Add to ORKGAn intriguing conjecture of Nandakumar and Ramana Rao is that for every convex body K ⊆ R2, and for any positive integer n, K can be expressed as the union of n convex sets with disjoint interiors and each having the same area and perimeter. The first difficult case- n = 3- was settled by Bárány, Blagojevi¢, and Szucs using powerful tools from algebra and equivariant topology. Here we give an elementary proof of this result in case K is a triangle, and show how to extend the approach to prove that the conjecture is true for triangles.Ministerio de Educación y CienciaEuropean Science FoundationNational Science Foundatio
summary:We define a proper triangulation to be a dissection of an integer sided equilateral triangle...
In this note we introduce a pseudometric on convex planar curves based on distances between normal l...
Frettlöh D, Richter C. Incongruent equipartitions of the plane into quadrangles of equal perimeters....
An intriguing conjecture of Nandakumar and Ramana Rao is that for every convex body K ⊆ R2, and for ...
We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise no...
AbstractWe show that for a given planar convex set K of positive area there exist three pairwise int...
There exist tilings of the plane with pairwise noncongruent triangles of equal area and bounded peri...
We describe a regular cell complex model for the configuration space F (Rd, n). Based on this, we us...
We consider generalizations of the honeycomb problem to the sphere S2 and seek the perimeter-minim...
summary:We define a proper triangulation to be a dissection of an integer sided equilateral triangle...
summary:We define a proper triangulation to be a dissection of an integer sided equilateral triangle...
We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and...
We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and...
We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and...
Let T be a tiling of the plane with equilateral triangles no two of which share a side. We prove tha...
summary:We define a proper triangulation to be a dissection of an integer sided equilateral triangle...
In this note we introduce a pseudometric on convex planar curves based on distances between normal l...
Frettlöh D, Richter C. Incongruent equipartitions of the plane into quadrangles of equal perimeters....
An intriguing conjecture of Nandakumar and Ramana Rao is that for every convex body K ⊆ R2, and for ...
We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise no...
AbstractWe show that for a given planar convex set K of positive area there exist three pairwise int...
There exist tilings of the plane with pairwise noncongruent triangles of equal area and bounded peri...
We describe a regular cell complex model for the configuration space F (Rd, n). Based on this, we us...
We consider generalizations of the honeycomb problem to the sphere S2 and seek the perimeter-minim...
summary:We define a proper triangulation to be a dissection of an integer sided equilateral triangle...
summary:We define a proper triangulation to be a dissection of an integer sided equilateral triangle...
We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and...
We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and...
We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and...
Let T be a tiling of the plane with equilateral triangles no two of which share a side. We prove tha...
summary:We define a proper triangulation to be a dissection of an integer sided equilateral triangle...
In this note we introduce a pseudometric on convex planar curves based on distances between normal l...
Frettlöh D, Richter C. Incongruent equipartitions of the plane into quadrangles of equal perimeters....
