We propose an algorithm for reconstructing a tree path from a root to a primitive Pythagorean triple. The algorithm has polynomial time complexity with respect to the input length relating to the “size” of the primitive Pythagorean triple.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. J. M. Barning, “On Pythagorean and quasi-Pythagorean triangles and a generation process with the help of unimodular matrices,” Math. Centrum, Amsterdam, Afd. Zuivere Wisk. ZW 1963-011 (1963).
A. Hall, “Genealogy of Pythagorean triads,” Math. Gazette 54, No. 390, 377–379 (1970).
D. Romik, “The dynamics of Pythagorean triples,” Trans. Am. Math. Soc. 360, No. 11, 6045–6064 (2008).
A. R. Kanga, “The family tree of Pythagorean triples,” Bull. Inst. Math. Appl. 26, No. 1–2, 15–17 (1990).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 12, No. 3, 2012, pp. 95–102.
Rights and permissions
About this article
Cite this article
Emelyanov, P.G. Path Reconstruction in the Barning–Hall Tree. J Math Sci 202, 72–79 (2014). https://doi.org/10.1007/s10958-014-2034-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-014-2034-5