Take a piece of paper and make a bunch of folds so that the final
construction is laying flat. Now with one straight cut, crop across
all the folds. What are the forms you can make this way?
The origami purist eschews the blade, limiting himself to the activity
of creasing, but in single-cut origami that purism is augmented by
a lone slice. Before Houdini turned his talents to escape, he astonished
audiences by making a single-cut five-pointed star. Another magician,
Gerald Loe, explored the problem in greater depth and in his book,
Paper Capers, detailed how with one cut he could fold paper to produce
any specific letter of the alphabet. How universal is this method?
Is there a folding in which a single cut will produce, say, the form
of a fish or the figure of a unicorn?
It turns out the answer is yes. In 1997, three researchers in Canada
(Erik Demaine, Martin Demaine and Anna Lubiw) proved that any polygonal
shape can be produced from a sheet of paper by a single cut. The more
complex the form, the more folds you need, but theoretically there
is no limit. We can even produce multiple shapes – it’s
easy to make one star, but if you know how to fold the right way a
single cut will yield two stars, or five stars, or a hundred stars.
Letters of the alphabet may also be combined so that a properly folded
single-cut could produce any given word or phrase – your name,
the make of your car, or the entire text of King Lear.