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Chanele Royal January 10, 2008
Computational Foundations Mathematician Essay
Pythagoras
Pythais also known as Pythagoras was born between the days of c. 580 B.C.-572 B.C. in Samos, a Greek island in the eastern Aegean, off the coast of Asia Minor. As a young man he left his birth place for Croton, Calabria, in southern Italy, to escape the tyrannical government of Polycrates. Soon later he headed off to Memphis in Egypt and study with the priests there who were renowned for their wisdom. In Egypt Pythagoras learned some geometric principles which eventually inspired his formulation the theorem that is now called by his name. Pythagoras established a secret religious society very similar to the earlier Orphic cult. Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and form an elite circle of followers around himself called Pythagoras.
There were very strict rules of conduct in this cultural center. He had opened his school to male and female students alike. Those that had joined the inner circle of Pythagoras’s society called themselves Mathematikoi. They lived at the school, owned no personal possessions and were required to assume a mainly vegetarian diet which is meat that could be sacrificed was allowed to be eaten. Other students lived in the neighboring areas were permitted to attend Pythagoras’s school. They were known as Akousmatikoi, these students were permitted to eat meat and own personal belongings. Pythagoras followed a structured life of religious teachings, common meals, exercise, reading and philosophical study. Music was 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 was familiar with the Jewish beliefs, incorporating some of them in his own philosophy. Pythagoras is commonly given credit for discovering the Pythagorean Theorem, a theorem in trigonometry that states that in a right-angled triangle the square of the hypotenuse, the side that is opposite of the right angle, c, is equal to the sum of the squares of the other two sides, a and b, a squared + b squared = c squared. While the theorem that now bears his name was known and previously utilized by the Babylonians, and Indians, he, or his students, are thought to have constructed the first proof; because of secretive nature of his school and the custom of its students to attribute everything to their teacher, there is no evidence that Pythagoras himself worked on or proved this theorem. For that matter, there is no evidence that Pythagoras had worked on any mathematical problems. Some of Pythagoras influences were Thales, Anaximander and Pherecydes. Pythagoras has influenced many people and groups like Philolaus, Alcmaeon, Parmenides, Plato, Euclid, Empedocles, Hippasus and Kepler.
The organization was in some ways a school, a brotherhood and even a monastery. It was based upon Pythagoras’ religious teachings and was very secretive. At first, the school was highly concerned with the morality of society. Members were required to live ethically, love one another, share political beliefs, practice pacifism, and devote themselves to the mathematics of nature. Pythagoras’s followers were commonly called “Pythagoreans”. For the most part we remember them as philosophical mathematicians who had an influence on the beginning of axiomatic geometry, which after two hundred years of development was written down by Euclid in The Elements.
One of Pythagoras’s major accomplishments was the discovery that music was based on proportional intervals of the numbers one through four. He believed that the numbers system, and therefore the universe system, was based on the sum of these numbers: ten. Pythagoras believed that odd numbers were masculine and even numbers were feminine. He discovered the theory of mathematical proportions, constructed from three to five geometrical solids. Hippasos also discovered irrational numbers, but the idea was unthinkable to Pythagoras, and according to one version was executed. Pythagoras also had discovered squared numbers he found that if he had took four small stones and rearranged them in a square and counted all the stones together you would get four squared. They equaled the sum total of stones in the square arrangement, hence the name “Square Root”. Pythagoras died between the days of c.500 B.C -490 B.C. near the age of 90. Pythagoras is known as “the father of numbers”. One of Pythagoras most famous quote is “number is the ruler of forms and ideas and the cause of gods and demons”. Pythagoras may be gone, but he still lives on.
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