466
Views
0
CrossRef citations to date
0
Altmetric
Articles

An Accessible Proof of Hurwitz’s Sums of Squares Theorem

&
Pages 422-436 | Received 19 Jul 2020, Accepted 06 Jan 2021, Published online: 18 Oct 2022

References

  • Baez, J. C. (2002). The octonions, Bull. Amer. Math. Soc. 39(2): 145–205. DOI: 10.1090/S0273-0979-01-00934-X.
  • Cayley, A. (1845). On Jacobi’s elliptic functions …and on quaternions. Philos. Mag. 26: 208–211. Collected Math. Papers 1: 127. DOI: 10.1017/cbo9780511703676.022.
  • Cayley, A. (1858). A memoir on the theory of matrices. Philos. Trans. Royal Soc. London 148: 17–37. Collected Math. Papers 2: 475–496. DOI: 10.1017/cbo9780511703683.053.
  • Conway, J. H., Smith, D. A. (2003). On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. New York: A K Peters/CRC Press.
  • Dickson, L. E. (1912). Linear algebras. Trans. Amer. Math. Soc. 13: 59–73. DOI: 10.1090/s0002-9947-1912-1500905-3.
  • Dickson, L. E. (1914). Linear Algebras. Cambridge: Cambridge Univ. Press.
  • Dickson, L. E. (1919). On quaternions and their generalization and the history of the eight square theorem. Ann. Math. 2nd ser. 20(3): 155–171. DOI: 10.2307/1967865.
  • Hamilton, W. R. (1835). Theory of conjugate functions, or algebraic couples; with a preliminary and elementary essay on algebra as the science of pure time. Trans. Royal. Irish Acad. 17: 293–422; Mathematical Papers 3: 76–96.
  • Hamilton, W. R. (1967). The Mathematical Papers of Sir William Rowan Hamilton, vol. 3. (Halberstam, H., Ingram, R. E., editors). Cambridge: Cambridge Univ. Press.
  • Hurwitz, A. (1898). Über die Composition der quadratischen Formen von beliebig vielen Variablen, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse. 309–316. Mathematische Werke 2: 565–571. DOI: 10.1007/978-3-0348-4160-3_39.
  • Rice, A., Brown, E. (2016). Commutativity and collinearity: A historical case study of the interconnection of mathematical ideas. Part I. BSHM Bull. J. Br. Soc. Hist. Math. 31(1): 1–14. DOI: 10.1080/17498430.2015.1046037.
  • Rice, A., Brown, E. (2021). Why Hamilton couldn’t multiply triples. Coll. Math. J. 52(3): 185–192. DOI: 10.1080/07468342.2021.1897418.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.