Difference between revisions of "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). | 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). | ||
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Figure: s086060b | 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 | + | 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]]. |
Latest revision as of 09:41, 15 April 2014
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.
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
Solid angle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Solid_angle&oldid=31702