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Dergiler / Hagia Sophia Journal of Geometry / 2023 / Cilt: 5 Sayı: 1

On the Thales Theorem in the Iso-Taxicab Plane

Ziya AKÇA
Selahattin NAZLI
Sayfa
15–20
Yayın Tarihi
2023-06-26
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper, we study the Iso-taxicab analogues of the intercept theorem, also known as Thales's theorem is an important theorem in elementary geometry.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:There are non-Euclidean geometries that are both accessible in a very concrete form and close to Euclidean geometry in their basic structure.
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Temel Bulgular & Veri:There are non-Euclidean geometries that are both accessible in a very concrete form and close to Euclidean geometry in their basic structure.
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Sonuç & Katkı:In this paper, we study the Iso-taxicab analogues of the intercept theorem, also known as Thales's theorem is an important theorem in elementary geometry.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:The plane $\mathbb{R}_{\pi 3}^{2}$ · Thales theorem · non-Euclidean geometry

Abstract

There are non-Euclidean geometries that are both accessible in a very concrete form and close to Euclidean geometry in their basic structure. In this paper, we study the Iso-taxicab analogues of the intercept theorem, also known as Thales's theorem is an important theorem in elementary geometry.

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Bu Makaleye Atıf Yap

AKÇA, Z., NAZLI, S. (2023). On the Thales Theorem in the Iso-Taxicab Plane. Hagia Sophia Journal of Geometry, Cilt: 5 Sayı: 1, 15–20. https://ajindex.com/articles/946104

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Kaynakça (13)

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  2. Bayar, A., Ekmekçi, S., & Z. Akça (2008). On the plane geometry with generalized absolute value metric. Mathematical problems in Engineering, 1-8.
  3. 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.
  4. Bayar, A., Ekmekçi, S., & Öztürk, ̇I. (2015). On complex numbers and Taxicab plane. Mathematical Sciences and Applications E-Notes, 3(1), 58-64.
  5. Çolakoğlu, H.B., & Kaya, R. (2008). Taxicab versions of the Pythagorean theorem. Pi Mu Epsilon Journal, 12(9), 535-539.
  6. Ekmekçi, S., Akça, Z., & Altıntaş K. (2015). On trigonometric functions and norm in the generalized taxicab metric. Mathematical Sciences And Applications E-Notes, 3(2), 27-33.
  7. 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.
  8. Sowell, K. O. (1989). Taxicab geometry—a new slant. Mathematics Magazine, 62(4), 238-248.
  9. Kocayusufoğlu, İ. (2000). Trigonometry on Iso-taxicab geometry. Mathematical and Computational Applications, 5(3), 201-212.
  10. Bayar, A., & Kaya, R. (2011). On isometries of $\mathbb{R}_{\pi n}^{2}.$. Hacettepe Journal of Mathematics and Statistics, 40(5), 673-679.
  11. Akça, Z., & Nazlı, S. (2022). On the versions in the plane $\mathbb{R}_{\pi3}^{2}$ of some Euclidean theorems. New Trends in Mathematical Sciences, 10(1), 20-27.
  12. Nazlı, S., & Akça, Z. (2020). On the trigonometric functions in $\mathbb{R}_{\pi 3}^{2}$. Konuralp Journal of Mathematics, 8(2), 429-437.
  13. Akça, Z., & Nazlı, S. (2022). On 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.