Proof of conic sections with the Pythagorean triples.

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1 total messages Started by Choung-Ming Chi Sun, 30 May 1993 22:13

#2028

Author: Choung-Ming Chi
Date: Sun, 30 May 1993 22:13

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This message is intended for all thoses who are excellent in Math. Has anyone
out there ever proved or know a  proof to relate the pythagorean
triples(3,4,5; 5,12,13; 8,15,17; etc.) with conic section's(ellipses,
hyperperbolas, and others) verticies, foci, major, and minor axes?

In another words Prove pythagorean triples exists in the equation for the
ellipse x^2/16 + y^2/9 = 1. A^2=16 and B^2=9. Reminder for the ellipse
A^2= B^2 + C^2, and for the hyperpola C^2= A^2 + B^2.

Please, if you know what I am talking about and know a proof for it, I would
appreciate it if you could send it to CHI@MACC.wisc.edu. If you are a little
confused by the examples please tell me so I can clear it up. In any case, I
need your help to find the proof. Thank you.

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