Elliptic Inversions in Taxicab Geometry

Year 2024, Volume: 24 Issue: 2, 266 - 272, 29.04.2024

Zeynep Can

https://doi.org/10.35414/akufemubid.1353161

Abstract

The goal of this research is to introduce inversion with respect to an ellipse which is a generalization of the classical circular inversion in taxicab plane and to investigate general properties and basic concepts of this transformation in taxicab geometry. The cross ratio is preserved under the elliptic inversion in taxicab plane though this transformation is not an isometry. Thus some properties such as cross ratio and harmonic conjugates of the elliptic inversions in R_T^2 are also studied.

Keywords

Inversion, elliptic inversion, taxicab metric, cross ratio, harmonic conjugates

Taksi Geometride Eliptik İnversiyonlar

Abstract

Bu çalışmanın amacı klasik çembersel inversiyonların bir genelleştirmesi olan elipse göre inversiyonları taksi düzleminde çalışmak ve bu dönüşümün genel özelliklerini ve temel yapılarını taksi geometride araştırmaktır. Bu dönüşüm bir izometri olmasa da çapraz oran taksi düzleminde eliptik inversiyonlar altında korunur. Bu yüzden bu araştırmada eliptik inversiyonların çapraz oran ve harmonik eşlenik gibi bazı özellikleri üzerine de R_T^2 de çalışılmıştır.

Keywords

inversiyon, eliptik inversiyon, taksi metriği, çapraz oran, harmonik eşlenik

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