What kind of education did pythagoras have

Many of the practices of the society he created later in Italy can be traced to the beliefs of Egyptian priests, such as the codes of secrecy, striving for purity, and refusal to eat beans or to wear animal skins as clothing.

Ten years later, when Persia invaded Egypt, Pythagoras was taken prisoner and sent to Babylon in what is now Iraq , where he met the Magoi, priests who taught him sacred rites. Iamblichus AD , a Syrian philosopher, wrote about Pythagoras, "He also reached the acme of perfection in arithmetic and music and the other mathematical sciences taught by the Babylonians His methods of teaching were not popular with the leaders of Samos, and their desire for him to become involved in politics did not appeal to him, so he left.

Pythagoras settled in Crotona, a Greek colony in southern Italy, about BC, and founded a philosophical and religious school where his many followers lived and worked. The Pythagoreans lived by rules of behavior, including when they spoke, what they wore and what they ate. Pythagoras was the Master of the society, and the followers, both men and women, who also lived there, were known as mathematikoi. They had no personal possessions and were vegetarians.

Another group of followers who lived apart from the school were allowed to have personal possessions and were not expected to be vegetarians. They all worked communally on discoveries and theories. Pythagoras believed:. Because of the strict secrecy among the members of Pythagoras' society, and the fact that they shared ideas and intellectual discoveries within the group and did not give individuals credit, it is difficult to be certain whether all the theorems attributed to Pythagoras were originally his, or whether they came from the communal society of the Pythagoreans.

Some of the students of Pythagoras eventually wrote down the theories, teachings and discoveries of the group, but the Pythagoreans always gave credit to Pythagoras as the Master for:. Pythagoras studied odd and even numbers, triangular numbers, and perfect numbers. Pythagoreans contributed to our understanding of angles, triangles, areas, proportion, polygons, and polyhedra. Pythagoras also related music to mathematics. Pythagoras was dragged into all sorts of diplomatic missions by his fellow citizens and forced to participate in public affairs.

He knew that all the philosophers before him had ended their days on foreign soil so he decided to escape all political responsibility, alleging as his excuse, according to some sources, the contempt the Samians had for his teaching method. Pythagoras founded a philosophical and religious school in Croton now Crotone, on the east of the heel of southern Italy that had many followers. Pythagoras was the head of the society with an inner circle of followers known as mathematikoi.

The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict rules.

The beliefs that Pythagoras held were [ 2 ] :- 1 that at its deepest level, reality is mathematical in nature, 2 that philosophy can be used for spiritual purification, 3 that the soul can rise to union with the divine, 4 that certain symbols have a mystical significance, and 5 that all brothers of the order should observe strict loyalty and secrecy.

Both men and women were permitted to become members of the Society, in fact several later women Pythagoreans became famous philosophers. The outer circle of the Society were known as the akousmatics and they lived in their own houses, only coming to the Society during the day.

They were allowed their own possessions and were not required to be vegetarians. Of Pythagoras's actual work nothing is known. His school practised secrecy and communalism making it hard to distinguish between the work of Pythagoras and that of his followers. Certainly his school made outstanding contributions to mathematics, and it is possible to be fairly certain about some of Pythagoras's mathematical contributions.

First we should be clear in what sense Pythagoras and the mathematikoi were studying mathematics. They were not acting as a mathematics research group does in a modern university or other institution. There were no 'open problems' for them to solve, and they were not in any sense interested in trying to formulate or solve mathematical problems.

Rather Pythagoras was interested in the principles of mathematics, the concept of number, the concept of a triangle or other mathematical figure and the abstract idea of a proof.

As Brumbaugh writes in [ 3 ] :- It is hard for us today, familiar as we are with pure mathematical abstraction and with the mental act of generalisation, to appreciate the originality of this Pythagorean contribution. In fact today we have become so mathematically sophisticated that we fail even to recognise 2 as an abstract quantity.

There is another step to see that the abstract notion of 2 is itself a thing, in some sense every bit as real as a ship or a house. Pythagoras believed that all relations could be reduced to number relations. As Aristotle wrote:- The Pythagorean This generalisation stemmed from Pythagoras's observations in music, mathematics and astronomy.

Pythagoras noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments.

In fact Pythagoras made remarkable contributions to the mathematical theory of music. He was a fine musician, playing the lyre, and he used music as a means to help those who were ill. Pythagoras studied properties of numbers which would be familiar to mathematicians today, such as even and odd numbers, triangular numbers , perfect numbers etc. However to Pythagoras numbers had personalities which we hardly recognise as mathematics today [ 3 ] :- Each number had its own personality - masculine or feminine, perfect or incomplete, beautiful or ugly.

This feeling modern mathematics has deliberately eliminated, but we still find overtones of it in fiction and poetry. Of course today we particularly remember Pythagoras for his famous geometry theorem. Although the theorem, now known as Pythagoras's theorem, was known to the Babylonians years earlier he may have been the first to prove it. Proclus , the last major Greek philosopher, who lived around AD wrote see [ 7 ] :- After [ Thales , etc. Again Proclus , writing of geometry, said:- I emulate the Pythagoreans who even had a conventional phrase to express what I mean "a figure and a platform, not a figure and a sixpence", by which they implied that the geometry which is deserving of study is that which, at each new theorem, sets up a platform to ascend by, and lifts the soul on high instead of allowing it to go down among the sensible objects and so become subservient to the common needs of this mortal life.

Heath [ 7 ] gives a list of theorems attributed to Pythagoras, or rather more generally to the Pythagoreans. We should note here that to Pythagoras the square on the hypotenuse would certainly not be thought of as a number multiplied by itself, but rather as a geometrical square constructed on the side.

To say that the sum of two squares is equal to a third square meant that the two squares could be cut up and reassembled to form a square identical to the third square. This is certainly attributed to the Pythagoreans but it does seem unlikely to have been due to Pythagoras himself. This went against Pythagoras's philosophy the all things are numbers, since by a number he meant the ratio of two whole numbers.

However, because of his belief that all things are numbers it would be a natural task to try to prove that the hypotenuse of an isosceles right angled triangle had a length corresponding to a number. It is thought that Pythagoras himself knew how to construct the first three but it is unlikely that he would have known how to construct the other two.

He also recognised that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realise that Venus as an evening star was the same planet as Venus as a morning star. References show. Biography in Encyclopaedia Britannica. M Cerchez, Pythagoras Romanian Bucharest, Diogenes Laertius, Lives of eminent philosophers New York, P Gorman, Pythagoras, a life C Byrne, The left-handed Pythagoras, Math.

Intelligencer 12 3 , 52 - Canada 7 2 , - Ense nanza Univ. G Tarr, Pythagoras and his theorem, Nepali Math. Annalen - 49 , - , - Additional Resources show. Honours show. Cross-references show.