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Dergiler / Hagia Sophia Journal of Geometry / 2024 / Cilt: 6 Sayı: 2

On the Generalized Taxicab Apollonian Sets

Süheyla Ekmekçi(ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ)0000-0003-2820-2096
Sayfa
1–12
Yayın Tarihi
2024-12-31
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

By examining various configurations based on the positions of given points, the generalized taxicab Apollonian sets are systematically classified and characterized.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this work, the concept of Apollonian set is explored in the framework of the generalized taxicab plane and named as the generalized taxicab Apollonian sets.
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Temel Bulgular & Veri:It is determined that these sets do not conform to the properties of generalized taxicab circles; rather, the closed simple rectilinear figures are composed of line segments.
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Sonuç & Katkı:By examining various configurations based on the positions of given points, the generalized taxicab Apollonian sets are systematically classified and characterized.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Generalized taxicab distance · generalized taxicab plane · Apollonian sets

Abstract

In this work, the concept of Apollonian set is explored in the framework of the generalized taxicab plane and named as the generalized taxicab Apollonian sets. It is determined that these sets do not conform to the properties of generalized taxicab circles; rather, the closed simple rectilinear figures are composed of line segments. By examining various configurations based on the positions of given points, the generalized taxicab Apollonian sets are systematically classified and characterized.

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Bu Makaleye Atıf Yap

Ekmekçi, S. (2024). On the Generalized Taxicab Apollonian Sets. Hagia Sophia Journal of Geometry, Cilt: 6 Sayı: 2, 1–12. https://ajindex.com/articles/1490426

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Kaynakça (17)

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  11. Altıntaş, A. (2009). The application of some geometric problems on Euclidean plane using generalized taxi metric (Manhattan metric) (in Turkish). Master’s Thesis, Eskişehir Osmangazi University, Eskişehir.
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  13. Ekmekçi, S., Bayar, A., & Altıntaş, A. (2015). On the group of isometries of the generalized taxicab plane. International Journal of Contemporary Mathematical Sciences, 10(4), 159–166.
  14. Ekmekçi, S., Akça, Z., & Altıntaş, A. (2015). On trigonometric functions and norm in the generalized taxicab plane. Mathematical Sciences And Applications E-Notes, 3(2), 27–33.
  15. Bahuaud, E., Crawford, S., Fish, A., Helliwell, D., Miller, A., Nungaray, F., Shergill, S., Tiffay, J., & Velez, N. (2020). Apollonian sets in taxicab geometry. Rocky Mountain Journal of Mathematics, 50(l), 25–39.
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  17. Akça, Z., & Kaya, R. (1997). On taxicab trigonometry. Jour. of Inst. of Math & Comp. Sci. (Math. Ser.), 10(3), 151–159.