Skip to main content
SpringerLink
Log in

The Fibonacci Octonions

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

In the present paper, we introduce the Fibonacci and Lucas octonions and give the generating function and Binet formulae for these octionions. In addition, we give some identities and properties of them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. Culbert, Cayley-Dickson algebras and loops. Journal of Generalized Lie Theory and Applications Vol. 1 (2007) no. 1, 1–17.

  2. Halici S.: On Fibonacci quaternions. Adv. Appl. Clifford Algebr. 22(2), 321–327 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  3. Horadam A.F.: Complex Fibonacci Numbers and Fibonacci Quaternions. Amer. Math. Montly 70, 289–291 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  4. Horadam A.F.: Quaternion Recurrence Relations. Ulam Quarterly 2, 22–33 (1993)

    MathSciNet  Google Scholar 

  5. Iyer M.R.: A note On Fibonacci Quaternions. The Fib. Quarterly 3, 225–229 (1969)

    MathSciNet  Google Scholar 

  6. Serôdio R.: On octonionic polynomials. Adv. Appl. Clifford Algebras 17(2), 245–258 (2007)

    Article  MATH  Google Scholar 

  7. Tian Y.: Matrix representations of octonions and their applications. Adv. Appl. Clifford Algebras 10(1), 61–90 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science and Arts, Department of Statistics, Kırıkkale University, Kırıkkale, Turkey

    Osman Keçilioğlu & Ilker Akkus

Authors
  1. Osman Keçilioğlu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ilker Akkus
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Osman Keçilioğlu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Keçilioğlu, O., Akkus, I. The Fibonacci Octonions. Adv. Appl. Clifford Algebras 25, 151–158 (2015). https://doi.org/10.1007/s00006-014-0468-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-014-0468-y

Keywords

Search

Navigation