Grade School Triangles
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 completely and present an elegant complement called Ailles' rectangle that deserves to be in every geometry teacher's toolkit.
Calcut, Jack S. 2010. "Grade School Triangles." American Mathematical Monthly 117(8): 673-685.
Mathematical Association of America
American Mathematical Monthly