Comments on: Pythagorean Triples and the Unit Circle — for RMO
https://mathhothouse.me/2014/09/22/pythagorean-triples-and-the-unit-circle/
Mathematics demystifiedSun, 26 Oct 2014 06:09:00 +0000
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By: suryakalia
https://mathhothouse.me/2014/09/22/pythagorean-triples-and-the-unit-circle/comment-page-1/#comment-2
Sun, 26 Oct 2014 06:09:00 +0000http://mathhothouse.wordpress.com/?p=201#comment-2Just after the first step we needed rational points on the unit circle. We may write the general solution as x=1cosΔ y=1sinΔ where both sine and cosine are rational. Converting it to tan(Δ/2)=m we get x=(1-m^2)/(1+m^2) and y=2m/(1+m^2) where m is any positive rational number.
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