Decagon: symbol with unique properties

The mystique of the golden ratio

The mystique of numbers goes back to the Pythagoreans. For them, numbers had a symbolic value. The number "one" represented reason, for only reason could produce a consistent and harmonious body of knowledge. Even numbers were feminine f numbers, and odd numbers were masculine.

The number "two", the first even number, symbolized opinion, since the notion of opinion implies the possibility of a contrary opinion, and therefore of at least two opinions.

The number "three", the first triangular number, is also the first masculine number. The number "four" symbolized justice and fairness, as it was the first number obtained by multiplying equal numbers, i.e. the first square number.

As we saw earlier, the sequence of the first four integers 1,2,3,4 was called the Tetractys, and their sum 1 + 2 + 3 + 4 = 10 gives the Decade. The Tetractys was so important to the Pythagoreans that it is explicitly mentioned in the formula of the sacred oath by which their members committed themselves to secrecy.

The mystical value of the Tetractys was based as much on the symbols constituted by the numbers 1, 2, 3 and 4 as on the numerical relationships between these numbers.

What's more, certain musical ratios are obtained by the ratio of the numbers in the Tetractys: 1/2 gives the octave, 3/4 the fourth and 2/3 the fifth.

For the Pythagoreans, the Decad was the ideal number symbolizing the universe as they conceived it in accordance with this belief. For them, there were ten moving bodies in the heavens: Mercury, Venus, Mars, Jupiter, Saturn, the Sun, the Moon and the starry sphere. In addition, the earth revolved around a central fire that could not be seen because it was on the uninhabited side of the earth, its light and heat reflected by the Sun. The tenth body was called Antikton or anti-Earth. This body was also in revolution around the central fire, but on the opposite side of the Earth, so could not be seen.

Furthermore, if we divide the Decade by two, we obtain the Pentad, which symbolized marriage, as the number "five" is the union of "two", the first even or feminine number, and "three", the first masculine number. These considerations created a close relationship between the mysticism of the numbers ten and five and the mysticism of the golden ratio through the decagon and pentagon. So it's hardly surprising that the Pythagoreans regarded the pentagram (star pentagon) as a symbol of perfection, life, beauty and love, and used it as a sign of recognition.

This mysticism underpinned the use of the pentagram in the arts, both for aesthetic purposes and to invoke or propitiate secret forces. The pentagram is found in the rose windows of certain cathedrals, such as Saint-Ouen church in Rouen, Amiens cathedral and Saint-Rémi church in Troyes. It also features on the coat of arms and flag of Morocco and on the flags of several other countries.

The pentagonal structures found in certain flowers and starfish, as well as spiral growths, are further motifs that give the golden ratio a special meaning and associate it with beauty.