#### Publication Date

9-3-2010

#### Abstract

In this paper, we seek a family of triangles that have integer sides and integer area. We focus mainly on scalene triangles since it is impossible to have such triangles that are equilateral and isoceles triangles with these properties are fairly simple to construct. We restrict the scalene triangles we study to Nearly Equilateral Triangles which have consecutive integer sides. In the process of constructing this family, we find an application of Pell's Equation. We follow this with a few other interesting notes on Pell's Equation.

#### Degree Name

Mathematics

#### Level of Degree

Masters

#### Department Name

Mathematics & Statistics

#### First Advisor

Stone, Alexander

#### First Committee Member (Chair)

Umland, Kristin

#### Second Committee Member

Lorenz, Jens

#### Language

English

#### Keywords

Triangle, Pell's equation.

#### Document Type

Thesis

#### Recommended Citation

Christensen, Laurel. "Pell's Equation and nearly equilateral triangles." (2010). http://digitalrepository.unm.edu/math_etds/11