History Of Golden Section Ludovica Boncompagni – Italy Evaggelia Antonaki – Greece Team Coordinator – Enrica Maragliano - Italy

What is Golden Section? This is an irrational number (it is not represantable with a fraction) and algebric (it’s the solution of the polynomial equation n2-n-1=0) It can be approximated, with increasing precision, by the ratio of two consecutive terms of any succession in which an+1=an+an-1 We have that an/an-1  φ= 1,

Wonderful phi Golden Section is the only non natural number whose mutual and whose square keep unchanged its decimal part. φ = 1, … φ2 = 2, … 1/φ = 0, …

The golden section has always had a great influence on many subjects: Geometry Architecture Art Music Science(botanic)

Egyptians and Greeks It appears that the Egyptians may have used both pi and phi in the design of the Great Pyramids. The Greeks based the design of the Parthenon on this proportion

Geometry Pythagoras was the first who discovered a “golden proportion” drawing a regular pentagram, which has a regular pentagon inscribed within it(and that was the Pythagorean's symbol as well).

Also Euclid provides the first known written definition of what is now call “golden ratio” The golden ratio (phi) represented as a line divided into two segments A and B, such that the entire line is to the longer A segment as the A segment is to the shorter B segment”

Fibonacci Fibonacci discovered the first sequence ever known in Europe examining at the same time a practical problem which dealt with the development of a hypothetical population of rabbits based on idealized assumptions. He noticed that, after every monthly birth, the number of the rabbits couples increased from 1 to 2 to 3 to 5 to 8 to 13 etc., and understood that the sequence moved on by adding the previous two numbers, a sequence which could theoretically continue without ending.

The special meaning of “Phi” Phi is the first letter of Phidias, who used the golden ratio in his sculptures, as well as the Greek equivalent to the letter "F," the first letter of Fibonacci. Phi is also the 21st letter of the Greek alphabet, and 21 is one of numbers in the Fibonacci series.

Phi as a door to understanding life The description of this proportion as Golden and Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life. That's an incredible role for a single number to play, but then again this one number has played an incredible role in human history and in the universe at large.

In the end, the golden section has always fascinated us, and it will continue because of his component of irrationality and inexplicability.