and living so near Thales' home city of Miletus, it may be that Phthagoras studied under the older man. He then appears to have sojourned in Egypt and may even have indulged in more extensive travel. Returning home, he found Samos under the tyranny of Polycrates and ionia under the dominion of the Persians; accordingly, he migrated to the Greek seaport of Crotoma, located in southern Italy. There he founded the famous Pythagorean school, which, in addition to beong an academy for the study of philosophy, mathematics, and natural science, developed onto a closely knit brotherhood with secret rites and observances. In time, the influence and aristocratic tendencies of the brotherhood became so great that the democratic forces of southern Italy destroyed the buildings of the school and caused the society to disperse. According to one report, Pythagoras fled to Metapontum where he died, maybe murdered, at an advanced age of seventy-five to eighty. The brotherhood, although scattered, continued to exist for at least two centuries more.
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ERATOSTHENES(ca. 203 B.C)
Eratosthenes was a native of Cyrene, on the south coast of the Mediterranean Sea, and was only a few uears younger than Archimedes. He spent many years of his early life in Athens and, at about the age of forty, was invited by Ptolemy ¥² of Egypt to come to Alexandria as turor to his son and to serve as chief librarian at the University there. It is told that in old age, about 194 B.C. he became almostblind from lphthalmia and committed suicide by voluntary stavation.
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Eratosthenes was singularly gifted in all the branches of knowledge of his time. He was distinguished as a mathemarician, an astronomer, a tgeographer, an historian, a philosopher, a poet, and an athlete. It is said that the students at the University of Alexandria used to call himpentathlus, the champion in five athletic sports. He was also called Beta, and some speculation has been offered as to the possible origin of this nickname. some believe that it was because his broad and brilliant knowledge caused him to be looked upon as a second Plato. A less kind explanation is that, although he was gifted in many field in many fields, he always failed to top his contemporaries in any one brach; in other words, he was always second best. Each of these explanations weakens somewhat when it is learned that certain astronomer Apollonius (very likely Apollonius of Perga) was called Epsilon. Because if this, the historian James Gow has suggested that perhaps Beta and Epsilon arose simply fron the Greek numbers (2 and5) of certain offices or lecture rooms at the University particularly associated with the two men. On the other hand, Ptolemy Hephaesitio claimed that Apollonius was called Epsilon because he studied the moon, of which the letter e symbol.
In arithmetic, Eratosthenes is noted for a device known as the sieve, which is used for finding all the prime numbers less than a given number n. One writes down, in order and starting with 3, all the odd numbers less than n. The composite numbers in the sequence are then sifted out by crossing off, from 3, every third number, then from the next remaining number, 5, every fifth number, then from the next remaining number,7, every seventh number, from the next remaining number, 11, every eleventh number, and so on. In the process some number will be crossed off more than once. All the remaining number along with the number 2, constitute the list of primes less than n. |
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