It's unlikely that da Vinci was interested in the numeric value of the position of the navel.[br]However no higher math is needed, only the Pythagorean theme and the proportions given by da Vinci himself:[br][list][*][i]From above the chest to the top of the head is 1/6 of the length of the man.[/i][/*][*][i]The lenght of the outstreched arms equals[i] the length of the man[/i].[/i][/*][*][i]The maximum with of the shoulders is 1/4 [i]of the length of the man[/i].[/i][/*][*][i]From the armpit to the elbow is 1/8 [i]of the length of the man[/i].[/i][/*][*][i]From the elbow to the fingertips is 1/4 [i]of the length of the man[/i].[br][br][/i][/*][/list]According tho this we can draw a horizontal line at 1/6 of the upper side of the square and divide it into 8.[br]WIth 1 as the side of the square you've got all the information needed to calculate x, the position of the navel.

The resultat is at least remarkable: The difference of [math]\varphi[/math] regarding to the exact position of the navel is 1.95% and nearly 2 keer as big as the difference of 3/5 to the exact position.[br]So one could name 3/5 as the position then [math]\varphi[/math] and that's what renaissance artists and comments on Vitruvius do. Saying tha the navel is 'approximately at [math]\frac{\sqrt{5}-1}{2}[/math] of the man's height' sounds rather silly when 3/5 is more reliable. More, it's an insult for the genius that's da Vinci. The constructie of the ratio [math]\varphi[/math] is easy. And nevertheless da Vinci wouldn't have done better than 'approximtely'...[br]It's weird that both drawing and comments are full of unit fractions, while we would pretend that the fraction [math]\frac{\sqrt{5}-1}{2}[/math], which isn't mentioned anywhere' would be the only one that counts.[br]Nevertheless the myth of the navel as the perfect illustration of the golden section remains a widespread story.[br]Se non è vero è ben trovato...