#### Presentation Title

Characterization of Pythagorean Triples in the Root 2 Field Extension of the Rational Numbers

#### Presentation Type

Oral Presentation

#### School

School of Sciences and Social Sciences

#### Discipline

Mathematics

#### Mentor

Vincent Ferlini

#### Abstract

In high school, every geometry student learns the Pythagorean Theorem, which states that a triangle ABC with sides a, b, and c is a right triangle if and only if a^{2} + b^{2} = c^{2}. A Pythagorean triple is a triple of three positive integers (a, b, c) that satisfies the Pythagorean Theorem and all Pythagorean triples can be both generated and characterized with one formula. In this talk, we will characterize Pythagorean triples in the root 2 field extension of the rational numbers and compare those triples with Pythagorean triples in the integers.

Characterization of Pythagorean Triples in the Root 2 Field Extension of the Rational Numbers

In high school, every geometry student learns the Pythagorean Theorem, which states that a triangle ABC with sides a, b, and c is a right triangle if and only if a^{2} + b^{2} = c^{2}. A Pythagorean triple is a triple of three positive integers (a, b, c) that satisfies the Pythagorean Theorem and all Pythagorean triples can be both generated and characterized with one formula. In this talk, we will characterize Pythagorean triples in the root 2 field extension of the rational numbers and compare those triples with Pythagorean triples in the integers.