The Haberdasher's Problem

The haberdasher's problem is Dudeney's best-known geometrical discovery. The problem is to cut an equilateral triangle into four pieces that can be reassembled to form a square. A remarkable feature of this puzzle is that the pieces can be hinged at three vertices, to form a chain that can be closed clockwise to make the triangle and counter-clockwise to make the square. Dudeney rendered the figure into a brass-hinged mahogany model, which he used for demonstrating the problem before the Royal Society in 1905.