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.)

We are actually being asked to distort the circumference of the circle so that it becomes a lineal border around a slot through which the hypothetical coin will pass.

C=2πr;

Diam. of coin = C/2
                    = 2π(1/2)/2     [radius = 1/2    π = pi]
                    = 2π/(2*2)   
                    = π/2
                     ≈ 3.14/2
                     = 1.57

 [Charlie's coin √2 ≈1.4 would fit through, but we can go higher]

Posted by brianjn on 2006-05-30 00:53:36