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: | Journal Article |
| Language: | English |
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AMER INST MATHEMATICAL SCIENCES-AIMS
2019
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| Subjects: | |
| Online Access: | http://purl.org/au-research/grants/arc/DP160104994 http://hdl.handle.net/20.500.11937/90797 |
| _version_ | 1848765431064559616 |
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| author | Overmars, A. Ntogramatzidis, Lorenzo Venkatraman, S. |
| author_facet | Overmars, A. Ntogramatzidis, Lorenzo Venkatraman, S. |
| author_sort | Overmars, A. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| 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 | 2025-11-14T11:35:08Z |
| format | Journal Article |
| id | curtin-20.500.11937-90797 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:35:08Z |
| publishDate | 2019 |
| publisher | AMER INST MATHEMATICAL SCIENCES-AIMS |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-907972023-04-20T02:00:27Z A new approach to generate all Pythagorean triples Overmars, A. Ntogramatzidis, Lorenzo Venkatraman, S. Science & Technology Physical Sciences Mathematics, Applied Mathematics Pythagorean triples Diophantine equations Euclidean triples Platonic triples right angle triangles PARAMETRIZATION 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. 2019 Journal Article http://hdl.handle.net/20.500.11937/90797 10.3934/math.2019.2.242 English http://purl.org/au-research/grants/arc/DP160104994 http://creativecommons.org/licenses/by/4.0 AMER INST MATHEMATICAL SCIENCES-AIMS fulltext |
| spellingShingle | Science & Technology Physical Sciences Mathematics, Applied Mathematics Pythagorean triples Diophantine equations Euclidean triples Platonic triples right angle triangles PARAMETRIZATION Overmars, A. Ntogramatzidis, Lorenzo Venkatraman, S. A new approach to generate all Pythagorean triples |
| 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 | Science & Technology Physical Sciences Mathematics, Applied Mathematics Pythagorean triples Diophantine equations Euclidean triples Platonic triples right angle triangles PARAMETRIZATION |
| url | http://purl.org/au-research/grants/arc/DP160104994 http://hdl.handle.net/20.500.11937/90797 |