SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 16 Issue: 1

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

Ziya Akça(ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ)0000-0001-6379-0546
Pages
—
Publication Date
2024-06-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Its triangle inequality, Schwarz inequality properties and geometrical interpretation in the Plane $\mathbb{R}_{\pi 3}^{2}$ are given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, norm in the Plane $\mathbb{R}_{\pi 3}^{2}$ is produced naturally from a different vector norm.
📊
Key Findings & Data:In this study, norm in the Plane $\mathbb{R}_{\pi 3}^{2}$ is produced naturally from a different vector norm.
💡
Conclusion & Impact:Its triangle inequality, Schwarz inequality properties and geometrical interpretation in the Plane $\mathbb{R}_{\pi 3}^{2}$ are given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Iso- taxicab distance · Non-Euclidean geometry · Norm

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.

🔖

Cite This Article

Akça, Z. (2024). On the Norm in the Plane $\mathbb{R}_{\pi 3}^{2}$. Turkish Journal of Mathematics and Computer Science, Volume: 16 Issue: 1. https://doi.org/10.47000/tjmcs.1366843

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Akça, Z., Nazlı, S., On the trigonometric functions in R2π3, Konuralp Journal of Mathematics, 8(2020), 429–437.
  2. Akça, Z., Nazlı, S., On the versions in the plane R2π3 of some Euclidean theorems, New Trends in Mathematical Sciences, 10(2022), 20–27.
  3. Akça, Z., Bayar, A., Ekmekçi, S., The norm in CC plane geometry, The Pi Mu Epsilon Journal, 6(2007), 321–324.
  4. Akça, Z., Kaya, R., On the norm in higher dimensional taxicab spaces, Hadronic J. Suppl, 19(4)(2004), 491–501.
  5. Bayar, A., Ekmekçi, S., The Chinese Checker Sine and Cosine functions, International Journal of Mathematics and Analysis, 1(3)(2006), 249–259.
  6. Bayar, A., Kaya, R., On isometries of R2πn, Hacettepe Journal of Mathematics and Statistics, 40(5)(2011), 673–679.
  7. 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.
  8. Ekmekçi, S., Bayar, A., Akça, Z., On the plane geometry with generalized absolute value metric, Math. Probl. Eng., 1(0)(2008), 1–8.
  9. Ekici, C., Kocayusufoğlu, İ., Akça, Z., The norm in taxicab geometry, Tr.J.of Mathematics, 22(3)(1998), 295–307.
  10. Kocayusufoglu, İ., Ada, T., On the iso-taxicab trigonometry, Applied Sciences, 8(2006), 101–111.
  11. Kocayusufoglu, İ.,, Trigonometry on iso-taxicab geometry, Mathematical and Computational Applications, 5(3)(2002), 201–212.
  12. Nazlı, S., On the plane geometry R2π3, Doctoral Dissertation, Eskis¸ehir Osmangazi University, (2020), 1–118.
  13. Moore, C., Hatfield, A., Klette, R., Chebolu, S., Warden, E., Trigonometric functions in the p-norm, https://arxiv.org/pdf/2109.14036.pdf.
  14. 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.
  15. Sowell, K. O.,Taxicab geometry-a new slant, Mathematics Magazine, 62(1989), 238–248.
  16. 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.