ASTB03 – Assignment 1 – Eratosthenes and the size of the Earth

Eratosthenes was a Greek scientist who was born in Cyrene, Libya around 276 BC and died around 194 BC. He was very knowledgeable in various subjects such as mathematics, geography, philosophy, and astronomy. However, he was never really considered to be at the top of any field in particular. Even though he was never considered to be at the top of any specific field, he was able to become the Director of the Library of Alexandria.

Eratosthenes accomplished many different scientific achievements throughout his life. He created maps which included what we would now call today the longitude and latitude lines. Another map he created was the route of the Nile River to Khartoum. Also, with regards to the Nile, Eratosthenes was one of the first people to give a correct explanation as to why the Nile flooded, his reason being that there was heavy rainfall at the source of the river, which in turn led to the flooding that occurred downstream.

Another one of his achievements include creating a timeline of scientific and political events after the siege of Troy. He also is credited with the invention of the discipline of Geography, while he was the Director of the Library of Alexandria.

There are a couple of achievements that Eratosthenes accomplished that he is most known for. The first is in the field of mathematics, called The Sieve of Eratosthenes. The Sieve of Eratosthenes is a logical method which can be used to find the prime numbers up to any given number. It was an important theory at the time, and while not the exact same, it is still a very important method in Number Theory today.

The second major accomplishment that Eratosthenes is commonly known for is that he was able to accurately measure the size of the Earth. While as the Director of the Library of Alexandria, Eratosthenes learned that in Syene(today known as Aswan), at noon during the summer solstice, no buildings cast shadows. He also noticed that in Alexandria, at the same time, the buildings there did cast a small shadow. He first had to make two assumptions. The first assumption he made was that the earth was spherical and the second assumption he made was that the sun was far enough away from the earth that the suns rays were parallel when they reached the earth. With those assumptions, he then measured the angles of the shadows of the buildings in Alexandria. Knowing the approximate distance between Syene and Alexandria, as well as the approximate angle of the shadows that the buildings were casting, which was measured to be approximately 7 degrees, Eratosthenes figured out that the angle measured was about one fiftieth of a full circle, and thus, the distance between Syene and Alexandria represented approximately one fiftieth of the circumference of the earth. With that, he then multiplied the distance between Syene and Alexandria by 50 to get the approximate value of the circumference of the earth.

The value calculated by Eratosthenes was approximately 250000 stadia. The precision of this value has been debated due to the fact that the exact value of a stadia has been debated. Due to the uncertainty of the stadia, the accuracy of the value calculated by Eratosthenes was said to be anywhere within 1%-30%.

I think the calculation was a success because of how accurate the value in the end was to what we know the actual size of the earth is. It was also a success because Eratosthenes needed to make assumptions that, at the time, were not obvious, such as the suns rays being parallel when it reached the earth and the earth itself being spherical.

As we can see, Eratosthenes accomplished many things that have gone on to become important stepping stones to many things that we now know today.

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