@article {MATHEDUC.05556180,
author = {Maeda, Yoichi},
title = {Observing a solid angle from various viewpoints.},
year = {2008},
journal = {Yokohama Mathematical Journal},
volume = {54},
number = {2},
issn = {0044-0523},
pages = {155-160},
publisher = {Yokohama National University, Faculty of Engineering, Department of Mathematics, Yokohama},
abstract = {Summary: Let $AOB$ be a triangle in $\Bbb R^3$. When we look at this triangle from various viewpoints, the angle $\angle AOB$ changes its appearance, and its `visual size' is not constant. In [{\it Y. Maeda} and {\it H. Maehara}, Lecture Notes in Computer Science. 2866. Berlin: Springer, 200--203 (2003)], it is proved 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 $O$. In this paper, a simpler proof of this result is presented. Furthermore, we extend the result to the case of a solid angle in $\Bbb R^4$.},
msc2010 = {G75xx (K55xx)},
identifier = {2009e.00457},
}