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The Farey Sum of Pythagorean and Eisenstein Triples

Yıl 2024, Cilt: 12 Sayı: 1, 28 - 35, 28.01.2024

Mircea Crasmareanu

https://doi.org/10.36753/mathenot.1316554

Öz

A composition law, inspired by the Farey addition, is introduced on the set of Pythagorean triples. We study some of its properties as well as two symmetric matrices naturally associated to a given Pythagorean triple. Several examples are discussed, some of them involving the degenerated Pythagorean triple $(1, 0, 1)$. The case of Eisenstein triples is also presented.

Anahtar Kelimeler

Farey sum Pythagorean (Eisenstein) triple Symmetric matrix

Kaynakça

  • [1] Kramer, Jürg., Pippich, A. M. V.: Snapshots of modern mathematics from Oberwolfach: Special values of zeta functions and areas of triangles. Notices of American Mathematical Society, 63(8), 917-922 (2016).
  • [2] Bonahon, F.: Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots. American Mathematical Society; Princeton, NJ: Institute for Advanced Study. 2009.
  • [3] Katok, S., Ugarcovici I.: Symbolic dynamics for the modular surface and beyond. Bulletin of American Mathematical Society, New Ser. 44(1), 87-132 (2007).
  • [4] Hatcher, A.: Topology of Numbers. American Mathematical Society. 2022.
  • [5] Jitman, S., Sangwisut, E.: The group of primitive Pythagorean triples and perplex numbers. Mathematics Magazine. 95(4), 285-293 (2022).
  • [6] Crasmareanu, M.: The diagonalization map as submersion, the cubic equation as immersion and Euclidean polynomials. Mediterranean Journal of Mathematics. 19(2), 65 (2022).
  • [7] Barron, E. N.: Game Theory: An Introduction. 2nd. Revised and Enlarged ed., JohnWiley & Sons. 2013.
  • [8] Crasmareanu, M.: Conics from the Cartan decomposition of SO(2; 1). Mathematics. 11(7), 1580 (2023).
  • [9] Pluta, K., Roussillon, T., Coeurjolly, D., Romon P., Kenmochi, Y., Ostromoukhov V.: Characterization of bijective digitized rotations on the hexagonal grid. Journal of Mathematical Imaging and Vision. 60(5), 707-716 (2018).

Yıl 2024, Cilt: 12 Sayı: 1, 28 - 35, 28.01.2024

Mircea Crasmareanu

https://doi.org/10.36753/mathenot.1316554

Öz

Kaynakça

  • [1] Kramer, Jürg., Pippich, A. M. V.: Snapshots of modern mathematics from Oberwolfach: Special values of zeta functions and areas of triangles. Notices of American Mathematical Society, 63(8), 917-922 (2016).
  • [2] Bonahon, F.: Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots. American Mathematical Society; Princeton, NJ: Institute for Advanced Study. 2009.
  • [3] Katok, S., Ugarcovici I.: Symbolic dynamics for the modular surface and beyond. Bulletin of American Mathematical Society, New Ser. 44(1), 87-132 (2007).
  • [4] Hatcher, A.: Topology of Numbers. American Mathematical Society. 2022.
  • [5] Jitman, S., Sangwisut, E.: The group of primitive Pythagorean triples and perplex numbers. Mathematics Magazine. 95(4), 285-293 (2022).
  • [6] Crasmareanu, M.: The diagonalization map as submersion, the cubic equation as immersion and Euclidean polynomials. Mediterranean Journal of Mathematics. 19(2), 65 (2022).
  • [7] Barron, E. N.: Game Theory: An Introduction. 2nd. Revised and Enlarged ed., JohnWiley & Sons. 2013.
  • [8] Crasmareanu, M.: Conics from the Cartan decomposition of SO(2; 1). Mathematics. 11(7), 1580 (2023).
  • [9] Pluta, K., Roussillon, T., Coeurjolly, D., Romon P., Kenmochi, Y., Ostromoukhov V.: Characterization of bijective digitized rotations on the hexagonal grid. Journal of Mathematical Imaging and Vision. 60(5), 707-716 (2018).
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalarda Dinamik Sistemler
Bölüm Articles
Yazarlar

Mircea Crasmareanu 0000-0002-5230-2751

Erken Görünüm Tarihi 8 Aralık 2023
Yayımlanma Tarihi 28 Ocak 2024
Gönderilme Tarihi 19 Haziran 2023
Kabul Tarihi 5 Aralık 2023
Yayımlandığı Sayı Yıl 2024 Cilt: 12 Sayı: 1

Kaynak Göster

APA Crasmareanu, M. (2024). The Farey Sum of Pythagorean and Eisenstein Triples. Mathematical Sciences and Applications E-Notes, 12(1), 28-35. https://doi.org/10.36753/mathenot.1316554
AMA Crasmareanu M. The Farey Sum of Pythagorean and Eisenstein Triples. Math. Sci. Appl. E-Notes. Ocak 2024;12(1):28-35. doi:10.36753/mathenot.1316554
Chicago Crasmareanu, Mircea. “The Farey Sum of Pythagorean and Eisenstein Triples”. Mathematical Sciences and Applications E-Notes 12, sy. 1 (Ocak 2024): 28-35. https://doi.org/10.36753/mathenot.1316554.
EndNote Crasmareanu M (01 Ocak 2024) The Farey Sum of Pythagorean and Eisenstein Triples. Mathematical Sciences and Applications E-Notes 12 1 28–35.
IEEE M. Crasmareanu, “The Farey Sum of Pythagorean and Eisenstein Triples”, Math. Sci. Appl. E-Notes, c. 12, sy. 1, ss. 28–35, 2024, doi: 10.36753/mathenot.1316554.
ISNAD Crasmareanu, Mircea. “The Farey Sum of Pythagorean and Eisenstein Triples”. Mathematical Sciences and Applications E-Notes 12/1 (Ocak 2024), 28-35. https://doi.org/10.36753/mathenot.1316554.
JAMA Crasmareanu M. The Farey Sum of Pythagorean and Eisenstein Triples. Math. Sci. Appl. E-Notes. 2024;12:28–35.
MLA Crasmareanu, Mircea. “The Farey Sum of Pythagorean and Eisenstein Triples”. Mathematical Sciences and Applications E-Notes, c. 12, sy. 1, 2024, ss. 28-35, doi:10.36753/mathenot.1316554.
Vancouver Crasmareanu M. The Farey Sum of Pythagorean and Eisenstein Triples. Math. Sci. Appl. E-Notes. 2024;12(1):28-35.
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