TL;DR
This paper introduces new irrational relations for Pythagorean triples, expanding the understanding of their mathematical structure beyond integer solutions.
Contribution
It presents novel irrational relations associated with Pythagorean triples and establishes a connection between these relations and the hypotenuse.
Findings
Existence of irrational numbers related to Pythagorean triples
New relations linking these irrationals to the hypotenuse
Enhanced understanding of Pythagorean triple properties
Abstract
In this note we show that in addition to two integers forming a Pythagorean triple, there also exist two irrational numbers in terms of which this Pythagorean triple can also be obtained. We also put forward a relation between these two pairs and the hypotenuse of a Pythagorean triangle.
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Taxonomy
TopicsMathematics and Applications