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The origin of the Beauregard–Suryanarayan product on Pythagorean triples

  • Shaul ZemelEmail author
Article
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Abstract

We show how the multiplicative structure on Pythagorean triples defined by Beauregard–Suryanarayan arises from automorphisms of the hyperbolic plane, and how the structure theorem of this product follow naturally from this connection. We also show how the natural involution on Pythagorean triples is related to Pell’s equation with the parameter 2, and prove a generalization of this phenomenon.

Keywords

Pythagorean triples Binary quadratic forms Pell’s equation 

Mathematics Subject Classification

11E16 11D57 

Notes

References

  1. 1.
    Beauregard, R.A., Suryanarayan, E.R.: Pythagorean triples: the hyperbolic view. College Math. J. 27(3), 170–181 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Eckert, E.J.: The group of primitive Pythagorean triangles. Math. Mag. 57(1), 22–27 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    McCullough, D.: Height and excess of Pythagorean triples. Math. Mag. 78(1), 26–44 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Taussky, O.: Sums of squares. Am. Math. Monthly 77, 805–830 (1970)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Università degli Studi di Ferrara 2019

Authors and Affiliations

  1. 1.Einstein Institute of MathematicsThe Hebrew University of Jerusalem, Edmond Safra CampusJerusalemIsrael

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