Tilings with noncongruent triangles. (October 2018)

• Record Type: Journal Article
• Authors: Kupavskii, Andrey; Pach, János; Tardos, Gábor
• Is Part Of: European journal of combinatorics. Volume 73(2018)
• Page Start: 72
• Page End: 80
• Publication Date: 2018-10
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2018.05.005
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise noncongruent triangles of equal area and equal perimeter. We also show that any tiling of a convex polygon with more than three sides with finitely many triangles contains a pair of triangles that share a full side.