Unit dual split quaternions and arcs of dual hyperbolic spherical triangles

Hesna Kabadayı

doi:10.1501/Commua1_0000000731

Unit dual split quaternions and arcs of dual hyperbolic spherical triangles

Year 2015, Volume: 64 Issue: 2, 35 - 45, 01.08.2015

Hesna Kabadayı

https://doi.org/10.1501/Commua1_0000000731

Abstract

In this paper we obtain the cosine hyperbolic and sine hyperbolic
rules for a dual hyperbolic spherical triangle T(A; ~ B; ~ C~) whose arcs are represented by dual split quaternions.

Keywords

Hyperbolic spherical trigonometry, split quaternion, Lorentzian space

References

S. Altmann, “Rotations, Quaternions, and Double Groups”. Clarendon Press, Oxford 1972.
R. Ablamowicz and G. Sobczyky, “Lectures on Cliğord (Geometric) Algebras and Applica- tions” Birkhäuser, Boston 2004.
C. Mladenova, “Robot problems over con…gurational manifold of vector-parameters and dual vector-parametes” J. Intelligent and Robotic systems 11 (1994) 117-133.
E. Ata, Y. Yayli, “Split Quaternions and Semi-Euclidean Projective Spaces” Caos Solitons Fractals 41 ( 2009), no.4, 1910-1915.
E. Ata, Y. Yayli, “Dual Quaternions and Dual Projective Spaces” Chaos Solitons Fractals 40 ( 2009), no.3, 1255-1263.
J. P. Ward, “Quaternions and Cayley Numbers” Kluwer Academic Publisher, 1997.
G. R. Veldkamp, “On the Use of Dual Numbers, Vectors and Matrices in instantaneous, 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.
A. Özdemir, M. Kazaz, “Hyperbolic Sine and Cosine Rules for Geodesic Triangles on The Hyperbolic Unit Sphere H2”, Mathematical and Computational Applications, Vol. 10, No.2, 209, 2005.
”, Mathematical and Computational Applications, Vol. 10, No.2, H. H. U¼gurlu, A. Çalı¸skan, “The Study Mapping for Directed Space-like and Time-like lines in Minkowski 3-Space R1”, Mathematical and Computational Applications, Vol. 1, No. 2 pp.142-148,1996.
John G. Ratcliğe, “ Foundation of hyperbolic Manifolds (Graduate Text in Mathematics)” Sipringer-Verlag Newyork, Berlin 1991
L. Kula and Y. Yayli, “ Dual Split Quaternions and Screw Motions in Minkowski 3-Space” Iranian Journal of Sciences & Technology, Transaction A. Vol. 30, no. 3, 245-258. Address : Ankara University, Science Faculty, Mathematics Department, Tando¼gan, Ankara

Year 2015, Volume: 64 Issue: 2, 35 - 45, 01.08.2015

Hesna Kabadayı

https://doi.org/10.1501/Commua1_0000000731

Abstract

References

S. Altmann, “Rotations, Quaternions, and Double Groups”. Clarendon Press, Oxford 1972.
R. Ablamowicz and G. Sobczyky, “Lectures on Cliğord (Geometric) Algebras and Applica- tions” Birkhäuser, Boston 2004.
C. Mladenova, “Robot problems over con…gurational manifold of vector-parameters and dual vector-parametes” J. Intelligent and Robotic systems 11 (1994) 117-133.
E. Ata, Y. Yayli, “Split Quaternions and Semi-Euclidean Projective Spaces” Caos Solitons Fractals 41 ( 2009), no.4, 1910-1915.
E. Ata, Y. Yayli, “Dual Quaternions and Dual Projective Spaces” Chaos Solitons Fractals 40 ( 2009), no.3, 1255-1263.
J. P. Ward, “Quaternions and Cayley Numbers” Kluwer Academic Publisher, 1997.
G. R. Veldkamp, “On the Use of Dual Numbers, Vectors and Matrices in instantaneous, 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.
A. Özdemir, M. Kazaz, “Hyperbolic Sine and Cosine Rules for Geodesic Triangles on The Hyperbolic Unit Sphere H2”, Mathematical and Computational Applications, Vol. 10, No.2, 209, 2005.
”, Mathematical and Computational Applications, Vol. 10, No.2, H. H. U¼gurlu, A. Çalı¸skan, “The Study Mapping for Directed Space-like and Time-like lines in Minkowski 3-Space R1”, Mathematical and Computational Applications, Vol. 1, No. 2 pp.142-148,1996.
John G. Ratcliğe, “ Foundation of hyperbolic Manifolds (Graduate Text in Mathematics)” Sipringer-Verlag Newyork, Berlin 1991
L. Kula and Y. Yayli, “ Dual Split Quaternions and Screw Motions in Minkowski 3-Space” Iranian Journal of Sciences & Technology, Transaction A. Vol. 30, no. 3, 245-258. Address : Ankara University, Science Faculty, Mathematics Department, Tando¼gan, Ankara

There are 14 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	Hesna Kabadayı This is me
Publication Date	August 1, 2015
Published in Issue	Year 2015 Volume: 64 Issue: 2

Cite

APA	Kabadayı, H. (2015). Unit dual split quaternions and arcs of dual hyperbolic spherical triangles. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 64(2), 35-45. https://doi.org/10.1501/Commua1_0000000731
AMA	Kabadayı H. Unit dual split quaternions and arcs of dual hyperbolic spherical triangles. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2015;64(2):35-45. doi:10.1501/Commua1_0000000731
Chicago	Kabadayı, Hesna. “Unit Dual Split Quaternions and Arcs of Dual Hyperbolic Spherical Triangles”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64, no. 2 (August 2015): 35-45. https://doi.org/10.1501/Commua1_0000000731.
EndNote	Kabadayı H (August 1, 2015) Unit dual split quaternions and arcs of dual hyperbolic spherical triangles. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64 2 35–45.
IEEE	H. Kabadayı, “Unit dual split quaternions and arcs of dual hyperbolic spherical triangles”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 64, no. 2, pp. 35–45, 2015, doi: 10.1501/Commua1_0000000731.
ISNAD	Kabadayı, Hesna. “Unit Dual Split Quaternions and Arcs of Dual Hyperbolic Spherical Triangles”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64/2 (August 2015), 35-45. https://doi.org/10.1501/Commua1_0000000731.
JAMA	Kabadayı H. Unit dual split quaternions and arcs of dual hyperbolic spherical triangles. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2015;64:35–45.
MLA	Kabadayı, Hesna. “Unit Dual Split Quaternions and Arcs of Dual Hyperbolic Spherical Triangles”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 64, no. 2, 2015, pp. 35-45, doi:10.1501/Commua1_0000000731.
Vancouver	Kabadayı H. Unit dual split quaternions and arcs of dual hyperbolic spherical triangles. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2015;64(2):35-4.