# Eratosthenes

**Eratosthenes** is considered the **first scientist** in the history of the world who managed to measure with excellent precision the **circumference** of our **earth** at a time when people thought that the world was flat instead of being round.

**Personal information:**

**When was he born:**276 BC**Where he was born:**Cyrene, Libya**When he died:**194 BC**Where he died:**Alexandria, Egypt

## Who was Eratosthenes?

Eratosthenes was an important Greek **mathematician** and **astronomer** , who for many decades was **director** of the **Alexandrian** library and was recognized as one of the most important minds of his time.

## Biography of Eratosthenes:

Eratosthenes of Cyrene was born in 276 BC in **Cyrene** , North Africa, and **died** in 194 BC in **Alexandria** , Egypt. He was a disciple of the Greek poet **Callimachus of Cyrene** and the grammarian **Lisanias** , director of the **Library of Alexandria** and friend of **Archimedes** . His enemies called him the ” **Beta** “, because according to what they thought, he was second best in everything. Those who knew and appreciated him, however, called him the ” **Alpha** ” because they knew he was the first in almost everything.

Eratosthenes ended his days dying of **voluntary starvation** at age 80, as he was extremely **depressed** for having lost his sight.

## Contributions and inventions:

One of the main contributions of Eratosthenes to **science** and **astronomy** was his important work regarding the **measurement** of the **earth** . Eratosthenes, studying the papyri in the library of Alexandria, found a report in which it was said that when the sun’s rays fell on a rod during the noon of **the**** summer ****solstice** , no **shadow** was produced .

He correctly assumed that, if the Sun was located at a great distance, its rays when reaching the earth should reach it in parallel, assuming that the earth was flat as it was considered at that time and therefore there should be differences between the shadows cast by objects at the same time on the same day, regardless of location. However, when it was shown that this did happen, he deduced that the earth **was not flat** and using the known **distance** between the two cities and the measured angle of the shadows, he calculated the **circumference** of the **earth** at approximately 250 stadia, about 40,000 kilometers, an estimate. which was almost close to reality.

Other of his contributions was that he managed to calculate the **distance** to the **Sun** in 804,000,000 **stages** and the **distance** to the **Moon** in 780,000 stages. He managed to measure the **inclination** of the **ecliptic** at 23º 51 ′ 15 ″ quite well and with great precision.

Another of his important astronomical works was a **catalog** of about 675 **stars** . He also created one of the most advanced **calendars** for his time and a **chronological history** of the world since the beginning of the Trojan War.

He conducted research in geography drawing **maps** of the known world, vast stretches of the **River Nile,** and described the **Eudaimon** region , which we now know as Yemen in Arabia. He also invented the **sieve of Eratosthenes** .

## Eratosthenes sieve:

The sieve consists of a method that allows us to find all the **prime numbers** smaller than a given natural number ” **N** “. This algorithm could be summarized as follows:

- It should start with the
**number 2**, we highlight the number 2 as a prime, but we**cross out**all**multiples**of 2 (that is, we cross out 4, 6, 8, etc.). - Then we continue with the next number that is not crossed out in the table, the
**number 3**,**we highlight**the number 3 as a**prime**and we**cross out**all the**multiples**of 3 (that is, we cross out 6, 9, 12, etc.). - The next number that is not crossed out in the table is
**number 5**, so we must highlight it as a**prime**and cross out all**multiples**of 5 (that is, we cross out 10, 15, 20, etc.). - This process must be
**repeated**until we reach the number N, having previously crossed out all the multiples of the prime numbers found.

## Land measurement:

To achieve **measurements** of the **earth he** invented and used a **trigonometric** method , different notions of **latitude** and **longitude** that had already been introduced in the area of science, apparently by **Dicearco** , for which he well deserves the title of father of **geodesy** .

## Importance:

His importance to the modern world is not based solely on the fact that he made significant progress in the area of **geometry** ; but he owes the *” sieve of Eratosthenes “* , a system to determine prime numbers was one of the most important

**geographers**and he drew a

**map**of the

**River Nile**to Khartum, in which he showed its two Ethiopian tributaries, and giving the first explanation Satisfactory on why the Nile River was flooding. In addition, he drew up a

**calendar**with

**leap**years , drew up a small

**stellar catalog**, was a

**poet,**and wrote treatises on

**Ethics.**

## Works of Eratosthenes:

Among his most important works we can mention the following:

**Erigone’s works**: it was the best known and it was an**astronomical**and**geographical****poem**that deals with the shape of the**Earth**, its temperature, the different climates and the constellations .**Treatises of moral philosophy**and other philosophical works. All his works were closely linked to**mathematics**.**The Chronography**: in this work he manages to collect the dates of the most important**literary**and**political**events that had occurred so far; It is believed that The Olympics, cited by Diogenes Laercio and Athenaeus, were part of the Chronography.**Treatise on the ancient Attic comedy**: of it are**Arjitectonic**and**Skenographic**fragments in which he spoke of the decoration, costumes, declamation and plot of works by**Aristophanes**and**Cratino**among others.- He studied the
**work of Homer**and wrote a**biography**on the life of the poet that has not survived to this day.

## Phrases:

There are no recognized phrases of Eratosthenes, but there are two phrases written by Carl Sagan that reflect his essence:

*“Eratosthenes had no other***tools**than sticks, eyes, feet and head and a great desire to experiment with these tools correctly deduced the**circumference**of the**earth**with enormous precision and a minimum error percentage.*“Eratosthenes criticized***Aristotle**for his blind**chauvinism**, he believed that in all countries there were good and bad things.”