Hinged Dissections: From Equilateral Triangle to Square

How to cut an equilateral triangle so that the pieces can be reassembled to form a square was discovered by Dudeney in the 1900s. This Demonstration includes his method along with two other versions (discovered by Greg Frederickson a hundred years later) that show that the pieces can be linked with imaginary hinges to close back and forth from triangle to square and vice versa.