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Article: Visual angle on the unit sphere.
- Article from:
- Electronic Journal of Mathematics and Technology
- Article date:
- October 1, 2008
- Author:
CopyrightCOPYRIGHT 2008 Mathematics and Technology, LLC. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract
Let AOB be a triangle in the three dimensional Euclidean space [R.sup.3]. When we look at this triangle from various viewpoints, the angle [angle]AOB changes its appearance, and its 'visual size' is not constant. This visual angle is realized on the unit sphere [S.sup.2] centered at O. In this paper, we will investigate the contours of visual size in the unit sphere. Several geometric properties and a stochastic property are presented.
1. Introduction
We see various angles in our daily lives. Each angle has a certain size, however, its appearance changes according to our viewpoint. We call the appearance visual angle. Note that visual ...