ERATOSTHENES: BIOGRAPHY AND CONTRIBUTIONS TO GEOGRAPHY AND MATHEMATICS - HISTORY - 2025

Eratosthenes (276 BC - 194 BC) was an Ancient Greek scientist and philosopher who did work in astronomy, geometry, geography, mathematics, as well as poetry and history. He became famous for being the first to calculate, with considerable precision, the circumference of the earth.

He lived in Athens until Ptolemy Evergetes, the king of Egypt, entrusted Eratosthenes with the direction of the Library of Alexandria, which became the most important center of knowledge in the region.

Portrait of Eratosthenes

He was called Pentathlos, a title that was given to those who were victors in the five tests of the Olympic games, because he dedicated himself to cultivating all areas of knowledge.

He created a method that was baptized as the Sieve of Eratosthenes by which he calculated the prime numbers. He also tried to determine the obliquity of the ecliptic.

To calculate the circumference of the earth Eratosthenes used a method that has been used until our time, this consists of measuring a meridian. He set the circumference measurement at 252,000 stadia, which is approximately 39,691 kilometers.

For his studies on the earth, Eratosthenes is known as the "father of geography." He published a book that he called Geographika, it was there that he first coined the term geography. In the text he described the inhabited earth and the people who lived there.

He did not use the mythological descriptions that were common at the time, but relied on military texts to carry out his work.

He also made a chart with the chronology of the Egyptian kings of Thebes, wrote about the conquests of Alexander the Great, and made a description of Greece at that time. For his contributions to philosophy, Eratosthenes was called the second Plato.

Eratosthenes was a lover of the theater and wrote a series of twelve books that he titled Ancient Comedy. In the same way, he wrote poetry and his themes included the stories of the constellations.

Biography

Early years

Eratosthenes was born in approximately 276 BC in Cyrene, a Greek city located in North Africa, in what is now the lands of Libya. He was the son of Aglaus, of whom no historical record is preserved, so it is thought that he was not from an important family at the time.

Despite not possessing a prominent ancestry, Eratosthenes did come from a city that had achieved recognition by the men who were born in it. Cyrene was founded by Greeks from Thera before 600 BC, and it prospered as an independent city until the arrival of the Hellenic era.

Cyrene was absorbed into the Ptolemaic monarchy of Egypt, which ruled from Alexandria, the cultural and commercial center of the Mediterranean. There was the great bookstore, a museum and a school of advanced studies.

Eratosthenes followed in the footsteps of other academics in his city and trained with Lysanias, an expert in grammar. Despite the fact that in Greek times young people from wealthy families had more access to education, there were male academies.

The children were trained from the age of seven in subjects such as literature, sports and music. It is thought that Eratosthenes may also have been a pupil of Callimachus.

Athens

The main interest of Eratosthenes in youth was philosophy and that vocation led him to Athens at the age of 15. There it remained, approximately, for 25 years. Then he trained and became famous as an academic.

In Athens he met so many philosophers that he was both amazed and overwhelmed. He first studied with Zeno at the school of the Stoics. Also with one of his students, Aristón de Chios, of whom he wrote a biography. But he did not find in them a style that appealed to him.

Later he joined the Platonists as a pupil of Arcesilao. It was then that Eratosthenes created a work called Platonicus, in which, following Plato's method, he explored mathematical and cosmological issues. At that time he also wrote Peri agath ō n kai kak ō n, a text that was lost.

After these experiences he became disenchanted with philosophy and decided to dedicate himself to poetry. Thus began the fame of Eratosthenes, since in his new field he achieved the recognition he had desired.

Of his first works as a poet the texts are not preserved either; however, some names were passed on to posterity through quotations from other Greeks. Hermes was one of his works, in which he addressed the life of the god, and another was named Erigone.

Alexandria

It is believed that it was Eratosthenes' fame as a poet that attracted the attention of Ptolemy III Evergetes, who called him to Alexandria to tutor his son, as well as offering him a position as director of the city library.

Ptolemy III was not moved only by his interest in the work of Eratosthenes, but also by political motives. The city of Cyrene had spent an independent period from Egypt until the marriage between Ptolemy III and Berenice, the daughter of Magas, governor of that city.

In the quest to secure his newly regained domain, Ptolemy III saw fit to satisfy the people of Cyrene by offering a position as important as that of chief keeper of the great library of Alexandria to Eratosthenes.

During the period in which Eratosthenes was in charge of the Library of Alexandria, great advances were made in it. He acquired works such as the great dramas of Aeschylus and Euripides. They also expanded the studies in Sophocles.

At this time Eratosthenes took advantage of his position and the access to the information he had to learn about the most diverse subjects. However, he never wanted to specialize in a single subject, for which some reproached him.

Death

Eratosthenes died in Alexandria, approximately 194 BC, when he was 82 years old. Some time ago he had gone blind from cataracts and is believed to have committed suicide by starvation.

Despite his great contributions to science, his work was not replicated by many others, apparently because he did not get enough students to pass on his discoveries and theories.

However, his contributions to the study of the earth gave him the title of father of geography. During his life Eratosthenes was a lover of knowledge in all its areas.

Jobs

Land measurements

Eratosthenes knew from readings he had taken in Alexandria that during the summer solstice in Siena, at noon the sun was just overhead. So, he measured the angle of elevation during the same period and at the same time in Alexandria with the help of a gnomon.

He also measured the length of the shadow on the ground. With these data (length of the shadow and length of the rod), Eratosthenes calculated the angle of the sun's rays in 1/50 of a circumference. However, he assumed that Siena was right over the Tropic of Cancer, a fact that was incorrect.

