Pythagoras' Theorem
In any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Pythagoras statue in the Museo Capitalano, Rome.
In the middle of a sheet of cardboard draw a right-angled triangle and a square on each side. Locate the centre of the middle-sized square. Call it A. Through A draw a line parallel to the hypotenuse and then a line through A perpendicular to the hypotenuse (as illustrated).
Cut out shapes 1,2,3,4,5 and 6.
Try to fit 1,2,3,4 and 5 on 6, thus verifying the theorem of Pythagoras. This construction is known as Perigal's dissection.
Can you explain why Perigal's dissection works?
Henry Perigal was a Stockbroker and amateur astronomer. In 1830 he announced a single and elegant proof of the theorem of Pythagoras.


Home | Geometry | Historical Profile | Proof 1 | Proof 2 | Proof 3 | Proof 4 | Proof 5 | Proof 6

© Copyright 1997, Crux Multimedia