24 citations · 24 across the 10 of their papers we have counts for
10 papers
On the maximum volume solid wrappable by a given sheet of paper
R Nandakumar
We consider the problem of wrapping three-dimensional solid bodies with a given planar sheet of paper, where the paper may be folded or wrinkled but not stretched or torn. We propo…
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…
A Set of Questions in Combinatorial and Metric Geometry
R. Nandakumar
We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the sam…
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…
A Note on Edge Guards in Art Galleries
R. Nandakumar
We examine the Art Gallery Problem with Edge Guards. We present a heuristic algorithm to arrange edge guards to guard only the inward side of the walls of any N-vertex simple polyg…
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…
'Congruent Partitions' of Polygons - a Short Introduction
R. Nandakumar
We introduce the problem of partitioning 2D regions (usually convex regions) into mutually congruent pieces ('tiles').
'Fair' Partitions of Polygons - an Introduction
R. Nandakumar, N. Ramana Rao
We address the question: Given a positive integer , can any 2D convex polygonal region be partitioned into convex pieces such that all pieces have the same area and same per…