[Illustration]
If that ancient architect had arranged his five crescent tiles in the
manner shown in the following diagram, every tile would have been
watched over by, or in a line with, at least one crescent, and space
would have been reserved for a perfectly square carpet equal in area to
exactly half of the pavement. It is a very curious fact that, although
there are two or three solutions allowing a carpet to be laid down
within the conditions so as to cover an area of nearly twenty-nine of
the tiles, this is the only possible solution giving exactly half the
area of the pavement, which is the largest space obtainable.