Mathematics

The Life and Work of Eratosthenes

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14 December 2020                

Read time: 3 minutes

Introduction

Is it possible for a person to be an expert in Geography, Mathematics, and Astronomy in one lifetime?

Sounds very difficult, Doesn't it?

Eratosthenes was a great Greek mathematician. He is also well-known for his priceless contributions in many fields, such as Geography, Astronomy, and History.

He contributed to a wide range of fields. He was also a poet and a music theorist.

He yearned to understand and decode all the complexities in the world.

You will read more about his life and work in this article.

The Life and Work of Eratosthenes-PDF

Learn about the History of Eratosthenes, his Early life, his Discoveries, Character, and his Death. Here is a downloadable PDF to explore more.

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Early Life of Eratosthenes

Eratosthenes was born in Cyrene, Greece (now a part of Libya, North Africa) in 276 B.C.E.

Eratosthenes did a major part of his studies in Athens.

Eratosthenes was born in Cyrene, Greece (now a part of Libya, North Africa)

His teacher Ariston of Chios, a philosopher, was the founder of the Stoic school of philosophy.

Eratosthenes also learned the art of poetry under a scholar called Callimachus. He wrote poems called Hermes and Erigone.

He also wrote Chronographies, which compiled all important dates starting from the Trojan War in chronological order.

Eratosthenes’s excellence in multiple fields impressed the pharaoh Ptolemy III Eurgetes who invited Eratosthenes to be the librarian for the grand Alexandrian University.

Eratosthenes promptly accepted the responsibility. He worked on expanding the library’s holdings to a great extent during his tenure.

He was also a friend of the renowned mathematician and physicist Archimedes.


Work and Contributions of Eratosthenes

Eratosthenes made many contributions in the fields of Mathematics, Astronomy, Geography, and History. But his calculation of the earth’s radius/circumference is the most famous of all his achievements.

Circumference calculation

We will look at a simplified version of Eratosthenes’s method given by Cleomedes.

The method adopted to calculate the circumference:

  • Considering earth as a circular/spherical shape, he tried to locate the center of that circle to calculate its circumference/radius

    picture of a globe: calculating circumference of earth

  • He knew the distance between the cities Alexandria and Syene to be approximately 5000 stadia (a unit used to measure distance in those days in Greece)

  • His plan was to measure the sun’s angle of elevation (ϴ) at noon of the summer solstice in Alexandria.

  • This was achieved by placing a rod of known length vertically on the ground. The angle of elevation was then calculated by observing the length of the rod’s shadow.

  • Once the angle (ϴ) was obtained, the circumference was calculated using the values of angle and the arc length (which is the distance between Alexandria and Syene)

This was quite a remarkable achievement by Eratosthenes considering the tools and resources which were at his disposal at that time.

Sieve of Eratosthenes

Another major achievement of Eratosthenes is the creation of a Sieve that determines all prime numbers up to a given number (n).

This was the algorithm suggested by Eratosthenes for the same.

Algorithm (to find all prime numbers up to a number n):

  • Make a list of all the numbers starting from 2 to the given number (n).
  • Strike off all the multiples of 2
  • Now, move to the next smallest number after 2 which has not been already struck in the previous step.
  • Now strike all the multiples of this new number
  • Now again, move to the next smallest number which has not been struck and go on to strike its multiples.
  • This process is repeated multiple times to arrive at the final list of all prime numbers up to the number n

algorithm suggested by Eratosthenes

His other works include,

  • Devising a calendar that asserted that there were 365 days in a year and that there would be a leap year (366 days) once in every four years
  • His measurement of the tilt of the earth’s axis - degree of obliquity
  • His invention of the armillary sphere which was used in Astronomy to determine the positions of celestial objects
  • His logical explanation that the River Nile flooded every year because of the heavy seasonal rains at its source
  • His sketch of a world map by bringing together all the bits and pieces of information known then. He used parallels and meridians to locate any place on the map.

world map by erastothenes: meridians to locate any place on the map


Multifaceted Personality

Eratosthenes produced works that covered vast areas of knowledge including Mathematics, Geography, Astronomy, History and Poetry.

He wrote Literary criticism and also on Philosophy, Grammar, Comedies, and a lot more.

Eratosthenes produced works which covered vast areas of knowledge

Not often do we find a personality who has a grasp of such a wide range of subjects.

His contribution to every field of study was quite significant and paved the way for further research and discoveries.

It is said that his friends/peers nicknamed him Beta (this is the second letter in the list of Greek alphabets) to indicate that he always fell a little short of being the best, in spite of his innumerable achievements. He was probably not given his due recognition during his time.


Last Days

As he aged, Eratosthenes contracted Ophthalmia and lost the ability to read and write.

It is said that this led him to voluntarily starve himself to death.

He died at the age of 82 in the city of Alexandria in 194 B.C.E


Conclusion

Even with the few amount of instruments and tools available at that time, Eratosthenes was unmatchable in his quest for knowledge.

His tremendous passion for knowledge ensured that he didn’t restrict himself to any particular subject, like most of the other great scholars in the world.

Not only did he wish to learn everything around him, but he was also determined to put all the knowledge to use.

He gathered and gifted numerous discoveries and solutions for the benefit of the world.

Eratosthenes is undoubtedly a monumental inspiration to all aspiring students!

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FAQs

Who was Eratosthenes?

Eratosthenes was a great Greek mathematician. He is also well-known for his priceless contributions in many fields, such as Geography, Astronomy, and History.

Where was Eratosthenes born?

Eratosthenes was born in Cyrene, Greece (now a part of Libya, North Africa) in 276 B.C.E. Eratosthenes did a major part of his studies in Athens.

How did Eratosthenes die?

As he aged, Eratosthenes contracted Ophthalmia and lost the ability to read and write. It is said that this led him to voluntarily starve himself to death. He died at the age of 82 in the city of Alexandria in 194 B.C.E

What is the Sieve of Eratosthenes?

Sieve of Eratosthenes is a sieve that determines all prime numbers up to a given number (n).

What are the major contributions of Eratosthenes?

  • Calculation of Circumference of Earth
  • Sieve of Eratosthenes to find prime numbers
  • The invention of the armillary sphere which was used in Astronomy to determine the positions of celestial objects
  • His sketch of a world map by bringing together all the bits and pieces of information known then.

External References

 


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