2012/03/29 by Emmanuel Tsukerman, Tsukerman, Emmanuel · 1 citation
Computer Science · Engineering · Mathematics · #51M04 #51M09 #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Structural Analysis and Optimization #math.MG #msc:51M04 #msc:51M09
paper · pdf · doi:10.48550/arxiv.1203.6429
13 pages, 7 figures
arxiv created 2012/03/29 · openalex publication_date 2012/03/29 · arxiv updated 2012/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The "Perpendicular Bisectors Construction" is a natural way to seek a replacement for the circumcenter of a noncyclic quadrilateral in the plane. In this paper, we generalize this iterative construction to a construction on polytopes with n vertices in (n-2)-dimensional Euclidean, Hyperbolic and Elliptic geometries. We then show that a number of nice properties concerning this iterative construction continue to hold in these geometries. We also introduce an analogue of the isoptic point of a quadrilateral, which is the limit point of the Perpendicular Bisectors Construction, in ℝn and prove some of its properties.