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.)

If we can consider the thickness of the coin to be negligible...

A circular hole in a piece of paper can be manipulated into a slit with negligible thickness, but length (pi)(d)/2. In this case, ~1.57 inches. You just have to use some origami know-how.

Fold the paper in half along the diameter of the hole. You're looking at a semicircular hole in the paper, at the top of a tent shape of paper for illustration's sake.

Using the apex of each semicircle-- 90 degrees from the first fold in the paper-- pinch the paper at each apex and crease downward towards the bottom of each corner of the tent. This is only necessary to guide the excess paper out of the way when the hole, NOT the paper, is stretched in the next step.

Now it should be simple to take the corners of the semicircle, where that first fold bisected the circular hole, and pull them apart as far as possible, until the hole becomes a slit with length (pi)(d)/2. The creases towards the bottom of the tent that you made should absorb the excess paper moving out of the way to accommodate the hole's stretching, without stretching the paper whatsoever.

Posted by Jordie on 2006-06-04 22:35:31