View source for Solid angle

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A part of space bounded by all the half-lines going from one point (the vertex) through the points of a closed curve (see Fig. a, Fig. b).

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/s086060a.gif" />

Figure: s086060a

<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/s086060b.gif" />

Figure: s086060b

A particular case of a solid angle is that of a [[Polyhedral angle|polyhedral angle]]. One takes as measure of a solid angle the ratio of the surface cut out by it on a sphere centred at the vertex to the squared radius of this sphere. For example, the solid angle containing $1/8$ of the space (an octant) is measured by the number $4\pi R^2/8R^2=\pi/2$. The unit of measurement of solid angles is the [[Steradian|steradian]].



====Comments====
The solid angle represents the visual angle under which the curve is seen from the vertex.

====References====
"Solid Angle of Conical Surfaces, Polyhedral Cones, and Intersecting  Spherical Caps", http://arxiv.org/abs/1205.1396