A Metric Framework for Triangle Inequalities via Barycentric Coordinates

Xi Feng

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arXiv · 2506.10050

A Metric Framework for Triangle Inequalities via Barycentric Coordinates

Xi Feng

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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.

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Xi Feng. 2025-06-11. A Metric Framework for Triangle Inequalities via Barycentric Coordinates. https://arxiv.org/abs/2506.10050

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