:In 1735, Clairaut first defined the characteristic constant of an ellipsoid of revolution when he solved the problem in application to the astronomer Cassini's map of France.
12.
To make computations feasible, scientists defined ellipsoids of revolution; a given ellipsoid would be a good compromise for measurements in a given area, such as a country or continent.
13.
Typically the model is based on simplifying assumptions, such as that, under its self-gravitation and rotational motion, the planet assumes the figure of an ellipsoid of revolution.
14.
Scientific literature ( particularly geodesy ) often uses'ellipsoid'in place of'ellipsoid of revolution'and only applies the adjective'tri-axial'when treating the general case.
15.
On the ellipsoid of revolution, geodesics may be written in terms of elliptic integrals, which are usually evaluated in terms of a series expansion; for example, see Vincenty's formulae.
16.
It is an ellipsoid of revolution, whose short ( polar ) axis ( connecting the two flattest spots called geographical north and south poles ) is approximately aligned with the rotation axis of the Earth.
17.
Any planar cross section of an ellipsoid forms an ellipse on its surface : this degenerates to a circle for sections normal to the symmetry axis of an ellipsoid of revolution ( or all sections when the ellipsoid degenerates to a sphere .)
18.
:: : Steve's point is valid, but mostly nullified by the fact that the Earth's shape is very close to an ellipsoid of revolution whose polar axis is the same one that our latitude and longitude coordinates are based on.
19.
Note that for biaxial crystals the index ellipsoid will " not " be an ellipsoid of revolution ( " spheroid " ) but is described by three unequal principle refractive indices " n " ?, " n " ? and " n " ?.
20.
The fifth paper is " Elliptic and Hyperbolic Analysis " which considers the spherical law of cosines as the fundamental theorem of the sphere, and proceeds to analogues for the ellipsoid of revolution, general ellipsoid, and equilateral hyperboloids of one and two sheets, where he provides the hyperbolic law of cosines.
