English

Inequalities For Distances Between Triangle Centers

History and Overview 2023-09-26 v1 Metric Geometry

Abstract

In his seminal paper on triangle centers, Clark Kimberling made a number of conjectures concerning the distances between triangle centers. For example, if D(i;j)D(i; j) denotes the distance between triangle centers XiX_i and XjX_j , Kimberling conjectured that D(6;1)D(6;3)D(6; 1) \leq D(6; 3) for all triangles. We use symbolic mathematics techniques to prove these conjectures. In addition, we prove stronger results, using best-possible constants, such as D(6;1)(23)D(6;3)D(6; 1) \leq (2 -\sqrt3)D(6; 3).

Keywords

Cite

@article{arxiv.2309.13727,
  title  = {Inequalities For Distances Between Triangle Centers},
  author = {Stanley Rabinowitz},
  journal= {arXiv preprint arXiv:2309.13727},
  year   = {2023}
}
R2 v1 2026-06-28T12:30:55.555Z