Map folding

In combinatorial mathematics the map folding problem is the question of how many ways there are to fold a rectangular map along its creases. A related problem called the stamp folding problem is how many ways there are to fold a strip of stamps.^[1]

For example, there are six ways to fold a strip of three different stamps:

And there are eight ways to fold a 2×2 map along its creases:

The problem is related to a problem in the mathematics of origami of whether a square with a crease pattern can be folded to a flat figure. Some simple extensions to the problem of folding a map are NP-complete.^[2]

References

1. ^ Weisstein, Eric W., "Map Folding" from MathWorld.
2. ^ Esther M. Arkin, Michael A. Bender, Erik D. Demaine, Martin L. Demaine, Joseph S. B. Mitchell, Saurabh Sethia, Steven S. Skiena (September 2004). "When Can You Fold a Map?". Computational Geometry: Theory and Applications 29 (1): pp. 23–46. http://erikdemaine.org/papers/MapFolding/paper.pdf. 

See also

• Martin Gardner, "The Combinatorics of Paper Folding," Wheels, Life and Other Mathematical Amusements, New York: W. H. Freeman, 1983 pp. 60–61.
• "Folding a Strip of Labeled Stamps" from The Wolfram Demonstrations Project: http://demonstrations.wolfram.com/FoldingAStripOfLabeledStamps/

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