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Year 2022, Volume: 4 Issue: 2, 35 - 40, 30.12.2022

Ziya Akça Selahattin Nazlı

Abstract

Keywords

The plane $\mathbb{R}_{\pi 3}^{2}$ Carnot's theorem Pythagorean theorem

References

  • Sowell, K. O. (1989). Taxicab geometry—a new slant. Mathematics Magazine, 62(4), 238-248.
  • Kocayusufoğlu, I., & Ada, T. (2006). On the iso-taxicab trigonometry. Applied Sciences, 8, 101-111.
  • Kocayusufoğlu, İ. (2000). Trigonometry on iso-taxicab geometry. Mathematical and Computational Applications, 5(3), 201-212.
  • Bayar, A., & Kaya, R. (2011). On isometries of $\mathbb{R}_{\pi n}^{2}$. Hacettepe Journal of Mathematics and Statistics, 40(5), 673-679.
  • Bayar, A., Ekmekçi, S., & Özcan, M. (2009). On trigonometric functions and cosine and sine rules in taxicab plane. International Electronic Journal of Geometry, 2(1), 17-24.
  • Özcan, M., Ekmekçi, S., & Bayar, A. (2002). A note on the variation of the taxicab lengths under rotations. Pi Mu Epsilon Journal, 11(7), 381-384.
  • Akça, Z., & Nazlı, S. (2022). On the versions in the plane $\mathbb{R}% _{\pi 3}^{2}$ of some Euclidean theorems. New Trends in Mathematical Sciences, 10(1), 20-27.
  • Akça, Z., & Nazlı, S. (2022). The shortest distance of a point to the line in the plane $\mathbb{R}% _{\pi 3}^{2}$. New Trends in Mathematical Sciences, 10(4), 128-132.

On Carnot's Theorem in the Plane $\mathbb{R}_{\pi 3}^{2}$

Year 2022, Volume: 4 Issue: 2, 35 - 40, 30.12.2022

Ziya Akça Selahattin Nazlı

Abstract

In this paper, we consider the relationship between iso-taxicab distance and Euclidean distance and
give Carnot's theorem in the plane $\mathbb{R}_{\pi 3}^{2}$, the theorem can also be thought of as a generalization of the Pythagorean theorem.

Keywords

The plane $\mathbb{R}_{\pi 3}^{2}$ Carnot's theorem Pythagorean theorem

References

  • Sowell, K. O. (1989). Taxicab geometry—a new slant. Mathematics Magazine, 62(4), 238-248.
  • Kocayusufoğlu, I., & Ada, T. (2006). On the iso-taxicab trigonometry. Applied Sciences, 8, 101-111.
  • Kocayusufoğlu, İ. (2000). Trigonometry on iso-taxicab geometry. Mathematical and Computational Applications, 5(3), 201-212.
  • Bayar, A., & Kaya, R. (2011). On isometries of $\mathbb{R}_{\pi n}^{2}$. Hacettepe Journal of Mathematics and Statistics, 40(5), 673-679.
  • Bayar, A., Ekmekçi, S., & Özcan, M. (2009). On trigonometric functions and cosine and sine rules in taxicab plane. International Electronic Journal of Geometry, 2(1), 17-24.
  • Özcan, M., Ekmekçi, S., & Bayar, A. (2002). A note on the variation of the taxicab lengths under rotations. Pi Mu Epsilon Journal, 11(7), 381-384.
  • Akça, Z., & Nazlı, S. (2022). On the versions in the plane $\mathbb{R}% _{\pi 3}^{2}$ of some Euclidean theorems. New Trends in Mathematical Sciences, 10(1), 20-27.
  • Akça, Z., & Nazlı, S. (2022). The shortest distance of a point to the line in the plane $\mathbb{R}% _{\pi 3}^{2}$. New Trends in Mathematical Sciences, 10(4), 128-132.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ziya Akça 0000-0001-6379-0546

Selahattin Nazlı 0000-0002-1118-6125

Early Pub Date December 28, 2022
Publication Date December 30, 2022
Published in Issue Year 2022 Volume: 4 Issue: 2

Cite

APA Akça, Z., & Nazlı, S. (2022). On Carnot’s Theorem in the Plane $\mathbb{R}_{\pi 3}^{2}$. Hagia Sophia Journal of Geometry, 4(2), 35-40.
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