Home > Challenge, Geometry > Fun With One Cut

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.

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.

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

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

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

Check out more in my Fun With Folding section!

Click here to see more in Challenge.


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