I wonder how many of my readers, amongst those who have not given any
close attention to the elements of geometry, could draw a regular
pentagon, or five-sided figure, if they suddenly required to do so. A
regular hexagon, or six-sided figure, is easy enough, for everybody
knows that all you have to do is to describe a circle and then, taking
the radius as the length of one of the sides, mark off the six points
round the circumference. But a pentagon is quite another matter. So, as
my puzzle has to do with the cutting up of a regular pentagon, it will
perhaps be well if I first show my less experienced readers how this
figure is to be correctly drawn. Describe a circle and draw the two
lines H B and D G, in the diagram, through the centre at right angles.
Now find the point A, midway between C and B. Next place the point of
your compasses at A and with the distance A D describe the arc cutting H
B at E. Then place the point of your compasses at D and with the
distance D E describe the arc cutting the circumference at F. Now, D F
is one of the sides of your pentagon, and you have simply to mark off
the other sides round the circle. Quite simple when you know how, but
otherwise somewhat of a poser.
[Illustration]
Having formed your pentagon, the puzzle is to cut it into the fewest
possible pieces that will fit together and form a perfect square.
[Illustration]