Around the Carnot theorem

2013/08/28 by Djordje Baralić, Djordje Baralic, Baralic, Djordje
Mathematics · #14N05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #math.AG #msc:14N05

paper · pdf · doi:10.48550/arxiv.1308.6144

11 pages, 11 figures

arxiv created 2013/08/28 · openalex publication_date 2013/08/28 · arxiv updated 2013/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Carnot theorem and the configuration of points and lines in connection with it. It is proven that certain significant points in the configuration lie on the same lines and same conics. The proof of an equivalent statement formulated by Bradley is given. An open conjecture, established by Bradley, is proved using the theorems of Carnot and Menelaus.

Related

• Non-Euclidean Cross-Ratios and Carnot's Theorem for Conics
• A Six-Point Ceva-Menelaus Theorem
• On lines in a triangle tangent to a conic
• Conics associated with triangles, or how Poncelet meets Morley
• Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates