A new approach to generate all Pythagorean triples
This paper revisits the topic of Pythagorean triples with a different perspective. While several methods have been explored to generate Pythagorean triples, none of them is complete in terms of generating all the triples without repetitions. Indeed, many existing methods concentrate on generating pr...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-03-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2019.2.242/fulltext.html |
| _version_ | 1818668264427880448 |
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| author | Anthony Overmars Lorenzo Ntogramatzidis Sitalakshmi Venkatraman |
| author_facet | Anthony Overmars Lorenzo Ntogramatzidis Sitalakshmi Venkatraman |
| author_sort | Anthony Overmars |
| collection | DOAJ |
| description | This paper revisits the topic of Pythagorean triples with a different perspective. While several methods have been explored to generate Pythagorean triples, none of them is complete in terms of generating all the triples without repetitions. Indeed, many existing methods concentrate on generating primitive triples but do not cater to non-primitives. By contrast, the approach presented in this paper to parameterise the Pythagorean triples generates all of the triples in a unique way, i.e., without repetitions. We also explore the relation of this new parameterisation with the Pythagorean family of odd triples and with the Platonic family of even triples. |
| first_indexed | 2024-12-17T06:33:33Z |
| format | Article |
| id | doaj.art-284e764349414cb1879bb04da44cd646 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-17T06:33:33Z |
| publishDate | 2019-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-284e764349414cb1879bb04da44cd6462022-12-21T22:00:05ZengAIMS PressAIMS Mathematics2473-69882019-03-014224225310.3934/math.2019.2.242A new approach to generate all Pythagorean triplesAnthony Overmars0Lorenzo Ntogramatzidis1Sitalakshmi Venkatraman21 Department of Information Technology, Melbourne Polytechnic, VIC, Australia2 Department of Mathematics and Statistics, Curtin University, Perth (WA), Australia1 Department of Information Technology, Melbourne Polytechnic, VIC, AustraliaThis paper revisits the topic of Pythagorean triples with a different perspective. While several methods have been explored to generate Pythagorean triples, none of them is complete in terms of generating all the triples without repetitions. Indeed, many existing methods concentrate on generating primitive triples but do not cater to non-primitives. By contrast, the approach presented in this paper to parameterise the Pythagorean triples generates all of the triples in a unique way, i.e., without repetitions. We also explore the relation of this new parameterisation with the Pythagorean family of odd triples and with the Platonic family of even triples.https://www.aimspress.com/article/10.3934/math.2019.2.242/fulltext.htmlPythagorean triplesDiophantine equationsEuclidean triplesPlatonic triplesright angle triangles |
| spellingShingle | Anthony Overmars Lorenzo Ntogramatzidis Sitalakshmi Venkatraman A new approach to generate all Pythagorean triples AIMS Mathematics Pythagorean triples Diophantine equations Euclidean triples Platonic triples right angle triangles |
| title | A new approach to generate all Pythagorean triples |
| title_full | A new approach to generate all Pythagorean triples |
| title_fullStr | A new approach to generate all Pythagorean triples |
| title_full_unstemmed | A new approach to generate all Pythagorean triples |
| title_short | A new approach to generate all Pythagorean triples |
| title_sort | new approach to generate all pythagorean triples |
| topic | Pythagorean triples Diophantine equations Euclidean triples Platonic triples right angle triangles |
| url | https://www.aimspress.com/article/10.3934/math.2019.2.242/fulltext.html |
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