A Trillion Triangles

American Institute of Mathematics ^ | Sep 22, 2009 | Unknown.

[decimon]

September 22, 2009 -- Mathematicians from North America, Europe, Australia, and South America have resolved the first one trillion cases of an ancient mathematics problem. The advance was made possible by a clever technique for multiplying large numbers. The numbers involved are so enormous that if their digits were written out by hand they would stretch to the moon and back. The biggest challenge was that these numbers could not even fit into the main memory of the available computers, so the researchers had to make extensive use of the computers' hard drives.

According to Brian Conrey, Director of the American Institute of Mathematics, "Old problems like this may seem obscure, but they generate a lot of interesting and useful research as people develop new ways to attack them."

[dr_lew]

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!

[colorado tanker]

LOL!

[Billthedrill]

There’s gonna be an xkcd toon on this one and about 20 people in the country will understand it...