Journal for Geometry and Graphics 29 (2025), No. 1, 055--063
Copyright by the authors licensed under CC BY SA 4.0
Inequalities in Triangle Geometry: From Spherical to Hyperbolic
Ren Guo
Department of Mathematics, Oregon State University, Corvallis, U.S.A.
ren.guo@oregonstate.edu
Nilgün Sönmez
Department of Mathematics, Faculty of Science and Arts, Afyon Kocatepe University, Afyonkarahisar, Turkey
nceykab@aku.edu.tr
We establish hyperbolic analogues of ten inequalities for triangles in spherical geometry, originally presented by Mitrinovic, Pecaric, and Volenec in 1989. For comparison, the corresponding Euclidean versions are also included. Unified formulations of these inequalities across spherical, Euclidean, and hyperbolic geometries are provided. This work contributes to the broader effort of translating and unifying geometric results across the three classical geometries.
Keywords: Inequality, triangle, spherical geometry, hyperbolic geometry.
MSC: 51M09; 51M16, 52A40.
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