Fold And Cut Puzzles

Erik Demaine, Marty Demaine, and Anna Lubiw proved the following amazing thing a few years ago:

  • You can fold a piece of paper so that ANY shape with straight edges can be cut out of the paper with a single cut.

see Erik’s page on Fold-And-Cut problems to read more about the history of this fact. (Did you know that Betsy Ross cut out the five-pointed stars on the first American flag this way? I didn’t.) During (most of) the fall, I wrote some code with CGAL and Mathematica to generate fold-and-cut creases.

The resulting pictures made fun origami puzzles, so I’m posting them here for your amusement. Each of these images can be folded (along the creases shown) so that you can cut out the shaded letter with a single straight cut. You won’t need any ‘more’ creases, but you might not use all of the creases shown. You only have to crease the dotted lines, not the outline of the letter or shape. Can you do it?

DemoU DemoG DemoA

I suggest that you print out these PDF versions (U G A) and try it! Be sure to make the creases before you start folding.