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Eratosthenes


By the year 220 BC many people already thought the earth was round, but no one could tell what its circumference was. Disagreeing with this state of affairs, a Greek citizen named Eratosthenes resolved to remedy the failure. But if he was nonconformist, he was also self-indulgent. And besides being a commodist, an astronomer, he tried to solve the matter without having to leave the house, using the sun. So many calculations he made that he eventually found a suitable system by which he could establish that the globe had 40000 km in circumference.

More than 2000 years later, scholars came to check Eratosthenes' calculations and were surprised: the new measurement, made with precision equipment and modern calculation systems, resulted in a figure virtually identical to that of the wise. That is: 40070 Km.

Eratosthenes was born in Cyrene, a Greek colony of North Africa, around the year 276 BC Brilliant from a young age, studied with the best teachers of his time and so famously became, that Pharaoh Ptolemy III of Egypt gave him the direction of the Library. of Alexandria, as well as the position of preceptor of his son.

There was virtually no subject Eratosthenes was not interested in: philosophy, history, grammar, poetry, geography, and mathematics all attracted him, and on each of these subjects he wrote works of great value. Astronomy and numbers, however, were his favorite subjects, and as all Greek science at that time was influenced by the ideas of Pythagoras, Eratosthenes was formed by the Pythagorean line, which admitted very advanced theories of the time. He accepted, for example, that the earth was a loose sphere in space, rotating together with several others around a central core of fire - a preview of the system that only much later Copernicus would spell out.

For the Pythagoreans, the explanation of the world was in the numbers. And for them Eratosthenes guided his entire career. Writing a treatise on geography, he divided the globe into parallels and meridians, making geographical location a mathematical work — a system that continues to use today. It also showed in this work that it was possible to reach India from Spain. And it suggested the existence of inhabited land in the West - as Columbus would prove seventeen hundred years later, upon his arrival in America.

Dealing with prime numbers (divisible only by themselves and unity) was a serious problem for the mathematicians of Alexandria. Eratosthenes decided to solve it and indeed did so by creating a table of progressive eliminations, with which it became easy to determine whether a number was prime or not. Widely used since then, his method is still present in the arithmetic manuals, in which he appears as "the sieve of Eratosthenes".

With an admirable amount of discoveries and innovations to his credit, Eratosthenes lived to be 80 years old. And he did not wait for death to summon him: he preferred suicide and let himself die in starvation.

To measure the size of the earth, Eratosthenes reasoned as follows: Syene and Alexandria were situated almost on the same meridian - the circumference of the earth. Syene was practically over the Tropic of Cancer; so on midsummer day at noon the sun's rays shone perpendicularly - that is - to 900 - about the city. On the same day, at the same time, they were 810 over Alexandria (illustration below), 5000 stadiums (1000 km) away from Syene (illustration above). Seeing that a circumference segment measuring 5000 stages corresponded to a difference of 90 in the incidence of the sun's rays, Eratosthenes only had to make a simple three-rule to find the corresponding 3600 of the earth's circumference. The result was 200000 stadiums. Which is 40000 km.


Bibliography: Encyclopedic Dictionary Knowing - Cultural April