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

Item

Title

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

Description

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.

Vincent Ferlini

Contributor

Keene State College

Creator

Brooke M. Hatanaka

Date

2017-10-11

Identifier

http://hdl.handle.net/20.500.12088/8078

Subject

Mathematics

Type

Presentation

Rights

http://rightsstatements.org/vocab/InC/1.0/

Item sets

AEC 2017 School of Sciences and Social Sciences

Site pages

School of Sciences and Social Sciences