Albion College
Mathematics and Computer Science
COLLOQUIUM
Rational Approximations of $\sqrt{2}$: An Introduction to Isosceles Almost Right Triangles
David Friday, '04

### Macomb Community College

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.
3:30 PM
All are welcome!
Palenske 227
October 11, 2012