#### Presentation Title

Triples of Integers and Associated Triangles

#### Presentation Type

Oral Presentation

#### School

School of Sciences and Social Sciences

#### Discipline

Mathematics

#### Mentor

Vincent Ferlini

#### Abstract

If m and n are integers with 02-n^{2}, 2mn, m^{2}+n^{2}) are integer sides of a triangle with a right angle. We note that an integer is any positive or negative whole number. These are also known as Pythagorean triples. Our first triple, and the most simple of the three we will explore, is given such that if m and n are integers with 02, mn, m^{2}-n^{2}) are the sides of a triangle in which B=2A. In this talk, we shall explain where the restrictions for this triple come from, look at examples of triangles fitting this criteria, as well as present two other triples of integers based on m and n that characterize other types of triangles, where we will use Maple in order to simplify more complex equations.

Triples of Integers and Associated Triangles

If m and n are integers with 02-n^{2}, 2mn, m^{2}+n^{2}) are integer sides of a triangle with a right angle. We note that an integer is any positive or negative whole number. These are also known as Pythagorean triples. Our first triple, and the most simple of the three we will explore, is given such that if m and n are integers with 02, mn, m^{2}-n^{2}) are the sides of a triangle in which B=2A. In this talk, we shall explain where the restrictions for this triple come from, look at examples of triangles fitting this criteria, as well as present two other triples of integers based on m and n that characterize other types of triangles, where we will use Maple in order to simplify more complex equations.