**Reference**:- Therese C. Biedl, Erik D. Demaine, Martin L. Demaine, Anna Lubiw, and Godfried T. Toussaint, “Hiding Disks in Folded Polygons”, in
*Proceedings of the 10th Canadian Conference on Computational Geometry (CCCG'98)*, Montréal, Québec, Canada, August 10–12, 1998. **Abstract**:-
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. **Comments**:- This paper is also available from the electronic proceedings as http://cgm.cs.mcgill.ca/cccg98/proceedings/cccg98-biedl-hiding.ps.gz.
**Updates**:- One problem explored in this paper, packing the largest pair of equal-radius disks in a given polygon, have been further developed in several followup papers. See my webpage on wrapping for a summary and references.
Erin McLeish prepared an excellent webpage describing these and related results and algorithms, including a Java applet.

**Length**:- The paper is 11 pages and the talk is 20 minutes.
**Availability**:- The paper is available in PostScript (194k).
- The talk is also available in PostScript (148k).
- See information on file formats.
- [Google Scholar search]
**Related webpages**:- Wrapping Polyhedra

See also other papers by Erik Demaine.

Last updated January 18, 2021 by Erik Demaine.