A note on hyperbolic quaternions

İşıl Arda Kösal

doi:10.32323/ujma.380645

Research Article

A note on hyperbolic quaternions

Year 2018, Volume: 1 Issue: 3, 155 - 159, 30.09.2018

İşıl Arda Kösal

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

Cited By: 10

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.

Year 2018, Volume: 1 Issue: 3, 155 - 159, 30.09.2018

İşıl Arda Kösal

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

Cited By: 10

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	Research Article
Authors	İşıl Arda Kösal
Submission Date	January 18, 2018
Acceptance Date	February 28, 2018
Publication Date	September 30, 2018
Published in Issue	Year 2018 Volume: 1 Issue: 3

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	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.Arda Kösal İ. A note on hyperbolic quaternions. Univ. J. Math. Appl. [Internet]. 2018 Sept. 1;1(3):155-9. Available from: https://izlik.org/JA54SN98SM