A Metric Framework for Triangle Inequalities via Barycentric Coordinates
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912425585934336 |
|---|---|
| author | Feng, Xi |
| author_facet | Feng, Xi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Metric Framework for Triangle Inequalities via Barycentric Coordinates Feng, Xi Metric Geometry 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. |
| title | A Metric Framework for Triangle Inequalities via Barycentric Coordinates |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2506.10050 |