"By the toes of St. Moden," exclaimed Sir Hugh de Fortibus when this
puzzle was brought up, "my poor wit hath never shaped a more cunning
artifice or any more bewitching to look upon. It came to me as in a
vision, and ofttimes have I marvelled at the thing, seeing its exceeding
difficulty. My masters and kinsmen, it is done in this wise."
[Illustration]
The worthy knight then pointed out that the crescent was of a particular
and somewhat irregular form--the two distances _a_ to _b_ and _c_ to _d_
being straight lines, and the arcs _ac_ and _bd_ being precisely similar.
He showed that if the cuts be made as in Figure 1, the four pieces will
fit together and form a perfect square, as shown in Figure 2, if we there
only regard the three curved lines. By now making the straight cuts also
shown in Figure 2, we get the ten pieces that fit together, as in Figure
3, and form a perfectly symmetrical Greek cross. The proportions of the
crescent and the cross in the original illustration were correct, and
the solution can be demonstrated to be absolutely exact and not merely
approximate.
I have a solution in considerably fewer pieces, but it is far more
difficult to understand than the above method, in which the problem is
simplified by introducing the intermediate square.