Abstract
Spherical triangle in the n-dimensional unit sphere S n is classified into seven types according to side and angle. In this paper, we consider random spherical triangles in S n, and calculate the probabilities of seven types to which random spherical triangles belong. Each probability monotone converges to a certain value as the dimension n tends to infinity. As an application, we can estimate the expectation of numbers of division on acute triangulation of a random spherical triangle in S 2.
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© 2008 Springer-Verlag Berlin Heidelberg
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Maeda, Y. (2008). Seven Types of Random Spherical Triangle in S n and Their Probabilities. In: Ito, H., Kano, M., Katoh, N., Uno, Y. (eds) Computational Geometry and Graph Theory. KyotoCGGT 2007. Lecture Notes in Computer Science, vol 4535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89550-3_13
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DOI: https://doi.org/10.1007/978-3-540-89550-3_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89549-7
Online ISBN: 978-3-540-89550-3
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