UNIT DUAL QUATERNIONS AND ARCS

Hesna Kabadayı; Yusuf Yaylı

doi:10.1501/Commua1_0000000661

UNIT DUAL QUATERNIONS AND ARCS

Year 2010, Volume: 59 Issue: 2, 35 - 40, 01.08.2010

Hesna Kabadayı Yusuf Yaylı

https://doi.org/10.1501/Commua1_0000000661

Abstract

References

J. P. Ward, Quaternions and Cayley Numbers, Kluwer Academic Publisher, 1997.
G. R. Veldkamp, On the use of dual numbers, vectors and matrices in instantenaous, spatial kinematics, Mechanism and Machine Theory, 1976 vol. 11, pp. 141-156.
A. F. Beardon, The Geometry of Discrete Groups, Springer-Verlag, New York, Berlin 1983.
H. H. U¼gurlu and H. Gündo¼gan, The cosine hyperbolic and sine hyperbolic rules for dual hyperbolic spherical trigonometry, Mathematical and Computational Applications, Vol. 5, No. 3, 185-190, 2000.
M. Kazaz, H.H. U¼gurlu, A. Özdemir, The cosine rule II for a spherical triangle on the dual unit sphere S2, Math. Comput. Appl. 10 (2005), no.3, 313-320. Current address : Ankara University, Faculty of Sciences, Dept.of Mathematics, Ankara, TURKEY E-mail address : kabadayi@science.ankara.edu.tr, yayli@science.ankara.edu.tr URL: http://communications.science.ankara.edu.tr

UNIT DUAL QUATERNIONS AND ARCS

Year 2010, Volume: 59 Issue: 2, 35 - 40, 01.08.2010

Hesna Kabadayı Yusuf Yaylı

https://doi.org/10.1501/Commua1_0000000661

Abstract

In this paper we obtain sine and cosine rules for dual spherical
triangle on the dual unit sphere S^2 by representing great circle arcs by dual
quatrenions.

Keywords

sine rule, cosine rule, dual spherical triangle, dual quaternions, dualspherical trigonometry

References

J. P. Ward, Quaternions and Cayley Numbers, Kluwer Academic Publisher, 1997.
G. R. Veldkamp, On the use of dual numbers, vectors and matrices in instantenaous, spatial kinematics, Mechanism and Machine Theory, 1976 vol. 11, pp. 141-156.
A. F. Beardon, The Geometry of Discrete Groups, Springer-Verlag, New York, Berlin 1983.
H. H. U¼gurlu and H. Gündo¼gan, The cosine hyperbolic and sine hyperbolic rules for dual hyperbolic spherical trigonometry, Mathematical and Computational Applications, Vol. 5, No. 3, 185-190, 2000.
M. Kazaz, H.H. U¼gurlu, A. Özdemir, The cosine rule II for a spherical triangle on the dual unit sphere S2, Math. Comput. Appl. 10 (2005), no.3, 313-320. Current address : Ankara University, Faculty of Sciences, Dept.of Mathematics, Ankara, TURKEY E-mail address : kabadayi@science.ankara.edu.tr, yayli@science.ankara.edu.tr URL: http://communications.science.ankara.edu.tr

There are 5 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	Hesna Kabadayı This is me Yusuf Yaylı This is me
Publication Date	August 1, 2010
Published in Issue	Year 2010 Volume: 59 Issue: 2

Cite

APA	Kabadayı, H., & Yaylı, Y. (2010). UNIT DUAL QUATERNIONS AND ARCS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 59(2), 35-40. https://doi.org/10.1501/Commua1_0000000661
AMA	Kabadayı H, Yaylı Y. UNIT DUAL QUATERNIONS AND ARCS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2010;59(2):35-40. doi:10.1501/Commua1_0000000661
Chicago	Kabadayı, Hesna, and Yusuf Yaylı. “UNIT DUAL QUATERNIONS AND ARCS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 59, no. 2 (August 2010): 35-40. https://doi.org/10.1501/Commua1_0000000661.
EndNote	Kabadayı H, Yaylı Y (August 1, 2010) UNIT DUAL QUATERNIONS AND ARCS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 59 2 35–40.
IEEE	H. Kabadayı and Y. Yaylı, “UNIT DUAL QUATERNIONS AND ARCS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 59, no. 2, pp. 35–40, 2010, doi: 10.1501/Commua1_0000000661.
ISNAD	Kabadayı, Hesna - Yaylı, Yusuf. “UNIT DUAL QUATERNIONS AND ARCS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 59/2 (August 2010), 35-40. https://doi.org/10.1501/Commua1_0000000661.
JAMA	Kabadayı H, Yaylı Y. UNIT DUAL QUATERNIONS AND ARCS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2010;59:35–40.
MLA	Kabadayı, Hesna and Yusuf Yaylı. “UNIT DUAL QUATERNIONS AND ARCS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 59, no. 2, 2010, pp. 35-40, doi:10.1501/Commua1_0000000661.
Vancouver	Kabadayı H, Yaylı Y. UNIT DUAL QUATERNIONS AND ARCS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2010;59(2):35-40.