On the algebraic structure of Pythagorean triples
In: Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, Jg. 102 (2024-02-01), Heft 1, S. A3
Online
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Zugriff:
A Pythagorean triple is an ordered triple of integers (a,b,c) ≠ (0, 0, 0) such that a^2 + b^2 = c^2. It is well known that the set ℘ of all Pythagorean triples has an intrinsic structure of commutative monoid with respect to a suitable binary operation (℘,⋆). In this article, we will introduce the "commensurability" relation ℛ among Pythagorean triples, and we will see that it induces a group quotient, ℘/ℛ, which is isomorphic with the direct product of infinite (countable) copies of C∞, the infinite cyclic group, and a cyclic group of order 4. As an application, we will see that the acute angles of Pythagorean triangles are irrational when measured in degrees.
| Titel: |
On the algebraic structure of Pythagorean triples
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| Autor/in / Beteiligte Person: | Anatriello, Giuseppina ; Vincenzi, Giovanni |
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| Zeitschrift: | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, Jg. 102 (2024-02-01), Heft 1, S. A3 |
| Veröffentlichung: | Accademia Peloritana dei Pericolanti, 2024 |
| Medientyp: | academicJournal |
| ISSN: | 0365-0359 (print) ; 1825-1242 (print) |
| DOI: | 10.1478/AAPP.1021A3 |
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