Abstract
Let AOB be a triangle in R 3. When we look at this triangle from various viewpoints, the angle \(\angle AOB\) changes its appearance, and its ‘visual size’ is not constant. We prove, nevertheless, that the average visual size of \(\angle AOB\) is equal to the true size of the angle when viewpoints are chosen at random on the surface of a sphere centered at O. We also present a formula to compute the variance of the visual size.
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References
Jennings, G.A.: Modern Geometry with Applications. Springer, New York (1994)
Santaló, L.A.: Integral formulas in Crofton’s style on the sphere and some inequalities referring to spherical curves. Duke Math. J. 9, 707–722 (1942)
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© 2003 Springer-Verlag Berlin Heidelberg
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Maeda, Y., Maehara, H. (2003). Observing an Angle from Various Viewpoints. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_21
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DOI: https://doi.org/10.1007/978-3-540-44400-8_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20776-4
Online ISBN: 978-3-540-44400-8
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