will show how the triangular piece of cloth
may be cut
into four pieces that will fit together and form a perfect square.
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
K drop perpendiculars on EJ at L and M.
If you have done this
you will now have the required directions for the cuts.
exhibited this problem
before the Royal Society,
on 17th May 1905, and also at the Royal Institution in the following
month, in the more general form:—"A New Problem on
demonstration that an equilateral triangle can be cut into four pieces
that may be reassembled to form a square, with some examples of a
method for transforming all rectilinear triangles into squares by
was also issued as a
challenge to the readers of the Daily
Mail (see issues of 1st
1905), but though many
hundreds of attempts were sent in there was not a single
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
add an illustration showing
the puzzle in a
form, as it was made in polished mahogany with brass hinges for use by
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.