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The triangle comparison theorem for spheres

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Abstract

If two spherical triangles lying on a pair of spheres of different radii have the same edge-lengths, then each interior angle of the one on the sphere of larger radius is smaller than the corresponding interior angle of the other one. This is a consequence of Toponogov’s triangle comparison theorem. We prove this fact in an elementary way.

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Acknowledgements

Many thanks to the referee. By the referee’s suggentions, the paper is much improved.

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  1. Ryukyu University, Nishihara, Okinawa, 903-0213, Japan

    H. Maehara

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  1. H. Maehara
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Correspondence to H. Maehara.

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Maehara, H. The triangle comparison theorem for spheres. Beitr Algebra Geom 64, 1027–1031 (2023). https://doi.org/10.1007/s13366-022-00666-8

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  • DOI: https://doi.org/10.1007/s13366-022-00666-8

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