Paper-Cutting Trick

Date: 01/24/2001 at 11:08:16
From: Shirl Henderson
Subject: Paper-cutting trick

There is a way to cut a sheet of paper to make a hole big enough to 
walk through. I remember doing this for my students years ago, but 
cannot remember now how it was done. I do recall it's done by making a 
continuous cut in an 8 1/2 by 11 sheet of paper that results in a very 
large circle. The other "oldtimers" in my department recall the trick, 
but cannot remember how it was done either. Can you help?

Date: 01/24/2001 at 17:03:54
From: Doctor Rob
Subject: Re: Paper-cutting trick

Thanks for writing to Ask Dr. Math, Shirl.

Here is a rough diagram:

     o-------------------------------------------o
     |                                           |
     |   o-----------------+-----------------o   |
     |                     |                     |
     +-----------------o   |   o-----------------+
     |                     |                     |
     |   o-----------------+-----------------o   |
     |                     |                     |
     +-----------------o   |   o-----------------+
     |                     |                     |
     |   o-----------------+-----------------o   |
     |                     |                     |
     +-----------------o   |   o-----------------+
     |                     |                     |
     |   o-----------------+-----------------o   |
     |                     |                     |
     +-----------------o   |   o-----------------+
     |                     |                     |
     |   o-----------------+-----------------o   |
     |                     |                     |
     +-----------------o   |   o-----------------+
     |                     |                     |
     |   o-----------------+-----------------o   |
     |                                           |
     o-------------------------------------------o

The thinner you make the strips, and the more cuts from the sides
toward the middle, the larger the hole you get when you are done.
The cutting may be easier if you fold the paper in half lengthwise
before you start.

I'm afraid the cut can't be continuous.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/