The
illustration
will show how the triangular piece of cloth
may be cut
into four pieces that will fit together and form a perfect square.
Bisect
AB in D and BC in E; produce the line AE to F making EF equal to EB;
bisect AF in G and describe the
arc AHF; produce EB to H, and EH is the
length of the side of the required square; from E with distance EH,
describe the arc HJ, and make JK equal to BE; now, from the points D
and
K drop perpendiculars on EJ at L and M.

If you have done this
accurately,
you will now have the required directions for the cuts.

I
exhibited this problem
before the Royal Society,
at
Burlington House,
on 17th May 1905, and also at the Royal Institution in the following
month, in the more general form:—"A New Problem on
Superposition: a
demonstration that an equilateral triangle can be cut into four pieces
that may be reassembled to form a square, with some examples of a
general
method for transforming all rectilinear triangles into squares by
dissection."

It
was also issued as a
challenge to the readers of the *Daily
Mail* (see issues of 1st
and 8th
February
1905), but though many
hundreds of attempts were sent in there was not a single
solver.

Credit,
however, is due to Mr. C. W. M'Elroy, who alone sent me the correct
solution when I first published the problem in the *Weekly
Dispatch* in
1902.

I
add an illustration showing
the puzzle in a
rather curious
practical
form, as it was made in polished mahogany with brass hinges for use by
certain audiences.

It will be seen that the four pieces form a sort of
chain, and that when they are closed up in one direction they form the
triangle, and when closed in the other direction they form the square.