Inequalities For Distances Between Triangle Centers

2023/09/24 by Stanley Rabinowitz, Rabinowitz, Stanley
Mathematics · #51M04 (Primary) 51-08 (Secondary) #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2309.13727

openalex publication_date 2023/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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) denotes the distance between triangle centers X_i and X_j , Kimberling conjectured that D(6; 1) ≤ 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) ≤ (2 -√3)D(6; 3).

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