On Isosceles Sets in the 4-Dimensional Euclidean Space. (10th November 2010)

• Record Type: Journal Article
• Authors: Kido, Hiroaki
• Other Names: Chang Gerard Jennhwa Academic Editor.
• Is Part Of: International journal of combinatorics. Volume 2010(2010)
• Publication Date: 2010-11-10
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Periodicals; Electronic journals; 511.605
• DOI: 10.1155/2010/803210
• Languages: English
• ISSNs: 1687-9163

Abstract

Abstract : A subsetX in thek -dimensional Euclidean spaceℝ k that containsn points (elements) is called ann -point isosceles set if every triplet of points selected from them forms an isosceles triangle. In this paper, we show that there exist exactly two 11-point isosceles sets inℝ 4 up to isomorphisms and that the maximum cardinality of isosceles sets inℝ 4 is 11.