Hiding disks in folded polygons.
Thérèse Biedl, Erik D. Demaine, Martin L. Demaine, Anna Lubiw, Godfried T. Toussaint · 1998
This paper considers the problem of finding a simple fold of a given polygon P that "hides" (covers both sides of) the largest possible disk. We solve this problem by giving a polynomial-time algorithm to find the largest pair of equal-radius non-overlapping disks in a polygon P . The desired fold is then the perpendicular bisector of the centers of these two disks. We also present some conjectures for the more general multiple-fold case when P is a square.