On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$

Selahattin Nazlı; Ziya Akça

Research Article

Year 2020, Volume: 8 Issue: 2, 429 - 437, 27.10.2020

Selahattin Nazlı Ziya Akça

Abstract

References

[1] A. Bayar, R. Kaya, On Isometries of R2 pn, Hacettepe Journal of Mathematics and Statistics, Vol. 40 (5) (2011), 673-679.
[2] A. Bayar, S. Ekmekci, M. Ozcan, On Trigonometric Functions and Cosine and Sine Rules in Taxicab Plane, International Electronic Journal of Geometry, Vol. 2 , No. 1 (2009),17–24.
[3] A. Bayar, S. Ekmekci, On The Chinese Checker Sine and Cosine Functions, International Journal of Mathematics and Analysis, Vol. 1, No. 3 (2006), 249–259.
[4] M. Ozcan, S. Ekmekci, A. Bayar, A Note on The Variation of The Taxicab Lengths Under Rotations, Pi Mu Epsilon Journal, Vol. 11, No, 7 (2002), 381-384.
[5] I. Kocayusufoglu, Trigonometry on Iso-taxicab Geometry, Mathematical and Computational Applications, Vol. 5, No. 3 (2002),.201-212.
[6] I. Kocayusufoglu, T. Ada, On The Iso-taxicab Trigonometry, Applied Sciences, Vol. 8 (2006), 101-111.
[7] K. O. Sowell, Taxicab Geometry-a New Slant, Mathematics Magazine, 62, (1989), 238-248.
[8] K. Thompson, T. Dray, Taxicab Angles and Trigonometry, Pi Mu Epsilon J., Vol. 11(2000), 87-97.
[9] S. Ekmekci, Z. Akca, A. Altintas, On Trigonometric Functions and Norm in The Generalized Taxicab Metric, Math. Sciences and Applications E-Notes, Vol. 3, No. 2 (2015), 27–33.
[10] S. Ekmekci, A. Bayar, Z. Akca, On The Plane Geometry with Generalized Absolute Value Metric, Math. Probl. Eng., Vol. 1, No. 0 (2008), 1–8.
[11] W. E. Story, On The Non-Euclidean Trigonometry, American Journal of Mathematics, Vol. 4, No. 1 (1881), 332-335.
[12] Z. Akca, R. Kaya, On The Taxicab Trigonometry, J. of Inst. Math. Comput. Sci. Math. Ser., Vol. 10, No. 3 (1997), 151–159.

On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$

Year 2020, Volume: 8 Issue: 2, 429 - 437, 27.10.2020

Selahattin Nazlı Ziya Akça

Abstract

In this paper, we give trigonometric functions by using reference angle in the plane $ \mathbb{R}_{\pi 3}^{2}$ associated with the induced metric $d_{\pi 3}$ that\ is a member of the family of $d_{\pi n}-$distances. Also we investigate the change of the length a line segment under the rotations in the plane $\mathbb{R} _{\pi 3}^{2}$.

Keywords

non-Euclidean geometry, \textbf{\ }$d_{\pi 3}-$distances, trigonometric functions in the plane $\mathbb{R} _{\pi 3}^{2}$

References

[1] A. Bayar, R. Kaya, On Isometries of R2 pn, Hacettepe Journal of Mathematics and Statistics, Vol. 40 (5) (2011), 673-679.
[2] A. Bayar, S. Ekmekci, M. Ozcan, On Trigonometric Functions and Cosine and Sine Rules in Taxicab Plane, International Electronic Journal of Geometry, Vol. 2 , No. 1 (2009),17–24.
[3] A. Bayar, S. Ekmekci, On The Chinese Checker Sine and Cosine Functions, International Journal of Mathematics and Analysis, Vol. 1, No. 3 (2006), 249–259.
[4] M. Ozcan, S. Ekmekci, A. Bayar, A Note on The Variation of The Taxicab Lengths Under Rotations, Pi Mu Epsilon Journal, Vol. 11, No, 7 (2002), 381-384.
[5] I. Kocayusufoglu, Trigonometry on Iso-taxicab Geometry, Mathematical and Computational Applications, Vol. 5, No. 3 (2002),.201-212.
[6] I. Kocayusufoglu, T. Ada, On The Iso-taxicab Trigonometry, Applied Sciences, Vol. 8 (2006), 101-111.
[7] K. O. Sowell, Taxicab Geometry-a New Slant, Mathematics Magazine, 62, (1989), 238-248.
[8] K. Thompson, T. Dray, Taxicab Angles and Trigonometry, Pi Mu Epsilon J., Vol. 11(2000), 87-97.
[9] S. Ekmekci, Z. Akca, A. Altintas, On Trigonometric Functions and Norm in The Generalized Taxicab Metric, Math. Sciences and Applications E-Notes, Vol. 3, No. 2 (2015), 27–33.
[10] S. Ekmekci, A. Bayar, Z. Akca, On The Plane Geometry with Generalized Absolute Value Metric, Math. Probl. Eng., Vol. 1, No. 0 (2008), 1–8.
[11] W. E. Story, On The Non-Euclidean Trigonometry, American Journal of Mathematics, Vol. 4, No. 1 (1881), 332-335.
[12] Z. Akca, R. Kaya, On The Taxicab Trigonometry, J. of Inst. Math. Comput. Sci. Math. Ser., Vol. 10, No. 3 (1997), 151–159.

There are 12 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Articles
Authors	Selahattin Nazlı 0000-0002-1118-6125 Ziya Akça
Publication Date	October 27, 2020
Submission Date	November 7, 2019
Acceptance Date	October 30, 2020
Published in Issue	Year 2020 Volume: 8 Issue: 2

Cite

APA	Nazlı, S., & Akça, Z. (2020). On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$. Konuralp Journal of Mathematics, 8(2), 429-437.
AMA	Nazlı S, Akça Z. On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$. Konuralp J. Math. October 2020;8(2):429-437.
Chicago	Nazlı, Selahattin, and Ziya Akça. “On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$”. Konuralp Journal of Mathematics 8, no. 2 (October 2020): 429-37.
EndNote	Nazlı S, Akça Z (October 1, 2020) On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$. Konuralp Journal of Mathematics 8 2 429–437.
IEEE	S. Nazlı and Z. Akça, “On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$”, Konuralp J. Math., vol. 8, no. 2, pp. 429–437, 2020.
ISNAD	Nazlı, Selahattin - Akça, Ziya. “On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$”. Konuralp Journal of Mathematics 8/2 (October 2020), 429-437.
JAMA	Nazlı S, Akça Z. On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$. Konuralp J. Math. 2020;8:429–437.
MLA	Nazlı, Selahattin and Ziya Akça. “On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$”. Konuralp Journal of Mathematics, vol. 8, no. 2, 2020, pp. 429-37.
Vancouver	Nazlı S, Akça Z. On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$. Konuralp J. Math. 2020;8(2):429-37.

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