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On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$

Year 2024, Volume: 16 Issue: 1, 137 - 142, 30.06.2024
https://doi.org/10.47000/tjmcs.1366843

Abstract

In this study, norm in the Plane $\mathbb{R}_{\pi 3}^{2}$ is produced naturally from a different vector norm. Its triangle inequality, Schwarz inequality properties and geometrical interpretation in the Plane $\mathbb{R}_{\pi 3}^{2}$ are given.

Thanks

Hakem Önerisi Prof. Dr. Mine Turan DPÜ Matematik Bölümü (mine.turan@dpu.edu.tr Prof. Dr. Atilla Akpınar Uludağ Üni. Matematik Bölümü (aakpinar@uludag.edu.tr) Prof. Dr. Nedim Değirmenci Eskişehir Teknik Ün. Matematik Bölümü (ndegirmenci@eskisehir.edu.tr)

References

  • Akça, Z., Nazlı, S., On the trigonometric functions in R2π3, Konuralp Journal of Mathematics, 8(2020), 429–437.
  • Akça, Z., Nazlı, S., On the versions in the plane R2π3 of some Euclidean theorems, New Trends in Mathematical Sciences, 10(2022), 20–27.
  • Akça, Z., Bayar, A., Ekmekçi, S., The norm in CC plane geometry, The Pi Mu Epsilon Journal, 6(2007), 321–324.
  • Akça, Z., Kaya, R., On the norm in higher dimensional taxicab spaces, Hadronic J. Suppl, 19(4)(2004), 491–501.
  • Bayar, A., Ekmekçi, S., The Chinese Checker Sine and Cosine functions, International Journal of Mathematics and Analysis, 1(3)(2006), 249–259.
  • Bayar, A., Kaya, R., On isometries of R2πn, Hacettepe Journal of Mathematics and Statistics, 40(5)(2011), 673–679.
  • Ekmekçi, S., Akça, Z., Altıntas¸, A., On trigonometric functions and norm in the generalized taxicab metric, Mathematical Sciences And Applications E-Notes, 3(2)(2015), 27–33.
  • Ekmekçi, S., Bayar, A., Akça, Z., On the plane geometry with generalized absolute value metric, Math. Probl. Eng., 1(0)(2008), 1–8.
  • Ekici, C., Kocayusufoğlu, İ., Akça, Z., The norm in taxicab geometry, Tr.J.of Mathematics, 22(3)(1998), 295–307.
  • Kocayusufoglu, İ., Ada, T., On the iso-taxicab trigonometry, Applied Sciences, 8(2006), 101–111.
  • Kocayusufoglu, İ.,, Trigonometry on iso-taxicab geometry, Mathematical and Computational Applications, 5(3)(2002), 201–212.
  • Nazlı, S., On the plane geometry R2π3, Doctoral Dissertation, Eskis¸ehir Osmangazi University, (2020), 1–118.
  • Moore, C., Hatfield, A., Klette, R., Chebolu, S., Warden, E., Trigonometric functions in the p-norm, https://arxiv.org/pdf/2109.14036.pdf.
  • Özcan, M., Ekmekçi, S., Bayar, A., A note on the variation of the taxicab lengths under rotations, The Pi Mu Epsilon Journal, 11(7)(2002), 381–384.
  • Sowell, K. O.,Taxicab geometry-a new slant, Mathematics Magazine, 62(1989), 238–248.
  • Turan, M., Özcan, M., General equation for Chinese Checker conics and focus-directrix Chinese Checker conics, International Journal of Pure and Applied Mathematics, 30(3)(2006), 393–401.
Year 2024, Volume: 16 Issue: 1, 137 - 142, 30.06.2024
https://doi.org/10.47000/tjmcs.1366843

