Pythagoras of Samos

Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know little about his achievements. There is nothing that is truly accurate pertaining to Pythagoras’s writings. Today Pythagoras is certainly a mysterious figure. Little is known of Pythagoras’s childhood. Pythagoras’s father was Mnesarchus, and his mother was Pythais. Mnesarchus was a merchant who came from Tyre. Pythais was a native of Samos. As a child Pythagoras spent his early years in Samos, but traveled with his father.

There are accounts, that during their travels, Mnesarchus returned to Tyre with Pythagoras, and had him taught there by the Chaldaeans. Certainly growing up he was well educated, learning to play the lyre, learning poetry, and learning how to recite Homeric plays. (www. parmenides. com) There were three philosophers, though, who had an influence on Pythagoras while he was a young man. One of the most important was Pherekydes who was described as the teacher of Pythagoras. The other two philosophers were Thales and his pupil Anaximander, who both lived on Miletus.

Pythagoras visited Thales when he was between 18 and 20 years old. By this time Thales was an old man, and probably didnt teach him a great deal. Yet, he advised Pythagoras to travel to Egypt, and learn more in the field of mathematics and astronomy. Thales’s pupil, Anaximander, lectured in Miletus, and Pythagoras attended. Anaximander was interested in geometry and cosmology. Many of his ideas influenced Pythagoras’s own views. Pythagoras went to Egypt after a tyrant named Polycrates seized control of Samos. His time in Egypt was spent visiting many temples and taking part in many discussions with priests.

Later, in a temple at Diospolis, Pythagoras was accepted into priesthood after completing the rites necessary for admission. Pythagoras moved on and later learned geometry from the Egyptians, but it is likely that he was already acquainted with geometry from the teachings of Thales and Anaximander. (www. kyes-world. com) Cambyses II, the king of Persia, invaded Egypt. Pythagoras was captured, and taken prisoner in Babylon. Soon after Pythagoras left Babylon and returned to Samos, but it is nowhere explained how Pythagoras gained his freedom.

Polycrates had been killed, which may have been a factor in Pythagoras’s return to Samos. Darius of Persia had taken control of Samos after Polycratess death and still controlled the island during Pythagoras’s return. Pythagoras made a journey to Crete shortly after his return to Samos to study the system of laws there. After a short stay in Crete, Pythagoras found himself back in Samos. There he discovered a school called the semicircle. This was the site of his own philosophical teaching, spending most of the night and daytime there and doing research into the uses of mathematics.

He tried to use his unique method of teaching, which was similar to the lessons he had learned in Egypt, but Samians were not very keen on this. Pythagoras saw that the Samians were not giving him the respect and credit he deserved, so he moved on Pythagoras left and founded a philosophical/religious school in Croton on the southern tip of Italy. His school practiced secrecy and communalism making it hard to tell the difference between the work of Pythagoras and work of his followers. Although it did made outstanding contributions to mathematics.

Pythagoras gained many followers there, and became the head of a 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 werent acting as a mathematics research group does in a modern university. There were no open- problems for them to solve, and they were not in any sense interested in trying to create or solve mathematical problems. Rather Pythagoras was interested in teaching the principles of mathematics, the concept of number, and the concept of a triangle or other figure. (www. cdc. et/cbjlinks/Fun_Math_for_Kids. html) The mathematikoi were taught by Pythagoras himself and obeyed strict rules.

The beliefs that Pythagoras held were: (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. The outer circle of the Society was 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. Pythagoras studied properties of numbers, which is familiar to mathematicians today, such as even and odd numbers, triangular numbers, perfect numbers etc. However to Pythagoras numbers had personalities, masculine or feminine, perfect or incomplete, beautiful or ugly. (www. excite. com) Of course today we pretty much remember Pythagoras for his famous theorem. His view of mathematics is long gone. Today this list of theorems attributed to Pythagoras, or rather to the Pythagoreans, is the only contribution that we accept, know about, or put to good use. 1) The sum of the angles of a triangle is equal to two right angles. (2) The theorem of Pythagoras – for a right triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. (3) Constructing figures of a given area and geometrical algebra. For example they solved equations such as a (a – x) = x2 by geometrical means. (4) The discovery of irrationals. 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. (5) The five regular solids. 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. (6) In astronomy Pythagoras taught that the Earth was a sphere at the center of the Universe.

He also recognized that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realize that Venus as an evening star was the same planet as Venus as a morning star. (Primarily, as you can see, Pythagoras was a philosopher before a mathematician according to todays standards. ) Pythagoras’s Society at Croton was not unaffected by political events despite his desire to stay out of politics. Pythagoras went to Delos to nurse his old teacher Pherekydes who was dying. He stayed there for a few months until the death of his teacher, and then returned to Croton.

Upon his return, Croton attacked and defeated its neighbor Sybaris. (There are some suggestions that Pythagoras became involved in the dispute. ) Then Cylon, a noble from Croton, attacked the Pythagorean Society at. Pythagoras escaped to Metapontium and the most authors say he died there, some claiming that he committed suicide because of the attack on his Society. Though, this is just a speculation. The evidence is unclear as to when and where the death of Pythagoras truly occurred. The Pythagorean Society thrived for many years after this and spread from Croton to many other Italian cities.

It became political in nature, and spilt into a number of factions. (www. infoseek. com) Now Pythagoras is looked upon as a great contributor to the field of mathematics, and a mysterious person. The lack of hard-core information on this person is reflected by the small amount of publicity he himself has received. Certainly though, Pythagoras has, and will continue to live on through his theorems as long as they stand the test of time. Note: All information contained and used within this report was retrieved from the Internet. None of the information contained within has been proven to be irrefutable fact.


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