Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

Rational Approximations of $\sqrt{2}$:
An Introduction to Isosceles Almost Right Triangles

David Friday, '04

While visiting the Calculus and Physical Sciences Tutorial Lab at Grand Rapids
Community College, a question was posed: for what values of
$n$ will the sum of the first $n$
positive integers be a perfect square? A thorough investigation of the problem and the
introduction of the concept of an isosceles "almost" right triangle yielded a number of
interesting results. One of the results involves a sequence of rational numbers that converges to $\sqrt{2}$,
yielding some excellent approximations.