2010/07/09 by Yu-Dong Wu, Wu, Yudong, Zhi‐Hua Zhang +1
Engineering · Mathematics · #52A40 #52B11 #52B12 #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1007.1602
openalex publication_date 2010/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An n-simplex is called circumscriptible (or edge-incentric) if there is a sphere tangent to all its n(n + 1)/2 edges. We obtain a closed formula for the radius of the circumscribed sphere of the circumscriptible n-simplex, and also prove a double inequality involving the circumradius and the edge-inradius of such simplices. Among this inequality settles affirmatively a part of a problem posed by the authors.