Other things that Eratosthenes thought but did not turn out to be: the fact that the earth is a perfect sphere, that Alexandria is exactly north of Siena, and that the sun's rays are perfectly parallel.

Among the files at the disposal of Eratosthenes, it was stated that the distance between Siena and Alexandria was 5000 stadia. He established the value of each degree in 700 stadiums and a total circumference of 252,000, which corresponds to approximately 39,691 kilometers, since the stadium was a difficult measure to determine. At present it is known that the equatorial diameter is 40,075 kilometers.

Christopher Columbus was one of those who studied the work of Eratosthenes. Despite this, he did not believe in those projections, but in Toscanelli's, which stated that the earth was a third smaller. That is why he thought that he would reach Asia on his journey and did not realize that a new continent had arrived.

Geography

In his work Geographika, Eratosthenes described and mapped known territories. There he first coined the term "geography" and used his discoveries regarding the size and shape of the earth to represent it.

Eratosthenes united and organized in this work different information that he found in the Library of Alexandria. She divided the earth into 5 climatic zones: the frozen poles, under them two temperate zones and in the center a tropical belt that bordered the equator.

With the parallels and meridians, Eratosthenes located the known countries and cities. In addition, he calculated approximate distances between them. More than 400 places appeared in that work, but it was lost, except for the references of historians of the time.

Geographika had 3 volumes. In the first, Eratosthenes addressed the previous theories and compiled the existing information in the library. In the second, he showed his studies on the dimensions of the earth and the last was devoted to political geography.

Another of his great contributions to geography was the study and map that he made of the route of the Nile River from Khartoum, in which he included the Ethiopian tributaries. He was the first to affirm that the heavy rains in the headwaters could explain the floods in the lower part of the flow.

Math

He created an algorithm to find prime numbers that is known as the Sieve of Eratosthenes. This method consisted of creating a table with natural numbers between 2 and the desired quantity. Then the non-prime numbers are discarded.

It starts with 2 and all the numbers that are multiples of that first digit are crossed out, then the same is done with the next number that is not crossed out and so on.

Eratosthenes also found a solution to the so-called Deliano problem, or the doubling of the cube. He created a device called the mesolabe, a kind of abacus for measurements and proportions, which he dedicated to King Ptolemy III.

Aristotle was a friend of Eratosthenes and collaborated with the mathematical calculations for the creation of the mesolabe. He also dedicated The Method to Eratosthenes.

Dedication to Ptolemy III

The inscription that Eratosthenes made in the mesolabe that he gave to Ptolemy III, said:

"You have this at hand, friend, if you want double a small cube to get, or that transformation into any other solid figure, and also if you measured an enclosure or a silo in this way or the concave cavity of a well when you take the concurrences means between extreme limits within double rules ”.

Then he continued: "And do not try to understand the intricate tasks of the Archytas cylinders or the triple cuts of the cone of Menechmus or what the curved figure of the divine Eudoxus describes in its lines, because in these tablets you will easily find thousands of means even starting from poor start ”.

Finally he wrote: “Happy father, Ptolemy, because with your son you enjoy the age! Everything that pleases the Muses and kings you yourself gave to your son. And afterwards, Uranio Zeus, may the scepter of your hand guide it. This, so it happens, and when seeing the offering, someone says: this is the work of the Cyrenean Eratosthenes. "

Other contributions

He was nicknamed Beta by other Greeks of his time, in reference to the second letter of the alphabet. By this they meant to say that Eratosthenes was second best in all areas, as he never wanted to specialize in any.

Eratosthenes made calculations in which he discovered that in a year there were 365 days and every four years there were 366 days. He used as a basis the ecliptic movement, that is, the movement of the sun observed by the apparent changes of the same from the earth.

Eratosthenes was also interested in history and created a chronology of the world from the site of Troy to his time, taking as references the dates that appeared in literature and political writings.

Publications

References to the works of Eratosthenes are preserved thanks to other authors, since when the library of Alexandria was lost, practically all of his work was lost.

- Platonikos.

- Hermes.

- Erigone.

- Chronographs.

- Olympic winners.

- Περὶ τῆς ἀναμετρήσεως τῆς γῆς (From measurements of the Earth).

- Гεωγραϕικά (Geographika).

- Arsinoe (a biography of Queen Arsinoe, wife and sister of Ptolemy IV).

- Ariston.

References

1. Encyclopedia Britannica. (2018). Eratosthenes - Greek scientist. Available at: britannica.com.
2. En.wikipedia.org. (2018). Eratosthenes. Available at: en.wikipedia.org.
3. Gow, M. (2010). Measuring the Earth: Eratosthenes and his celestial geometry. Berkeley Heights, NJ: Enslow.
4. Eckerman, C. (2011). Eratosthenes (DW) Roller (ed., Trans.) Eratosthenes' Geography. Fragments Collected and Translated, with Commentary and Additional Material. Princeton and Oxford: Princeton University Press, 2010. ISBN: 978-0-691-14267-8. The Classical Review, 61 (01), pp.78-80.
5. Aves, A., Magill, F. and Moose, C. (1998). Dictionary of world biography. Chicago: Fitzroy Dearborn Publishers, pp. 401-405.
6. Grégoire, L. (1879). Encyclopedic dictionary of history, biography, mythology, and geography. Paris: Garnier, pp. 758.
7. O'Connor, J. and Robertson, E. (1999). Eratosthenes biography. School of Mathematics and Statistics, University of St Andrews, Scotland. Available at: -groups.dcs.st-and.ac.uk.