# haberdasher's puzzle

The haberdasher's puzzle is to cut an equilateral triangle into four pieces that can be rearranged to
make a square. It was the greatest mathematical discovery
of Henry Dudeney and published by
him, first in the *Weekly Dispatch* in 1902 and then as problem no. 26 in *The Canterbury Puzzles* (1907).^{1} The accompanying diagram
shows the solution, which Dudeney describes as follows:

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 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.

A remarkable feature of the solution is that the each of the pieces can be hinged at one vertex, forming a chain that can be folded into the square or the original triangle. Two of the hinges bisect sides of the triangle, while the third hinge and the corner of the large piece on the base cut the base in the approximate ratio 0.982: 2: 1.018. Dudeney showed just such a model of the solution, made of polished mahogany with brass hinges, at a meeting of the Royal Society on May 17, 1905.

### Reference

1. Dudeney, H. E. *The Canterbury Puzzles*. London: Nelson, 1907.
Reprinted Mineola, NY: Dover, 1958.