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

See the useful geometrical figures for this demonstration:

• The big green quadrilateral is a square (one right angle and four sides equal to X+Y).
• The small red quadrilateral is a square (one right angle and four sides equal to Z).
• The four blue/red triangles are equal (they are right angled triangles with two equal small sides X and Y).
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)

(CMAP28 WWW site: this page was created on 04/26/2017 and last updated on 05/03/2020 11:53:04 -CEST-)

[See the generator of this picture [Voir le générateur de cette image]]

[See all related pictures (including this one) [Voir toutes les images associées (incluant celle-ci)]]

[Please visit the related ImagesDidactiques picture gallery [Visitez la galerie d'images ImagesDidactiques associée]]
[Please visit the related NumberTheory picture gallery [Visitez la galerie d'images NumberTheory associée]]
[Go back to AVirtualMachineForExploringSpaceTimeAndBeyond [Retour à AVirtualMachineForExploringSpaceTimeAndBeyond]]
[The Y2K bug [Le bug de l'an 2000]]

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[Mail [Courrier]]
[About Pictures and Animations [A Propos des Images et des Animations]]