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| Title: | Mathematics at DEC |
|
| Moderator: | RUSURE::EDP |
|
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
1403.0. "Dandelin's ellipse" by HERON::BUCHANAN (Holdfast is the only dog, my duck.) Mon Mar 25 1991 11:37
There is a stunning geometric construction in this month's Scientific
American, which unifies two views of what constitutes an ellipse:
(1) intersection of a plane, P, with a cone
(2) define two foci: X & Y. consider the locus of those points A
such that |AX| + |AY| is constant.
The idea is to take definition (1), and consider the cone as being
divided into two regions. Inflate a sphere in each region to the maximal
possible size, such that each of the two spheres is tangent to P.
Question: are the points at which the spheres touch P just X & Y?
Prove it...
Regards,
Andrew.