Pell's Equation and nearly equilateral triangles

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.

Name thesis:degree_name

Mathematics

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Mathematics & Statistics

Year

2010

Author dc:creator

• Christensen, Laurel

Contributors dc:contributor

• Stone, Alexander
• Alexander Stone
• Jens Lorenz
• Kristin Umland

• Triangle
• Pell's equation.

Language dc:language

English

Identifier

https://digitalrepository.unm.edu/math_etds/11

OAI identifier oai:identifier

oai:digitalrepository.unm.edu:math_etds-1010