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In any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. | ![]() |
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![]() 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.
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