Albion College
Mathematics and Computer Science
Grade School Triangles and Ailles' Rectangle
Jack Calcut

Assistant Professor

Department of Mathematics

Oberlin College

In grade school, students learn a standard set of Euclidean triangles. Among this set, the usual 45-45-90 and 30-60-90 triangles are the only right triangles with rational angles and side lengths each containing at most one square root. Are there any other such right triangles? We answer this question and present an elegant complement, called Ailles' rectangle, that deserves to be in every geometry teacher's toolkit.
All are welcome!
Palenske 227
October 7, 2010