A note on hyperbolic quaternions

İşıl Arda Kösal

doi:10.32323/ujma.380645

EN

A note on hyperbolic quaternions

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.

Keywords

Hyperbolic quaternion,Euler’s formula,De Moivre’s formula

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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

İşıl Arda Kösal ^*
Türkiye

Publication Date

September 30, 2018

Submission Date

January 18, 2018

Acceptance Date

February 28, 2018

Published in Issue

Year 2018 Volume: 1 Number: 3

DOI

https://doi.org/10.32323/ujma.380645

IZ

https://izlik.org/JA54SN98SM

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

1.Arda Kösal İ. A note on hyperbolic quaternions. Univ. J. Math. Appl. 2018;1(3):155-159. doi:10.32323/ujma.380645

Chicago

Arda Kösal, İşıl. 2018. “A Note on Hyperbolic Quaternions”. Universal Journal of Mathematics and Applications 1 (3): 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

[1]İ. Arda Kösal, “A note on hyperbolic quaternions”, Univ. J. Math. Appl., vol. 1, no. 3, pp. 155–159, Sept. 2018, doi: 10.32323/ujma.380645.

ISNAD

Arda Kösal, İşıl. “A Note on Hyperbolic Quaternions”. Universal Journal of Mathematics and Applications 1/3 (September 1, 2018): 155-159. https://doi.org/10.32323/ujma.380645.

JAMA

1.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, Sept. 2018, pp. 155-9, doi:10.32323/ujma.380645.

Vancouver

1.İşıl Arda Kösal. A note on hyperbolic quaternions. Univ. J. Math. Appl. 2018 Sep. 1;1(3):155-9. doi:10.32323/ujma.380645