A New Generalization of the Pythagorean Triples
DOI:
https://doi.org/10.35819/remat2024v10i2id7083Keywords:
pythagorean equation, pythagorean triples, generalizationsAbstract
In this work, we revisit the Pythagorean equation and its solutions with natural coordinates, called Pythagorean triples, as well as some of its well-known generalizations. Moreover, we realize a study on the solutions with natural coordinates of a quadratic equation that extends the Pythagorean equation, obtaining expressions that allow us to characterize algebraically these solutions and present a new generalization of the Pythagorean triples.
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BANDEIRA, M. O.; SILVA FILHO, J. F. Um método geométrico para construção de ternos pitagóricos. Professor de Matemática Online. v. 8, n. 2, p. 222-235, 2020. DOI: https://doi.org/10.21711/2319023x2020/pmo817.
BARBOSA, J. L. M. Geometria Euclidiana. 10. ed. Rio de Janeiro: SBM, 2006.
BLEZ, M. A.; SILVA FILHO, J. F. Generalizando os Ternos Pitagóricos. Revista do Professor de Matemática. v. 98, p. 3-5, 2019.
BURTON, D. M. Elementary Number Theory. 7. ed. New York: Mc Graw Hill, 2011.
HEFEZ, A. Aritmética. 2. ed. Rio de Janeiro: SBM, 2016.
MAIA, J. E. S. B.; SILVA FILHO, J. F. Construindo Ternos Pitagóricos com Números Complexos. Revista do Professor de Matemática. v. 101, p. 19-21, 2020.
MUNIZ Neto, A. C. Geometria. Rio de Janeiro: SBM, 2013. Coleção Profmat.
ROCHA, S. Fábrica de Ternos Pitagóricos. Revista do Professor de Matemática. v. 55, 2004. Disponível em: https://rpm.org.br/cdrpm/55/6.htm. Acesso em: 30 jan. 2024.
ROTHBART A.; PAUSELL, B. Números Pitagóricos: Uma fórmula de fácil dedução e algumas aplicações geométricas. Revista do Professor de Matemática. v. 7, p. 49-51, 1985.
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Copyright (c) 2024 João Francisco da Silva Filho, Elenitha de Sousa Felix
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