According to Pythagoras an entity is called a number when the product of itself is greater than the sum of itself. One is not a number, according to the above definition, it is god, generator of numbers. Two is also not a number, because both the product and the sum are equal to each other, that is, it is a coexisting god, a second generator of numbers. The numbers start with three because 3 X 3 = 9 an
The Tetraktys is the Essence of Teaching and the Sacred Symbol of the Pythagoreans. It consists of the first ten numbers (1-10) arranged in four rows (one in the first row, two in the second, three in the third and four in the fourth row) as shown in the picture. Tetraktyn was called “Tetradas”[1] which in Pythagorean Philosophy is the essence and meaning of the number four. Tetraktys is the fourth “triangular number”[2] thus showing another view of the relationship of Tetrad and Tetraktyos. In any case, we should not forget the relation of Tetraktys with “Ten”. From this the Tetraktys is mentioned according to Iamblichus with the prepositional names: Cosmos (decoration, ornament), Pan (the god Panas – Pan = All), Uranus, Atlas, Key, Aion, Memory, Gnomon, Eimarmene, Kratos, Phanis, Helios, Pythmen et al. By studying the concepts of numbers found in the Tetractyn and their relationships, the Pythagoreans argue that one reaches the attainment of wisdom.
The main relationship of Tetrad and Tetraktyos can also be seen from the famous relationship of the first four numbers with the ten they produce when added (1+2+3+4=10). From these first four numbers (1, 2, 3 & 4), it is possible to construct the ratios: “by four” (4:3, fourth), “by five” (3:2, fifth), “by all ” (2:1, Octave), which attribute to music the mentioned harmonic musical intervals which Pythagoras was the first to precisely determine with numerical reasons. These proportions create Harmony, which for the Pythagoreans has a literally cosmic meaning (hence its name “Cosmos”). The Pythagoreans used the Tetraktyn to swear, even invoking Pythagoras as a god, as can be seen from the “Golden Epics” where it is stated:
“Yes, with the immortal soul, delivered four times
always of a permanent nature.”
(yes, but the one who delivered to our soul the tetractyn,
which is the source of eternal nature.)
Numbers are related to geometric shapes. Thus the unit is related to the point, the dyad to the line, the triad to the triangle, and the tetrad or tetraktys to the tetrahedron (or triangular pyramid), the first geometric solid. Its symbol was considered the square which was also the symbol of the divine and perfection.[5]. Also wisdom was considered to be acquired from the four esoteric sciences for the Pythagoreans of arithmetic, music, geometry and astronomy. It is a symbol of God Apollo and the Pythagoreans connect the Tetraktyn with the Oracle of Delphi, as seen in the important “hearing” about existence mentioned by Iamblichus[6]: “what is the Oracle in Delphi? Tetraktys” (what is the Oracle of Delphi? Tetraktys).
There is another Tetraktys, as mentioned in Plato’s Timaeus, which is called a double Tetraktys and consists of eight lines created by the first eight numbers (1, 2, 3, 4, 5, 6, 7, which in total give a total of 36 (1+2+3+4+5+6+7+8=36). From another point of view this Quadrilateral is created, and thus connected to the regular Quadrilateral Quadrilateral, by the sum of the first four odd numbers and of the first four integers: (1+3+5+7)+(2+4+6+8)=36 as mentioned by Plutarch in “On Isis and Osiris”.
GOLDEN RATIO Φ ON THE PYTHAGORIAN SYMBOL
PARTHENON WAS BUILT on the PRNICIPLES of PYTHAGORAS
The FIRST FLYING MASCHINE was BUILT by the GREEK PYTHAGOEIAN PHILOSOPHER ARCHYTAS in TARANTO(CORINTHIAN COLONY) SOUTHERN ITALY.
For the Pythagoreans, a politician was the person who, after having been taught philosophy, returned to the world to be useful to others.
He is not interested in positions and powers but in the improvement of society.
The one who chose to become a politician could not pass to the stage of a mathematician, that is, one who can deliver lessons and teach.
Those who could had the advantage of living near Pythagoras.
Friendship and companionship were of the highest importance for the Pythagoreans and they considered that universal love was reflected in these two elements.
They were bound by an oath of secrecy over the higher teaching, the ceremonies and the sacred symbols.
Pythagoras offered mankind a universal “successful experiment” for this and later Plato would call education with music and gymnastics!!!!
ONE OF THE BASIC PYTHAGORIAN GROUNDS FOR: ARCHITECTURE, GEOMETRY, MUSIC, STEREOMETRY, ASTRONOMY, HARMONY AND PHILOSOPPHY
WHAT DID PYTHAGORAS SAYABOUT WOMAN=ΓΥΝΗ/GYNE
https://euphoriatric.com/pythagoras-the-nine-muses/ 
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