A Metric Framework for Triangle Inequalities via Barycentric Coordinates

2025/06/11 by Xi‐Qiao Feng, Feng, Xi
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2506.10050

openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a unified metric-based framework for triangle geometric inequalities using barycentric coordinates. By interpreting classical inequalities as squared distances between points(a process termed metricization)we derive and refine numerous well-known inequalities. Furthermore, the squared-distance function ELD_I, measures distances from the incenter to points on the Euler line, also yielding generalized inequalities. The method offers geometric clarity and extends naturally to higher-dimensional and non-Euclidean settings.

Citations

• Metric Matrix in Barycentric Coordinates

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