arXiv subjects

R Nandakumar

Publications and source records attributed to R Nandakumar.

3 recordsLinked to original sources

arXiv2026

On the maximum volume solid wrappable by a given sheet of paper

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 propose a conjecture characterising the maximumvolume solid wrappable by any given sheet: the maximum is always achieved (or approached) by a non-convex body. In other words, for any convex solid wrappable by a given sheet, there exists a non-convex solid of strictly greater volume that the same sheet can wrap. We discuss related work, a key subquestion involving the sphere, and several further directions.

math.MG↗

arXiv2020

Oriented Convex Containers of Polygons -- II

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 examine some more possible oriented containers - semicircles, segments of circles and sectors - and raise some questions.

cs.CG↗

arXiv2018

Oriented Convex Containers of Polygons

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 direction on the plane (this direction is not necessarily an axis of symmetry) - and derive preliminary results.

math.GM↗