Tilings with noncongruent triangles

被引：5
|
作者：
Kupayskii, Andrey [1 ,2 ]
Pach, Janos [1 ,3 ]
Tardos, Gabor [3 ,4 ]
机构：
[1] Ecole Polytech Fed Lausanne, Lausanne, Switzerland
[2] MIPT, Moscow, Russia
[3] Renyi Inst, Budapest, Hungary
[4] Cent European Univ, Budapest, Hungary
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2018年 / 73卷
基金：
瑞士国家科学基金会; 俄罗斯基础研究基金会; 英国工程与自然科学研究理事会;
关键词：
CONVEX EQUIPARTITIONS;
D O I：
10.1016/j.ejc.2018.05.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码：72 / 80
页数：9
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