Barry Lake <[log in to unmask]> wrote:
>At 12:07 PM -0600 10/12/99, [log in to unmask] wrote:
> >See http://www.treasure-troves.com/math/SoddyCircles.html for an
> >excellent description and an excellent graphical treatment:
> >
> > Given three distinct points A, B, and C, let three Circles
> > be drawn, one centered about each point and each one tangent
> > to the other two...
>
>
>My only quibble with this (and it's a small quibble, indeed) is if points
>A, B, and C all happen to be on the same line, then it won't be possible to
>draw three such circles each tangent to the other two. Therefore, it won't
>be possible to create the inner or outer Soddy circles, either.
Your quibble is understandable, but check the "Given" description
above so that you can sleep better tonight. Try to have points A, B,
and C be on *the same* line AND to have *each* circle be tangent to
the other two :-)
A good mathematical statement is like a good poem: It says a lot with
the minimum of words. I believe the "Given" statement above is
extremely elegant (and, as it should, it says a lot, including a
pre-answer to your quibble).
>In any case, I have immensely enjoyed this thread (especially the website
>mentioned above, thanks Alfredo!).
My pleasure, indeed. In fact, I bought Eric's "Concise" (ha!)
Encyclopedia of Mathematics last year and the CD version, which I
carry with me all over the world (the CD, not the book :-)
>In solving the original problem I had to
>exercise some brain cells I forgot I had. Perhaps this will help in my
>"real" work...
Good. Oops, that's what I should be doing, instead of playing around
with mathematics :-)
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| r | Alfredo [log in to unmask]
| e | http://www.adager.com
| g | F. Alfredo Rego +1 208 726-9100
| a | Manager, R & D Labs Fax +1 208 726-2822
| d | Adager Corporation
| A | Sun Valley, Idaho 83353-3000 U.S.A.
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