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
-
•
the interior of a torus of minor radius and major radius with for ,
-
•
a shell of a sphere with inner radius and outer radius with
Title | solid of revolution |
---|---|
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 |