From: "Dwight K. Elvey" 
To: atm{at}shore.net
Reply-To: "Dwight K. Elvey" 


>From: "Bianco Giuseppe" 
>
>Even if I've a PhD in Astronomy and reasonable knowledge in optics, I'm
puzzled
by something which will be certainly solved by somebody in the list.
>Textbooks on mirror making say that, in order to "parabolize" a concave
spherical mirror, one should dig into the center of the surface;
conversely, in order to "hyperbolize" a convex spherical mirror,
one should depress the outer zones of the surface. To me, both those action
lead straight to an ellipsoidal figure. In fact, in the case of a concave
surface, a paraboloid results from flattening the outer zones with respect
to the center, and even more so in the case of an hyperboloid.
>Where's the trick? Thank you all in advance.
>
>Dr. Giuseppe Bianco
>Centro di Geodesia Spaziale "G. Colombo"
>Agenzia Spaziale Italiana
>75100 Matera (MT), Italy
>phone:+39-0835-377209
>fax:     +39-0835-339005
>e-mail: giuseppe.bianco{at}asi.it
>

Hi
 You need to think of these shapes as a continuum of shapes.
An ellipsoid is just a stretched shpere. A paraboliod is a particular one
that has been stretched to infinity. The hyperboloid is a continuation to
the stretching.
 To modify a sphere to any of these shapes, we can progress
the same way. The suggestions for where to remove the most material can be
used to change the shape from a sphere to ellipsoids, to a paraboloid and
then to hyperboloids. It is more a case of how much, not where. The where
is the same for all of them.
Dwight

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