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 re(3): My 2 cents worth by Salil)

You are quite convincing, and there seems to be a reasonable  possibility that you are correct.  A way to think of this is as a cloth pocket with a hole in it and a coin that has diameter somewhat greater than the hole (up to pi/2 times greater).  Then it looks like the coin could be lost if it manages to get positioned just right with respect to the hole.  The cloth around the hole would need to get pretty messed up, but maybe it doesn't need to be stretched. Cloth would certainly be better than paper to use for an experiment.

Posted by Richard on 2006-05-30 15:25:47