2025/04/25 by Xi‐Qiao Feng, Feng, Xi · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2505.06235
openalex publication_date 2025/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the concept of the metric matrix is introduced to establish a concise and unified formulation for the inner product in barycentric coordinates. Building on this framework, we explore the intrinsic algebraic identities of barycentric coordinates and their direct correspondence with geometric theorems. Through this approach, we derive a series of novel results and provide new proofs for several classical theorems in triangle geometry.