Presentation Title

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

Presenter Information

Brooke M. HatanakaFollow

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 a2 + b2 = c2. 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.

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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 a2 + b2 = c2. 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.