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).

Figure: s086060a

Figure: s086060b

A particular case of a solid angle is that of a 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.


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


"Solid Angle of Conical Surfaces, Polyhedral Cones, and Intersecting Spherical Caps",

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Solid angle. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article