solid of revolution
Let be a curve for in an interval satisfying for in . We may construct a corresponding solid of revolution, say . Intuitively, it is the solid generated by rotating the surface about the -axis.
The interior of a surface of revolution is always a solid of revolution. These include
Let be a simple closed curve with parametrization for in an interval satisfying for in . By the Jordan curve theorem, we may choose the set of points, , ”inside” the curve, i.e. let be the bounded connected component of the two connected components found in . Another sort of solid of revolution is given by . Intuitively, it is the solid generated by rotating about the -axis.
Some examples of this sort of solid of revolution include
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the interior of a torus of minor radius and major radius with for ,
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a shell of a sphere with inner radius and outer radius with
Title | solid of revolution |
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Canonical name | SolidOfRevolution |
Date of creation | 2013-03-22 17:19:57 |
Last modified on | 2013-03-22 17:19:57 |
Owner | nkirby (11104) |
Last modified by | nkirby (11104) |
Numerical id | 10 |
Author | nkirby (11104) |
Entry type | Definition |
Classification | msc 51M25 |
Related topic | SurfaceOfRevolution2 |