Mathematicians Solve 'Trillion Triangle' Problem

ScienceDaily (Sep. 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.

The problem, which was first posed more than a thousand years ago, concerns the areas of right-angled triangles. The surprisingly difficult problem is to determine which whole numbers can be the area of a right-angled triangle whose sides are whole numbers or fractions. The area of such a triangle is called a "congruent number." For example, the 3-4-5 right triangle which students see in geometry has area 1/2 × 3 × 4 = 6, so 6 is a congruent number. The smallest congruent number is 5, which is the area of the right triangle with sides 3/2, 20/3, and 41/6.

(Credit: Image courtesy of American Institute of Mathematics)

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