Answer :
A regular pentagon
may be cut into as few as six
pieces that will fit together without any turning over and form a
square, as I shall show below.
The best answer has been in
seven pieces.
The pentagon is
ABCDE. By the cut AC and the cut
FM (F being the middle point between A and C, and M being the same
distance from A as F) we get two pieces that may be placed in position
at GHEA and form the parallelogram GHDC.
We then find the mean
proportional between the length HD and the height
of the parallelogram.
This distance we mark off from C at K, then draw
CK, and
from G
drop the line GL, perpendicular to KC.
The rest is easy and rather
obvious. It will be seen that the six pieces will form either the
pentagon or the square.
