A demonstration of the Pythagoras' theorem [Une démonstration du théorème de Pythagore].




Let's build the following polygons:

==> ==> ==>


Please note that:

Then:
  Surface(Green Square)    =      Surface(Red Square)     +   4.Surface(Blue Triangle)
= +

             2                           2                             1         
     (X+Y)           =               Z               +          4.(---.X.Y)
                                                                       2         
           ___          ___ 
 2    2   /   \    2   /   \
X  + Y  + 2.X.Y = Z  + 2.X.Y
          \___/        \___/

  2    2    2
X  + Y  = Z

 CQFD


(Z, X and Y denoting respectively the hypotenuse and the two other sides of the four right angled triangles)



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