OF PYTHAGORAS AND THE PYTHAGOREAN THEOREM
"Pythagoras was born around 570 B.C. in the island of Samos in the Aegean Sea (off Asia Minor), and he emigrated sometime between 530 and 510 to Croton in the Dorian colony in southern Italy (then known as Magna Gracia). ... Perhaps following the advice of his presumed teacher, the mathematician Thales of Miletus, Pythagoras probably lived for some time (as long as twenty-two years, according to some accounts in Egypt, where he later learned mathematics, philosophy, and religious themes from the Egyptian priests. After Egypt was overwhelmed by Persian armies, Pythagoras may have been taken to Babylon, together with members of the Egyptian priesthood. To both of these peoples, mathematics provided practical tools in the form of "recipes" designed for specific calculations. Pythagoras on the other hand, was one of the first to grasp numbers as abstract entities that exist in their own right...
"Pythagoras established a strict routine for his students, paying particular attention to the hour of waking and the hour of falling asleep. Students were advised upon rising to repeat the verses:
"As soon as you awake, in order lay
the actions to be done the coming day."
"Similarly, at nightfall, they were to recite:
"Allow not sleep to close your eyes
Before three times reflecting on
Your actions of the day. What deeds
Done well, what not, what left undone?"
"Most of the details of Pythagoras' life and the reality of his mathematical contributions remain veiled in uncertainty....Pythagoras apparently wrote nothing, and yet his influence was so great that the more attentive of his followers formed a secretive society, or brotherhood, and were known as the Pythagoreans...
"Even though it is almost impossible to attribute with certainty any specific mathematical achievements either to Pythagoras himself or to his followers, there is no question that they have been responsible for a mingling of mathematics, philosophy of life, and religion unparalleled in history. In this respect it is perhaps interesting to note the historical coincidence that Pythagoras was a contemporary of Buddha and Confucius.
"Pythagoras is in fact credited with having coined the words "philosophy" ("love of wisdom") and "mathematics" ("that which is learned"). To him, a "philosopher" was someone who gives himself up to discovering the meaning and purpose of life itself....to uncover the secrets of nature." Pythagoras emphasized the importance of learning above all other activities, because, in his words, "most men and women by nature and birth, lack the means to advance in wealth and power, but all have the ability to advance in knowledge...
"Pythagoras and the Pythagoreans are best known for their presumed role in the development of mathematics and for the application of mathematics to the concept of order, whether it is musical order, the order of the cosmos, or even ethical order. Every child in school learns the Pythagorean theorem of a triangle that has a right (90 degree) angle (a right triangle)...."
pp.24-27, THE GOLDEN RATIO: THE STORY OF PHI, THE WORLD'S MOST ASTONISHING NUMBER, by Mario Livio (Broadway Books, div. of Random House, Inc., New York:2002)
