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        riddles >> medium >> Largest Ellipse Inside Pythagorean Triangle?
        
(Message started by: ThudanBlunder on Sep 27th, 2007, 4:15pm)
Title: Largest Ellipse Inside Pythagorean Triangle?
Post by ThudanBlunder on Sep 27th, 2007, 4:15pm
What is the area of the largest ellipse inscribable inside a 3 by 4 by 5 Pythagorean triangle?
Title: Re: Largest Ellipse Inside Pythagorean Triangle?
Post by Barukh on Sep 27th, 2007, 11:38pm
Icarus (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1048210101)!
Title: Re: Largest Ellipse Inside Pythagorean Triangle?
Post by ecoist on Nov 1st, 2007, 5:45pm
I checked your link, Barukh, and got the impression that, the triangle of smallest area circumscribing a circle is equilateral, is sort of obvious.  Took me some time to find an elementary proof, but I fear it is unnecessarily long (filling a 3x5 index card).  Is there a shorter proof, or is it a corollary of some other result?


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