Abstract by Jason Colgrove
Proving the Existence of Modified Grade School Triangles Using Cube Roots
A grade school triangle is a triangle with side lengths which are elements of a real quadratic number field. The side lengths follow the form u equals k plus l times the square root of d, where k and l are integers, d is a squarefree integer, and u, k, l, and d vary depending on the side in which it corresponds to. We are researching a modification of this by replacing square roots with cube roots. Our ultimate goal is to find the number of families of triangles that exist with such conditions.