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Fun With One Cut

Inspired by a brilliant talk by Erik Demaine, I started playing around with the famous one-cut problem:  given a shape made up of straight line segments, can you fold the paper flat in such a way that with only one straight cut your shape will appear?

Having no real experience with mathematical paper folding, I thought I’d try out a Koch Curve.  Well, a finite iteration of it, at least.

Koch 1

It seemed like the strategy was to use the symmetry of the shape to make all the line segments line up on each other.  So I folded down the middle, and then again down the new middle.

One-Cut Collage 1

 

I rotated the last shape and it seemed a little clearer how to continue.

One-Cut Collage 2

It seemed like all the lines were lined up, so to speak.  So I cut.  And voila!

Koch 2

Not too bad!  Now, if I could just figure out how to do this with non-symmetric figures.

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