When I was an undergrad, the field of [spherical trigonometry](https://en.wikipedia.org/wiki/Spherical_trigonometry) was cited as a once-popular area of math that has since died. Is this true? Are the results from spherical trigonometry relevant for contemporary research?



Is spherical trigonometry a dead research area?
It is not. As a proof, I will mention three relatively recent papers where I am a co-author:


M. Bonk and A. Eremenko, [Covering properties of meromorphic functions, negative curvature and spherical geometry](https://arxiv.org/abs/math/0009251), Ann of Math. 152 (2000), 551-592.


A. Eremenko, Metrics of positive curvature with conic singularities on the sphere, Proc. AMS, 132 (2004), 11, 3349--3355.


A. Eremenko and A. Gabrielov, [The space of Schwarz--Klein spherical triangles](http://jmag.ilt.kharkov.ua/jmag/pdf/16/jm16-0263e.pdf), Journal of Mathematical Physics, Analysis and Geometry, 16, 3 (2020) 263-282.


As you see, they are all published in mainstream math journals. All contain some new results on spherical triangles.
And I am not the only person who is involved in this business:


Feng Luo, [A characterization of spherical polyhedral surfaces](https://doi.org/10.4310/jdg/1175266233),
J. Differential Geom. 74(3): 407-424.


Edit. To address one comment: here is a forthcoming [conference on spherical geometry](http://www1.mat.uniroma1.it/people/mondello/ricerca/spherical2022/index.html)


