In the app 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).

You can change the initial regular polygon and the position of the following polygons by moving the red dot.

To see an animated version of the app, click here.

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