**The
incredible theorem of Pythagoras****, November
98**

You already
know that, in any right triangle, the sum of the squares of the lengths
of the legs (a and b) equals the square of the length of the hypothenuse
(c), in short: a^{2} + b^{2} = c^{2}.

Look at the diagram shown in fig. a) below, it visually demonstrates
that 3^{2} +
4^{2} = 5^{2}, according to the Pythagorean theorem.
Now, can you prove that the Pythagorean also works with triangles (fig.
b) or hexagons (fig. c)? The graphical proofs should be simple, in
order to understand them at a glance.

©96-98, Sarcone & Waeber, Lausanne
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