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.)

When you have made a fold in the paper that would go through the center of the hole, you have a semicircle cut out from either side of the fold.  Take a point along the semicircular arc, halfway between the two ends. Label the endpoints of the arc A and C, and the midpoint along the arc B.  Form a new crease there, at B, on either side of the first fold--or rather two creases on each side-- so as to pivot, say, point A, so that angle CBA is 180 degrees rather than 90 degrees. This will multiply the straight-line distance AC by sqrt(2), so that a coin with diameter sqrt(2) will fit through.

Posted by Charlie on 2006-05-29 12:59:01