Pythagoras's Society example essay topic

Pythagoras of Samos is a man who was more than just a mathematician. A Greek philosopher, founder of the Pythagorean brotherhood, he was an extremely important political figure for his time. He invented vegetarianism and created one of the first secret organizations. Not much is known about his mathematical achievements because he never wrote anything down. It is unsure where his views end and his disciple's views began. He influenced Plato and Aristotle and made contributions to the development of mathematics and western philosophy.

Details of Pythagoras's life stem from early biographies and there are conflicting reports of his birth date and death. It is clear that his father's name was Mnesarchus and his mother's name was Py thais. Mnesarchus was a merchant who originated from Tyre and who is thought that his father was seen as a hero to the village for bringing food to the people during a famine. It is said that he was granted citizenship to Samos instantly for his great effort. Pythagoras traveled to many places with his father and was taught by a group called the Chaldeans and intelligent men of Syria. Pythagoras's childhood was most likely spent learning to play the lyre, learning poetry and reciting Homer.

His physical appearance is unknown except for a scar he might have had on his thigh. Among his teachers there were three men that influenced him the most Pherekydes, Thales, and Anaximander. Thales might have been the most influential to Pythagoras' formulation of a mathematical following. He did not teach him very much on other subjects but peaked his interest in math and astronomy. Anaximander was Thales' pupil.

He gave lectures on geometry and cosmology and these ideas influenced Pythagoras as well. During his time in Egypt, Pythagoras spent time with priests and visiting temples. He also became a priest at the temple Dio polis. He was so intrigued by the traditions of the Egyptians that he incorporated the secrecy of the priesthood, the refusal to eat beans, and the refusal to wear clothes made from animal skins into his methods of teaching. While in Egypt, Pythagoras was captured and taken to Babylon.

In prison, Pythagoras learned about sacred rites and mystical worships of the gods from the Mago i. He also reached the pinnacle of perfection in arithmetic and music and the other mathematical sciences taught by the Babylonians. Pythagoras returned to Samos to find two rulers dead and the town in political turmoil. Pythagoras created his first school in the city of Samos. It was called the 'semicircle' of Pythagoras because this is where the citizens held meeting's on goodness and justice. It was only fitting that they have these discussions there because it was this man who made it his business to be interested in these subjects.

Outside the city he had a private cave that he called home to all of his philosophical teaching and mathematical research. Pythagoras left Samos for a number of reasons; the Samoans were rude to him and not interested in his new symbolic method of teaching, and the citizens wanted him to be a vital part in the town's public affairs and he wanted nothing more than not to be a part of that. Ultimately, he used the non-acceptance excuse to get away and move to a small town named Croton located in southern Italy. Living comfortably in Croton, Pythagoras founded the school he was known for. This philosophical and religious Society consisted of two circles inner being the most devout and outer given less restriction.

Pythagoras was at the head of the Society and the inner circle was named the mathematikoi. The mathematikoi lived permanently within the society, had no personal possessions and were vegetarians. They were taught directly by Pythagoras and were meant to obey 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". (Excite. com) Men and women were allowed to enter the Society and actually several women Pythagoreans became famous philosophers. The Pythagoreans believed in the idea of immortality and in the transmigration of souls.

The outer circle of the Society was known as the akousmatics. They were allowed to live in their own houses, possessions, and not required to be vegetarians. They did however come to the Society every day. It is hard to say which ideas that came from the Society were the complete works of Pythagoras or his followers. Pythagoras was interested in the principles of mathematics, the concept of number, the concept of a triangle or mathematical figure and the abstract idea of a proof.

Pythagoras believed that any relation could be reduced to a number relation. He thought that things are numbers and that the whole universe is a scale and a number. Pythagoras was a prominent musician and made notable advancements to the mathematical theory of music. He looked at whole numbers and ratios and recognized that these ratios could be applied to other instruments. He also studied the properties of numbers for example even and odd numbers, triangular, perfect numbers, and prime and square numbers.

On the other hand, Pythagoras looked at numbers as having personalities. They could be "masculine or feminine, perfect or incomplete, and beautiful or ugly" (excite. com). The Society cultivated the concept of number, which became for them the ultimate principle of all proportion, order, and harmony in the universe. (Encarta. com) Then came the famous Pythagorean theorem. It is said that the Babylonians knew of the theorem 1000 years ago but it was Pythagoras who first proved it on paper. The Pythagoreans continued to prove more theorems like these: (i) The sum of the angles of a triangle is equal to two right angles.

Also the Pythagoreans knew the generalization, which states that a polygon with n sides has sum of interior angles 2 n - 4 right angles and sum of exterior angles equal to four right angles. (ii) The theorem of Pythagoras - for a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. Note 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. ( ) Constructing figures of a given area and geometrical algebra. For example they solved equations such as a (a - x) = x 2 by Geometrical means. (iv) 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. (v) 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. (vi) 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. Pythagoras was not only a mathematician but a philosopher as well.

He held the following ideals about philosophy and ethics: "the dependence of the dynamics of world structure on the interaction of contraries, or pairs of opposites; the viewing of the soul as a self-moving number experiencing a form of metempsychosis, or successive reincarnation in different species until its eventual purification (particularly through the intellectual life of the ethically rigorous Pythagoreans); and the understanding that all existing objects were fundamentally composed of form and not of material substance". (excite. com) A Pythagorean doctrine identifies the as the center of the soul. The Pythagoreans held strict ethical practices. They were known for their mutual friendship, unselfishness, and honesty. Despite all of his efforts, Pythagoras's society was affected by politics. Pythagoras went to Delos to aide his ailing teacher Pherekydes. There was a war between Croton and its neighbor Sybaris and it is said that Pythagoras had been involved in some way.

Unexpectedly, his own Society was attacked by a noble from Croton. Pythagoras managed to escape but there are conflicting reports to when he actually perished. It is clear that the Society was thriving at the same time under attack for its ideals. At the time of Pythagoras's reported death the Society continued for many years and spread to other Italian countries. The Society also became politically involved and split into a number of sections. Pythagoras is a world-renowned contributor to mathematics and a mystifying person.

We can never know how much he truly gave or could have given to the math world, but his legacy lives on through his unbeatable achievements.

Bibliography

1. web 2. web The Mathematical Traveler: Exploring the Grand History of Numbers by Calvin C. Clawson, Perseus Books Group, April 19944.
Pythagoras". Microsoft Encarta Online Encyclopedia 2001 web.