The geometrical constructions of [math]\varphi[/math] and [math]\Phi[/math] aren't but variants on the construction of square roots of natural numbers, starting from a rectangular triangle with side 1.[br][list][*]With the Pythagorean thema one can find that the hypotenusa of a rectangular triangle with sides 1 is equal to [math]\sqrt{2}[/math].[/*][*]On this side you can construct another rectangular triangle with sides [math]1[/math] and [math]\sqrt{2}[/math] and hypothenusa [math]\sqrt{3}[/math], etc.[/*][/list]This construction is called [i]the [i]Pythagorean [/i]snail van [/i].