Brodie's Pentagon-to-Square Dissection
A regular pentagon is cut into three pieces that can be reassembled into a parallelogram. Next, the parallelogram is dissected into a square.
This dissection was given by Robert Brodie (1891) and is an improvement on Busschop's pentagon-to-square dissection.
G. N. Frederickson, Dissections: Plane & Fancy, New York: Cambridge University Press, 2002 p. 120.