AI Chat AI Image Generator AI Video Text to Speech

Tilings with noncongruent triangles

11/13/2017

∙

by Andrey Kupavskii, et al.

∙

∙

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 no convex polygon with more than three sides can be tiled with finitely many triangles such that no pair of them share a full side.

Andrey Kupavskii
35 publications
János Pach
9 publications
Gábor Tardos
6 publications

research

∙ 12/08/2017

Tilings of the plane with unit area triangles of bounded diameter

There exist tilings of the plane with pairwise noncongruent triangles of...

0 Andrey Kupavskii, et al. ∙

research

∙ 05/10/2022

Matrix pencils with the numerical range equal to the whole complex plane

The main purpose of this article is to show that the numerical range of ...

0 Vadym Koval, et al. ∙

research

∙ 05/04/2020

Equal Area Breaks: A Classification Scheme for Data to Obtain an Evenly-colored Choropleth Map

An efficient algorithm for computing the choropleth map classification s...

0 Anis Abboud, et al. ∙

research

∙ 11/26/2018

FPTAS for barrier covering problem with equal circles in 2D

In this paper, we consider a problem of covering a straight line segment...

0 Adil Erzin, et al. ∙

research

∙ 11/25/2022

On picking sequences for chores

We consider the problem of allocating m indivisible chores to n agents w...

0 Uriel Feige, et al. ∙

research

∙ 08/14/2020

On the Notion of Equal Figures in Euclid

Euclid uses an undefined notion of "equal figures", to which he applies ...

0 Michael Beeson, et al. ∙

research

∙ 09/13/2018

The Paulsen Problem Made Simple

The Paulsen problem is a basic problem in operator theory that was resol...

0 Linus Hamilton, et al. ∙