Answer :
The diagram shows how to cut into
five pieces to form a square.
The dotted lines are intended to show how
to find the points C and F—the only difficulty. A B is half B
D, and A E is parallel to B H.
With the point of the compasses at B
describe the arc H E, and A E will be the distance of C from
B.
Then F
G equals B C less A B.
This puzzle—with the added condition
that it shall be cut into four parts of the same size and
shape—I have not been able to trace to an earlier date than
1835.
Strictly speaking, it
is, in that form, impossible of solution; but I give the answer that is
always presented, and that seems to satisfy most people.
We are asked to assume that the two portions
containing the same letter—AA, BB, CC, DD—are
joined by "a mere hair," and are, therefore, only one piece.
To the
geometrician this is absurd, and the four shares are not equal in area
unless they consist of two pieces each.
If you make them equal in area,
they will not be exactly alike in shape.
