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A note on hyperbolic quaternions

Year 2018, , 155 - 159, 30.09.2018
https://doi.org/10.32323/ujma.380645

Abstract

In this work, we introduce hyperbolic quaternions and their algebraic properties. Moreover, we express Euler's and De Moivre's formulas for hyperbolic quaternions.

References

  • [1] Hamilton, W.R., Elements of Quaternions, London Longmans Green, 1866.
  • [2] Cho, E., De Moivre’s Formula for Quaternions, Appl. Math. Lett. 6 (1998), 33-35.
  • [3] Özdemir, M., The Roots of a Split Quaternion, Appl. Math. Lett. 22 (2009), 258-263.
  • [4] MacFarlane, A., Hyperbolic Quaternions, Proc. Roy. Soc. Edinburgh, 1900, pp. 169-181.
  • [5] Ward, JP., Quaternions and Cayley Numbers Algebra and Applications, Boston(SPA), Kluwer Academic, 1997.
  • [6] Demir, S., Tanışlı, M., Candemir, N., Hyperbolic Quaternions Formulation of Electromacnetism, Adv. Appl. Clifford Algebras, 20 (2010), 547-563.
  • [7] Niven I., The Roots of a Quaternion, Amer. Math. Monthly 449 (6) (1942) 386-388.
  • [8] Brand L., The Roots of a Quaternion, Amer. Math. Monthly 49 (8) (1942) 519–520.
Year 2018, , 155 - 159, 30.09.2018
https://doi.org/10.32323/ujma.380645

Abstract

References

  • [1] Hamilton, W.R., Elements of Quaternions, London Longmans Green, 1866.
  • [2] Cho, E., De Moivre’s Formula for Quaternions, Appl. Math. Lett. 6 (1998), 33-35.
  • [3] Özdemir, M., The Roots of a Split Quaternion, Appl. Math. Lett. 22 (2009), 258-263.
  • [4] MacFarlane, A., Hyperbolic Quaternions, Proc. Roy. Soc. Edinburgh, 1900, pp. 169-181.
  • [5] Ward, JP., Quaternions and Cayley Numbers Algebra and Applications, Boston(SPA), Kluwer Academic, 1997.
  • [6] Demir, S., Tanışlı, M., Candemir, N., Hyperbolic Quaternions Formulation of Electromacnetism, Adv. Appl. Clifford Algebras, 20 (2010), 547-563.
  • [7] Niven I., The Roots of a Quaternion, Amer. Math. Monthly 449 (6) (1942) 386-388.
  • [8] Brand L., The Roots of a Quaternion, Amer. Math. Monthly 49 (8) (1942) 519–520.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

İşıl Arda Kösal

Publication Date September 30, 2018
Submission Date January 18, 2018
Acceptance Date February 28, 2018
Published in Issue Year 2018

Cite

APA Arda Kösal, İ. (2018). A note on hyperbolic quaternions. Universal Journal of Mathematics and Applications, 1(3), 155-159. https://doi.org/10.32323/ujma.380645
AMA Arda Kösal İ. A note on hyperbolic quaternions. Univ. J. Math. Appl. September 2018;1(3):155-159. doi:10.32323/ujma.380645
Chicago Arda Kösal, İşıl. “A Note on Hyperbolic Quaternions”. Universal Journal of Mathematics and Applications 1, no. 3 (September 2018): 155-59. https://doi.org/10.32323/ujma.380645.
EndNote Arda Kösal İ (September 1, 2018) A note on hyperbolic quaternions. Universal Journal of Mathematics and Applications 1 3 155–159.
IEEE İ. Arda Kösal, “A note on hyperbolic quaternions”, Univ. J. Math. Appl., vol. 1, no. 3, pp. 155–159, 2018, doi: 10.32323/ujma.380645.
ISNAD Arda Kösal, İşıl. “A Note on Hyperbolic Quaternions”. Universal Journal of Mathematics and Applications 1/3 (September 2018), 155-159. https://doi.org/10.32323/ujma.380645.
JAMA Arda Kösal İ. A note on hyperbolic quaternions. Univ. J. Math. Appl. 2018;1:155–159.
MLA Arda Kösal, İşıl. “A Note on Hyperbolic Quaternions”. Universal Journal of Mathematics and Applications, vol. 1, no. 3, 2018, pp. 155-9, doi:10.32323/ujma.380645.
Vancouver Arda Kösal İ. A note on hyperbolic quaternions. Univ. J. Math. Appl. 2018;1(3):155-9.

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