$. An extension of Euler's inequality to a simplex in $n$-dimensional space is also generalized to spherical geometry.

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Karina Cho, Jacob Naranjo. 2018-05-26. Generalizations of Triangle Inequalities to Spherical and Hyperbolic Geometry. https://arxiv.org/abs/1805.11442

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