1d+-+Henry+Perigal+(1830)

Henry Perigal (1801 - 1898) discovered this "alternative and very beautiful solution to this problem [of proving the Pythagorean Theorem], known as Perigal's dissection (Moscovitch, 2001, p. 178)." Henry Perigal was a London Stockbroker and amateur mathematician when he discovered this dissection in 1830 (Stokes, 1975, p. 40). He shares that distinction with many great mathematicians -- that he wasn't one professionally. His dissection is so unique and simple in demonstration, it is commonly used in classrooms as a hands-on activity to demonstrate the theorem. media type="custom" key="6199757" Created using GeoGebra 3.2.40.0 GeoGebra - Dynamic Mathematics for Everyone []

This dissection, while a unique and interesting demonstration, is difficult to prove. Note the segment spanning top to bottom of the blue square is parallel to the hypotenuse of the triangle. The other segment is perpendicular to the first. Note also that the vertex of the four blue pieces is at the centroid of the square. This proof is for those who enjoy a challenge. Good luck!