On Menelaus’ and Ceva’s theorems in Nil geometry

Jenő Szirmai

doi:10.2478/ausm-2023-0008

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On Menelaus’ and Ceva’s theorems in Nil geometry

Acta Universitatis Sapientiae, Mathematica

Volume 15 (2023): Issue 1 (November 2023)

By: Jenő Szirmai

Open Access

|Nov 2023

Abstract

In this paper we deal with Nil geometry, which is one of the homogeneous Thurston 3-geometries. We define the “surface of a geodesic triangle” using generalized Apollonius surfaces. Moreover, we show that the “lines” on the surface of a geodesic triangle can be defined by the famous Menelaus’ condition and prove that Ceva’s theorem for geodesic trianglesistruein Nil space. In our work we will use the projective model of Nil geometry described by E. Molnár in [6].

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Articles in this issue

DOI: https://doi.org/10.2478/ausm-2023-0008 | Journal eISSN: 2066-7752

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Language: English

Page range: 123 - 141

Submitted on: Jul 11, 2022

Published online: Nov 15, 2023

Published in print: Nov 1, 2023

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

Thurston geometries,

Nil geometry,

geodesic triangles,

Menelaus’ and Ceva’s theorems

MSC:

53A20,

53A35,

52C35,

53B20

Related subjects:

Mathematics,

General mathematics

© 2023 Jenő Szirmai, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 15 (2023): Issue 1 (November 2023)