International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 3, Pages 217-222
doi:10.1155/S0161171200001198
Convex isometric folding
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.
Abstract
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:N→N, where N is a compact 2-manifold (orientable or
not), is 1/4.