The talk undertakes a very detailed, very visual, and quite elementary study of the Heron triangles of fixed area and perimeter. It circumvents the traditional approach to Heron triangles based on elliptic curves. Its key focus is on the geometry, calculus, and algebra of the associated area curve. The main result presents a simple sufficient condition for the existence of infinitely many Heron triangles with constant area and perimeter. An application to Diophantine equations is also given.
10/22/2018 - Elad Zelingher
(Yale) - TBA