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.

Raphael, Computer enhanced detail from The School of Athens 1510, Fresco Stanza della Segnatuza, Vatican, Rome.
The figures (on the right) illustrate one of the most ancient proofs of Pythagoras' theorem using "sand reckoning" technique. Manipulating in sand the impressions made by the right-angled trinagle result in patterns which provide a geometrical model used by Pythagoras to make his theorem.


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