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Paper-folding

Q: ??? Given a nice subset of the plane, is there a way to fold it (origami-style) that increases the circumference? What's the best definition of "nice" here?

What if we allow a general piecewise-isometric continuous map? Is this the same thing (ie are there such maps which can't be produced by a sequence of physical folds)?
rec.puzzles, 15 Apr 1996


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