APOLLONIUS, STEWART, CEVA, AND MENELAUS THEOREMS IN E^2, L^2, AND I^2

• 발행기관: 충청수학회
• 저자명: Jin Ju Seo
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 38, No. 3, 177~197쪽, 전체 21쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2025.08.31

국문 초록

This paper proposes a unified approach to Apollonius’s, Stewart’s, Ceva’s, and Menelaus’s theorems in Euclidean, Lorentzian, and Isotropic planes. These theorems, fundamental in triangle ge- ometry, are extended to non-Euclidean geometries, enabling a systematic exploration of the similarities and differences among these planes. Particular emphasis is placed on the unique properties of Lorentzian and Isotropic geometries compared to the Euclidean framework. This study aims to contribute to the understanding of geometric invariants and their extensions in non-Euclidean settings.

목차

1. Introduction

2. Preliminaries

3. Medians and Centroid in Triangles

4. Proportional Relationships of Internal and External Points in Triangles

References

키워드

Apollonius’s Theorem Stewart’s Theorem Ceva’s Theo- rem Menelaus’s Theorem Euclidean Plane Lorentzian Plane Isotropic Plane Non- Euclidean Geometry Geometric Invariants Triangle Geometry