Abstract

References

  • Akça, Z., Nazlı, S., On the trigonometric functions in R2π3, Konuralp Journal of Mathematics, 8(2020), 429–437.
  • Akça, Z., Nazlı, S., On the versions in the plane R2π3 of some Euclidean theorems, New Trends in Mathematical Sciences, 10(2022), 20–27.
  • Akça, Z., Bayar, A., Ekmekçi, S., The norm in CC plane geometry, The Pi Mu Epsilon Journal, 6(2007), 321–324.
  • Akça, Z., Kaya, R., On the norm in higher dimensional taxicab spaces, Hadronic J. Suppl, 19(4)(2004), 491–501.
  • Bayar, A., Ekmekçi, S., The Chinese Checker Sine and Cosine functions, International Journal of Mathematics and Analysis, 1(3)(2006), 249–259.
  • Bayar, A., Kaya, R., On isometries of R2πn, Hacettepe Journal of Mathematics and Statistics, 40(5)(2011), 673–679.
  • Ekmekçi, S., Akça, Z., Altıntas¸, A., On trigonometric functions and norm in the generalized taxicab metric, Mathematical Sciences And Applications E-Notes, 3(2)(2015), 27–33.
  • Ekmekçi, S., Bayar, A., Akça, Z., On the plane geometry with generalized absolute value metric, Math. Probl. Eng., 1(0)(2008), 1–8.
  • Ekici, C., Kocayusufoğlu, İ., Akça, Z., The norm in taxicab geometry, Tr.J.of Mathematics, 22(3)(1998), 295–307.
  • Kocayusufoglu, İ., Ada, T., On the iso-taxicab trigonometry, Applied Sciences, 8(2006), 101–111.
  • Kocayusufoglu, İ.,, Trigonometry on iso-taxicab geometry, Mathematical and Computational Applications, 5(3)(2002), 201–212.
  • Nazlı, S., On the plane geometry R2π3, Doctoral Dissertation, Eskis¸ehir Osmangazi University, (2020), 1–118.
  • Moore, C., Hatfield, A., Klette, R., Chebolu, S., Warden, E., Trigonometric functions in the p-norm, https://arxiv.org/pdf/2109.14036.pdf.
  • Özcan, M., Ekmekçi, S., Bayar, A., A note on the variation of the taxicab lengths under rotations, The Pi Mu Epsilon Journal, 11(7)(2002), 381–384.
  • Sowell, K. O.,Taxicab geometry-a new slant, Mathematics Magazine, 62(1989), 238–248.
  • Turan, M., Özcan, M., General equation for Chinese Checker conics and focus-directrix Chinese Checker conics, International Journal of Pure and Applied Mathematics, 30(3)(2006), 393–401.
There are 16 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Articles
Authors

Ziya Akça 0000-0001-6379-0546

Publication Date June 30, 2024
Published in Issue Year 2024 Volume: 16 Issue: 1

Cite

APA Akça, Z. (2024). On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$. Turkish Journal of Mathematics and Computer Science, 16(1), 137-142. https://doi.org/10.47000/tjmcs.1366843
AMA Akça Z. On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$. TJMCS. June 2024;16(1):137-142. doi:10.47000/tjmcs.1366843
Chicago Akça, Ziya. “On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$”. Turkish Journal of Mathematics and Computer Science 16, no. 1 (June 2024): 137-42. https://doi.org/10.47000/tjmcs.1366843.
EndNote Akça Z (June 1, 2024) On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$. Turkish Journal of Mathematics and Computer Science 16 1 137–142.
IEEE Z. Akça, “On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$”, TJMCS, vol. 16, no. 1, pp. 137–142, 2024, doi: 10.47000/tjmcs.1366843.
ISNAD Akça, Ziya. “On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$”. Turkish Journal of Mathematics and Computer Science 16/1 (June 2024), 137-142. https://doi.org/10.47000/tjmcs.1366843.
JAMA Akça Z. On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$. TJMCS. 2024;16:137–142.
MLA Akça, Ziya. “On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 1, 2024, pp. 137-42, doi:10.47000/tjmcs.1366843.
Vancouver Akça Z. On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$. TJMCS. 2024;16(1):137-42.