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| | '''Clairaut's relation''', named after [[Alexis Claude de Clairaut]], is a formula in classical [[differential geometry]]. The formula relates the distance ''r''(''t'') from a point on a [[great circle]] of the [[unit sphere]] to the ''z''-axis, and the angle ''θ''(''t'') between the tangent vector and the latitudinal circle: |
| | |
| | :<math> r(t) \cos \theta(t) = \text{constant}.\, </math> |
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| | The relation remains valid for a geodesic on an arbitrary [[surface of revolution]]. |
| | ==References== |
| | *M. do Carmo, ''Differential Geometry of Curves and Surfaces'', page 257. |
| | ==See also== |
| | *[[Clairaut's theorem]] |
| | |
| | [[Category:Differential geometry]] |
| | [[Category:Differential geometry of surfaces]] |
| | [[Category:Geodesy]] |
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| | |
| | {{differential-geometry-stub}} |
Latest revision as of 08:56, 7 November 2013
Clairaut's relation, named after Alexis Claude de Clairaut, is a formula in classical differential geometry. The formula relates the distance r(t) from a point on a great circle of the unit sphere to the z-axis, and the angle θ(t) between the tangent vector and the latitudinal circle:
The relation remains valid for a geodesic on an arbitrary surface of revolution.
References
- M. do Carmo, Differential Geometry of Curves and Surfaces, page 257.
See also
Template:Differential-geometry-stub