Generating Pythagorean numbers

Authors

  • Marco Vinicio Vásquez Bernal Universidad Nacional de Educación, UNAE, Javier Loyola, Azogues, Ecuador.
  • Mercedes Elizabeth Vásquez Chiquito Universidad Nacional de Educación, UNAE, Javier Loyola, Azogues, Ecuador.

DOI:

https://doi.org/10.18537/mskn.07.01.06

Keywords:

Pythagorean Theorem, thirds, squares, sum

Abstract

The paper presents a general way to define three natural numbers (triple) that satisfy the Pythagorean relationship; it is the sum of the squares of two numbers is equal to the square of a larger number, through a process much more general than known so far. We even propose formulas that in function of two parameters find these sets of three elements, the results of which are presented in tables. Results confirm the idea that there are an infinite number of triples that meet the Pythagorean relationship. Further the use of the tables is illustrated how to build relationships where the sum of the squares of more than two numbers equals the square of another.

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References

Alfred, U., 1964. Consecutive integers whose sum of squares is a perfect square. Mathematics Magazine, 37(1), 19-32.

Hope, F., 1998. Pythagorean triples revisited. Mathematics Teaching in the Middle School, 3(7), 478-479.

Li, M.-S., K. Robertson, T.J. Osler, A. Hassen, C.S. Simons, M. Wright, 2008. On numbers equal to the sum of two squares in more than one way. Department of Mathematics, Rowan University, Glassboro, NJ 08028. Disponible en: http://www.rowan.edu/colleges/csm/departments/math/ facultystaff/osler/110%20SUM%20OF%20TWO%20SQUARES%20IN%20MORE%20THAN%20ONE%20WAY%20MACE%20Small%20changes%20Oct%2008%20%20Submission.pdf, 11 pp.

MacKay, D., S. Mahajan, 2005. Numbers that are sums of squares in several ways. Disponible en: http://www.inference.phy.cam.ac.uk/mackay/sumsquares.pdf, 6 pp.

Roy, T., F.J. Sonia, 2012. A direct method to generate Pythagorean Triples and its generalization to Pythagorean Quadruples and n-tuples. Department of Physics, Jadavpur University, Kolkata 700032, India. Disponible en: http://arxiv.org/ftp/arxiv/papers/ 1201/1201.2145.pdf, 11 pp.

Scheinman, L.J., 2006. On the solution of the cubic Pythagorean Diophantine equation x3 + y3 + z3 = a3. Missouri Journal of Mathematical Sciences, 18(1), 1-14.

Vargas, J.A., 1994. Área de triángulos rectángulos. Revista de Educación Matemática, 2(3), 1-8.

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Published

2016-11-07

How to Cite

Vásquez Bernal, M. V., & Vásquez Chiquito, M. E. (2016). Generating Pythagorean numbers. Maskana, 7(1), 61–70. https://doi.org/10.18537/mskn.07.01.06

Issue

Vol. 7 No. 1 (2016)

Section

Research articles

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