Pythagorean triples: an approach to assist the teaching of mathematics

Authors

DOI:

https://doi.org/10.5902/2179460X68025

Keywords:

Prime numbers, Pythagorean theorem, Pythagorean tricks

Abstract

The present work is the result of the exploration of teaching methodologies that seek a greater interaction of the student with the approached concept. During the text we present methods to obtain the famous Pythagorean triples from concepts of number theory and algebra. Our proposal is to provide the teacher (reader) with theoretical mathematical tools with which he can better develop his practice in various mathematical contents. The search for new Pythagorean cracks has always been the target of fascination and study, both by professional mathematicians and curious students, so the theme here is developed and results already known to the community are presented and demonstrated in an unprecedented way, that is, with approaches mathematics that were not found in previous works.

Downloads

Download data is not yet available.

Author Biographies

Saulo Portes dos Reis, Federal Institute of São Paulo

Graduated in Physics (2007) and graduated in Mathematics - UNESP Faculdade de Engenharia de Ilha Solteira (2014). He holds a professional master's degree in Mathematics (PROFMAT) and a PhD in Materials Science from UNESP Faculdade de Engenharia de Ilha Solteira. He is currently a professor at the Federal Institute of São Paulo (Votuporanga campus).

Marina da Silva Margiotti Machado, Federal Institute of São Paulo

She has a degree in Literature with a major in French and a degree in Pedagogy. She has a master's degree in Education, in the research line Policies and Management of Educational Organizations. She currently works as a Teacher of Basic, Technical and Technological Education at IFSP in the area of Education / Pedagogy.

Dulcilene Aparecida Flores de, Secretaria da Educação do Estado de São Paulo

Graduated in Physics from the University Center of Votuporanga (1999). She is currently a teacher of Basic Education II at the Secretary of Education of the State of São Paulo. She has experience in the field of Physics.

Rafael Pupim Vignoto, Federal Institute of São Paulo

Student in the undergraduate course in Physics at the Federal Institute of São Paulo.

References

BENITO, M.; VARONA, J. L. Pytagorean triangles with legs less than n. Journal of computational and applied mathematics, [s.l.], v. 143 n. 1, p. 117-126, jun. 2002.

CREASE, R. P. As grandes equações: a história das fórmulas matemáticas mais importantes e os cientistas que as criaram. Rio de Janeiro: Zahar, 2011.

EVES, H. W. Introdução à história da matemática. 5ª ed. Campinas, SP: Unicamp, 2011.

FIRMIANO, A.; SANTOS, J. P. M.; ELOY, M. E.; CARDOSO, C. As infinitas trincas pitagóricas de Euclides. Revista eletrônica Paulista CQD, [s.l.], v. 17, p. 13-26, fev. 2020.

HEFEZ, A. Elementos de aritmética. 2ª ed. Rio de Janeiro: SBM, 2011.

JESUS, A. F.; SANTOS, J. P. M.; LINARES, J. L. Investigando fatores primos com trincas pitagóricas. Trilhas pedagógicas,. [s.l.], v. 10 n.12, p. 239-252, ago. 2020.

LOOMIS, E. S.; The Pythagorean proposition. 2ª ed. Washington DC: National council of teachers of mathematics, 1968.

ROQUE, T. História da matemática. Rio de Janeiro: Zahar, 2012.

SING , S. O último teorema de Fermat. 3ª ed. Rio de Janeiro: BestBolso, 2018.

STEWART, I. 17 Equações que mudaram o mundo. Rio de Janeiro: Zahar, 2013.

Published

2023-06-22

How to Cite

Reis, S. P. dos, Machado, M. da S. M., Dulcilene Aparecida Flores de, & Vignoto, R. P. (2023). Pythagorean triples: an approach to assist the teaching of mathematics. Ciência E Natura, 45, e10. https://doi.org/10.5902/2179460X68025

Most read articles by the same author(s)