Stele of King Djet

(1st Dynasty of Egypt: around 3150 b.C. to 2925 b.C., Louvre Museum, Paris, France)

There are several works from ancient Egypt in which it is possible to identify the presence of the golden ratio. However, it must be considered that, despite the remarkable skills in the field of arithmetic highlighted by the Egyptian people, there is no evidence related to the knowledge, by this people, of the value of the golden number φ .

A possible motivation for the introduction of golden rectangles in Egyptian works can be attributed to the use of particular geometric strategies, fractions and operations such as the square root, which were applied by the Egyptians in the construction of temples.

Golden rectangles are present, for example, in the stele of King Djet, that is a tombstone which takes its name from the pharaoh Djet and which comes from Abydos, a city in Upper Egypt. Observing the stele, two golden rectangles can be identified, the upper one, which contains the snake (symbol of the king) and the lower one in which the palace is depicted:

Funerary mask of Tutankhamun

(14th century b.C., Egyptian Museum, Cairo, Egypt)

The Egyptian mask of the pharaoh Tutankhamun has golden proportions. In fact, it can be perfectly inscribed in a pentagon and it follows the diagonals which form the pentagram.

Doryphoros

(Polycletus, 450 b.C., lost bronze original; the marble copy by an unknown artist is located in the Archaeological Museum of Naples, Italy)

In classical Greek sculpture the idea of beauty was associated with proportions. Each part of the body was in golden proportion to the others. An example is provided by the statue of Doryphoros (spear bearer) made by Polykleitos, an ancient Greek sculptor, bronzesmith and theorist, active about between 460 b. C. and 420 b.C. The bronze original of the statue has been lost, but the best Roman copy of the original was found in Pompeii.

The characteristic of the sculpture is represented to the proportions and the numerous golden rectangles into which the statue can be disassembled. In particular, the size of the head of the Doryphoros is exactly 8 times the length of the body. The number 8, given by the sum of 5 and 3, leads back to the Fibonacci sequence, characterized by the fact that the ratio between a number of the sequence and its previous one gets closer and closer to the golden number φ, as one proceeds in the number sequence:

1. Riace's bronzes

(5th century b.C., National Museum of Magna Grecia, Reggio Calabria, Italy)

2. Aphrodite Cnidia

(Praxiteles, around 360 b.C., Roman National Museum, Palazzo Altemps, Rome, Italy)

1. Riace's bronzes - They are two bronze statues of Greek origin, received in an exceptional state of conservation on 16 August 1972 near Riace Marina. The two statues are considered among the most significant sculptural masterpieces of Greek art. The hypotheses on their origin and on the authors are different, but there are still no elements capable of attributing them, with certainty, to a specific sculptor.

2. Aphrodite Cnidia - This marble sculpture, known today only through copies from the Roman era, is the first female nude in Greek art. The work was created by Praxiteles, considered one of the great masters of Greek sculpture of the 4th century b.C.

In both sculptures the following golden ratios can be identified:

AB : CB = CB : AC

AC : DC = DC : AD

CB : CE = CE : EB

1. 2.