International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 3, Pages 217-222

Convex isometric folding

E. M. Elkholy

Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Received 27 September 1993; Revised 5 June 1996

Copyright © 2000 E. M. Elkholy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce a new type of isometric folding called “convex isometric folding.” We prove that the infimum of the ratio VolN/Volφ(N) over all convex isometric foldings φ:NN, where N is a compact 2-manifold (orientable or not), is 1/4.