Michael:
> curiously my old unreliable dictionary that i like to keep next to
my old
> unreliable atlas was misleading me by qualifying a spheroid as a
particular
> sort of ellipsoid that is generated by revolving an ellipse around
one of
> its axes
>
> it defines ellipsoids generally as geometric surfaces whose plane
sections
> are all either ellipses or circles
>
True enough. It's just that all the reference ellipsoids used here
are oblate ellipsoids of rotation produced in exactly the way your
dictionary defines "spheroid" - ellipses spun around a principal
axis. So I guess I was misleading you by holding to the geographical
specifics.
The more general definition of ellipsoids allows for *triaxial*
ellipsoids - which would in fact provide a marginally better fit to
the geoid by having an elliptical equator, too, to bulge into that
New Guinea high and sink under the Indian Ocean low, but a better fit
won at the expense of horrible maths necessary to generate map
projections. So, yes, in principle you could have options 2 and 3 in
your original list as "spheroid" and "triaxial ellipsoid", but I
don't know if anyone has ever used a triaxial reference ellipsoid for
the Earth (once the maths got complicated and the computers got fast,
it was better just to go the whole hog to the geoid), but the
triaxials *are* very important when mapping potato-shaped small moons
of other planets.
Grant