5 papers
Oriented Convex Containers of Polygons -- II
R Nandakumar
We define an 'oriented convex region' as a convex region with a direction of symmetry. An earlier article had touched upon isosceles triangles, rectangles and ellipses. Here, we ex…
Oriented Convex Containers of Polygons
R Nandakumar
We consider the optimal containment of polygonal regions within convex containers with the special property of 'orientedness' - an oriented region enables us to choose a preferred…
Non-Tiles and Walls - A Variant on the Heesch Problem
Erich Friedman, R. Nandakumar
The Heesch problem 'grades' polygons that fail to tile the plane in terms of the number of layers (or corollas) of copies of it that can be formed around a central unit. We study t…
Convex Regions and their 'Fairest' Equipartitioning Fans
R. Nandakumar
A k-fan is a set of k half-lines (rays) all starting from the same point, called the origin of the fan. We discuss the partition of convex 2D regions into n (a positive integer) eq…
Cutting Mutually Congruent Pieces from Convex Regions
R. Nandakumar
What is the shape of the 2D convex region P from which, when 2 mutually congruent convex pieces with maximum possible area are cut out, the highest fraction of the area of P is lef…