Take a piece of paper and cut out a perfect circle with diameter 1 inch.
What is the diameter of the largest unaltered coin which may be passed through the hole without tearing it?
(Consider the coin to be very thin, and the paper to be very flexible and tear resistant, but not at all stretchy.)
(In reply to my guess
In playing around with a piece of paper, it seems that three folds on either side of the original crease work out easiest to do: two valley folds 45 degrees from the original crease that runs through the center of the hole, and one mountain fold midway between these two, and therefore at right angles to the original crease.
The two valley folds will have a dihedral angle of 90 degrees while the mountain fold will be 0 degrees as the two sides will be in contact.
Posted by Charlie
on 2006-05-29 13:10:19