2023/12/21 by Egor Bakaev, Bakaev, Egor, Павел Кожевников +1
Engineering · Mathematics · #51M04 #51N20 (Primary) #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2312.13893
openalex publication_date 2023/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two triangles are called orthologic if the perpendiculars from the vertices of one of them to the sides of the other are concurrent. In this paper, we explore the concept of orthology from various points of view. Mostly we work in terms of elementary geometry in ℝ2. In the final section, we relate the discussed concepts to ℝ4. A key idea in this paper is that two orthologic triangles generate a one-parameter (linear) family in which any two triangles are orthologic. Working with such a family can provide a natural approach to certain questions.