A Trillion Triangles

In 1225, Fibonacci (of "Fibonacci numbers" fame) showed that 5 and 7 were congruent numbers, and he stated, but did not prove, that 1 is not a congruent number. That proof was supplied by Fermat (of "Fermat's last theorem" fame) in 1659.

Found this pdf which gives Fermat's proof. It actually proves that no perfect square can be congruent, and uses Fermat's famous "method of infinite descent". That is, it proves that given any congruent perfect square, a smaller one can be derived, so there can be no smallest congruent perfect square, and this is a contradiction.

Anyway, I never heard of congruent numbers before, so thanks for the link. I came across a bunch of other number theory news in the process of ( minimally ) educating myself. These guys are busy, busy, busy!

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