ATRACTOR

Select the geometric proof you wish to see by clicking on the respective image.

Shortest diagonal (Proofs):

Second shortest diagonal

Longest diagonal

Regular Decagon

Can we find any other geometric proof of incommensurability between the diagonal and the side? Actually, for the kind of diagonals we considered above, the answer is no. To know why, check the following PDF documents (for now, only in Portuguese):

Incomensurabilidade entre a diagonal mais curta e o lado de um polígono regular

Fórmula para a razão entre as diagonais e o lado de um polígono regular

Incomensurabilidade entre a segunda diagonal mais curta e o lado de um polígono regular

Incomensurabilidade entre a diagonal mais longa e o lado de um polígono regular