. Both men and women were permitted to become members of the Society, in fact several later women Pythagoreans became famous philosophers. For the mathematikoi , being a Pythagorean was a question of innate quality and inner understanding. As a child Pythagoras spent his early years in Samos but travelled widely with his father. This generalisation stemmed from Pythagoras's observations in music, mathematics and astronomy. Pythagoras is believed to have eventually left Samos when he was about 40 years old during the reign of Polycrates. He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements.
The Pythagorean Theorem Pythagoras believed the earth was round and that the sun, moon, and other planets had their own movements. For instance, playing half a length of a guitar string gives the same note as the open string, but an octave higher; a third of a length gives a different but harmonious note; etc. The number 10 is arrived at when all the rows are added. He was one of the first to think that the earth was round, that all planets have an axis, and that all the planets travel around one central point. Pythagoras founded a philosophical and religious school in Croton now Crotone, on the east of the heel of southern Italy that had many followers. Because legend and obfuscation cloud his work even more than with the other pre-Socratics , one can say little with confidence about his life and teachings.
The other two philosophers who were to influence Pythagoras, and to introduce him to mathematical ideas, were and his pupil who both lived on Miletus. Instead they were taught laws of behavior and morality in the form of cryptic, brief sayings that had hidden meanings. In the visits to various places in Greece — Delos, Sparta, Phlius, Crete, etc. One member of his order, Hippasos , also discovered irrational numbers , but the idea was unthinkable to Pythagoras, and according to legend, Hippasos was executed. So he may or may not have discovered the theorem of geometry that bears his name. 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. 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.
Music featured as an essential organizing factor of this life: the disciples would sing hymns to Apollo together regularly; they used the lyre to cure illness of the soul or body; poetry recitations occurred before and after sleep to aid the memory. Pythagoras did not invent this idea, nor was he first to publish it. Non-whole number ratios, on the other hand, tend to give dissonant sounds. This suggests that the strange sayings were riddles for the initiated. Another legend, also taken from Brewer's Dictionary, describes his writing on the moon:.
He has been credited for the Pythagorean theorem which bears his name, possibly his greatest achievement. Although one of Pythagoras' contributions to mathematics was the Pythagorean Theorem, he also proved other axioms, worked on prime and composite numbers and found an irrational number. While the theorem that now bears his name was known and previously utilized by the Babylonians and Indians, he, or his students, are often said to have constructed the first proof. Odd numbers were masculine and even numbers were feminine. Some attribute it as a carefully constructed myth by followers of Plato over two centuries after the death of Pythagoras, mainly to bolster the case for Platonic meta-physics, which resonate well with the ideas they attributed to Pythagoras.
It is the foundation of the geometry still being taught in schools almost two and one-half millennium after Euclid's death. Damo is one of the daughters of Theano and Pythagoras. At the age of eighteen, Pythagoras traveled to Miletus to meet Thales, a master of mathematics and astronomy. There is some evidence to suggest that Pythagoras and Polycrates were friendly at first and it is claimed 5 that Pythagoras went to Egypt with a letter of introduction written by Polycrates. It is possible that Pythagoras had a variety of teachers as a boy and a young man.
They were the first ancient mathematicians to have the same priorities as modern mathematicians. 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. A key component to this religion and its two schools was the notion that mathematics was mystical, hence, appropriate as an influential basis for a religion. It moves from one being to another, sometimes from a human into an animal, through a series of reincarnations called transmigration until it becomes pure. Primarily, however, Pythagoras was a philosopher. Indeed, it is by no means clear whether many or indeed any of the theorems ascribed to him were in fact solved by Pythagoras personally or by his followers. These writers, late as they are, were among the best sources from whom Porphyry and Iamblichus drew, besides the legendary accounts and their own inventions.
They were not acting as a mathematics research group does in a modern university or other institution. Very strict rules of conduct governed this cultural center. It is probable that both were influenced by Orphism. It is not difficult to relate many of Pythagoras's beliefs, ones he would later impose on the society that he set up in Italy, to the customs that he came across in Egypt. Although the theorem, now known as Pythagoras's theorem, was known to the Babylonians 1000 years earlier he may have been the first to prove it. They performed purification rites and followed and developed various rules of living which they believed would enable their soul to achieve a higher rank among the gods. At first, the school was highly concerned with the morality of society.
This was, according to Iamblichus, used in part as an excuse for Pythagoras to leave Samos:-. Pythagoras and hisfollowers used lines, triangles, and squares made out of pebbles torepresent numbers. In fact today we have become so mathematically sophisticated that we fail even to recognise 2 as an abstract quantity. He himself claimed to have lived four lives that he could remember in detail, and heard the cry of his dead friend in the bark of a dog. Hence historians are often reduced to consider the statements based on their inherent probability, but even then, if all the credible stories concerning the history of Pythagoras were supposed true, his range of accomplishments and achievements would be impossibly vast. Pythagoras was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato, and through him, all of Western philosophy. This generalisation stemmed from Pythagoras's observations in music, mathematics and astronomy.