### Visualisation

In the *applet* below, we illustrate the procedure for
construction of new polygons used in the geometric proofs of
incommensurability between the shortest diagonal and the side of
the square, the regular pentagon (in the first proof given) and
the regular hexagon. In this case, the first four polygons
obtained are presented, where the initial polygon is shown in blue
and the others are shown in green, yellow and red, in that order.
Note that we obtain slightly different configurations if, in the
iterative proof procedure, we change the diagonal over which the
next polygon is constructed (although this does not change the
proof itself).

**Instructions:**

Click on the red dots to change the size and the position of the
initial regular polygon. You can also change the initial regular
polygon and the position of the following polygons by moving the
black dots.

To see an animated version of the *applet*, click here.

To see an animated version of the construction procedure of new regular pentagons in the second proof, click here.