Assignment 1. Ancient astronomy: The size of Earth

Eratosthenes of Cyrene
Eratosthenes is an ancient Greek Scientist who is famous for his achievement in Geography and Mathematics. He was born in the town of Cyrene, which is now in the Libya, North Africa, around 276 B.C. After many years study in Athens, he was appointed as the chief librarian of the Library of Alexandria in 236 BCE.

Achievement:
  • The Sieve of Eratosthenes: He produced a reliable method in discovering prime numbers, which is still important in modern mathematics. 
  • First time realized that Earth is a sphere and calculate its diameter with a good accuracy.
  • Invented Geography and the first person to explain the annual flood of River Nile.
  • Wrote Poems and works on astronomy, theatre, and ethics
The Sieve of Eratosthenes:
Eratosthenes invented a way to find the prime numbers, which are the numbers with no factors but 1 and themselves.
The method works this way:
  1. First, target a number that you want to check, like 110 for example, then write down all the numbers smaller than 110.
  2. Then, find the first prime number, erase the one before the first prime number. And erase every multiple of 2.
  3. Similarly, find the next prime number, which is 3. And erase every multiple of 3.
  4. Repeat this process until all the primes are found.
Measurement of Earth
During his working as the chief librarian in the library of Alexandria, he had learned that there is no shadow for the walls in the city of Syene at the midday of the longest day of the year. That is because the sun is directly overhead the wall in Syene. However, he found out that there is a small shadow for the wall in Alexandria at the same time. And Syene is to the south of Alexandria. So why is there a difference?
Eratosthenes made several assumptions to solve this problem:
  1.  Earth is a sphere, otherwise, there would not be a difference in shadow
  2. The sun's rays are parallel to one another when reaching the Earth
Basing on these two assumptions, by measuring the angle of the shadow in Alexandria and the distance between Alexandria and Syene, he calculated the circumference of Earth.


Like the picture above, z is the angle of the shadow. If the light ray is paralleled, the angel of shadow should equal to the angle of down drawing each wall to the Earth's center. The angle is about 7.2 degrees, which means the distance from Alexandria to Syene is about the 7.2/360 of Earth's circumference.
From the trade caravan, Eratosthenes knew the distance between Alexandria to Syene is about 5000 stadia, which is about 800 kilometers. By solving the equation, he calculated the circumference is about 250,000 stadia (40,000 kilometers), which is quite accurate comparing to nowadays satellites' measurement, around 40,075 kilometers.


By Ruoxi-2745



Reference:


https://www.britannica.com/biography/Eratosthenes

https://www.khanacademy.org/partner-content/big-history-project/solar-system-and-earth/knowing-solar-system-earth/a/eratosthenes-of-cyrene

 http://www-history.mcs.st-and.ac.uk/Biographies/Eratosthenes.html

 https://www.famousscientists.org/eratosthenes/

评论

  1. Vince2018年2月5日 06:14

    Thanks for the nice entry on Eratosthenes.

    The downside is that it is kind of short! I'd like to have had a little background on his life. The sieve was interesting, but the focus should have been more on his measurement of the size of Earth. Also, with what precision? Do you think it was a success?

    The references are nice to have, but they should be included in the main text (e.g. "This is something from [2] about Eratosthenes."). I'm also interested to read about your thoughts.

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