# PITs with Dr. Andy Miller

Our own Dr. Andy Miller will be speaking in the Math Club this

Wednesday, April 14th at 5pm in PSHC 1105.

He’ll be speaking about:

Title:  Primitive Integral Triangles With Given Defect

Abstract: A primitive integral triangle (or PIT for short) is a Euclidean triangle ∆ = ∆(a, b, c) whose side lengths are integers a, b and c with greatest common divisor equal to 1. If c ≥ a and c ≥ b then the defect of ∆ is the integer $d(\Delta) = a^2 +b^2 -c^2$. Consider the following problems:

• For a given integer d, is there a PIT with defect d?
• How many PIT’s have defect d?
• How can we determine the simplest PIT’s with defect d?
• Is there an algorithm for producing all PIT’s which have defect d?

In this presentation I will describe a framework for answering all of these questions. For example the set of all PIT’s with a given defect d can be represented by a schematic diagram such as the one shown below for d = 19.

Primitive integral triangles with defect 19

As always, there will be Free Pizza!