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Ellipsoid - Surface area | | Ellipsoid - Surface area: Encyclopedia II - Ellipsoid - Surface area | | The surface area of an ellipsoid is given by:
where
and F(θ,m) and E(θ,m) are the incomplete elliptic integrals of the first and second kind.
Exact formulae are:
If flat:
If prolate:
If oblate:
Approximate fo ...
See also:Ellipsoid, Ellipsoid - Parametrisation, Ellipsoid - Volume, Ellipsoid - Surface area, Ellipsoid - Linear transformations, Ellipsoid - Egg shape | | | Ellipsoid, Ellipsoid - Egg shape, Ellipsoid - Linear transformations, Ellipsoid - Parametrisation, Ellipsoid - Surface area, Ellipsoid - Volume, paraboloid, hyperboloid, reference ellipsoid, geoid | | |
| | | Ellipsoid: Encyclopedia II - Ellipsoid - Surface area
Ellipsoid - Surface area
The surface area of an ellipsoid is given by:
where
and F(θ,m) and E(θ,m) are the incomplete elliptic integrals of the first and second kind.
Exact formulae are:
If flat:
If prolate:
If oblate:
Approximate formula is:
If scalene:
Where p ≈ 1.6075 yields a relative error of at most 1.061% (Knud Thomsen's formula); a value of p = 8/5 = 1.6 is optimal for nearly spherical ellipsoids, with a relative error of at most 1.178% (David W. Cantrell's formula).
Other related archivesCartesian coordinate system, Surfaces, area, dimensional, egg, ellipse, elliptic integrals, empty, geoid, hyperboloid, intersection, linear transformation, mathematics, oblate, oval (geometry), paraboloid, plane, positive, prolate, quadric, real numbers, reference ellipsoid, rotation, spectral theorem, sphere, spheroid, symmetric 3-by-3 matrix, volume
 Adapted from the Wikipedia article "Surface area", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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