One story has it that when the Greek mathematician Hippasus of Metapontum


discovered in the fifth century B.C, that the Golden Ratio is a number that is neither a whole number (like the familiar 1,2,3,….) nor even a ratio of two whole numbers (like fractions ½, 2/3, ¼,…; known collectively as rational numbers), this absolutely shocked the others followers of the famous mathematician Pythagoras.The Pythagorean worldview was bases on an extreme admiration for the arithmos – for the presumed role in the cosmos.

Pitagoras and a child

The realization that there exist numbers, like the Golden Ratio, that go on forever without displaying any repetition or pattern caused as a true philosophical crisis.

Legend even claims that, overwhelmed with this stupendous  discovery, the Pythagoreans sacrificed a hundred oxen in awe, althoug this unlikely, given the fact that the Pythagoreans were vegetarians.



Less known than pi π, is our number phi Φ, which is in many respects even more fascinating. Suppose we ask you¸what do the delightful petal arrangement in red rose, Salvador Dali´s famous painting “Sacrament of the Last Supper”,

dali-last-supper 2

a certain number or geometrical proportions known since antiquity, a number that in the nineteenth century was given the honorifics “Golden Number”, “Golden Ratio” and “Golden Section”.A book published inItaly at the beginning of the sixteen century went so far as to call this ratio the “Divine Proportion”.



The Golden Ratio is a product of human invented geometry. Humans had no idea, however, into what magical faryland this product was going to lead them.

If geometry had not been invented al all, then we might have never known about the Golden Ratio.

But then, who knows?.It might have emerged as the output of a short computer program.

The Golden Ratio. Mario Livio. 20002.

12, bis 12, bis bis