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Was the Earth’s Circumference Calculated Over 2,000 Years Ago?

How Did They Calculate Circumference of the Earth

Scientists of the modern era have been making new discoveries is science. The fascinating thing is that over 2,000 years ago, without all of our modern technology, a mathematician correctly estimated the Earth’s circumference.

Eratosthenes was easily the most famous mathematician in his era. Also poet, writer, and astronomer, he was nothing short of accomplished. He was born in Cyrene, Greece, which is now a part of modern day Libya.

While what he did was mind-blowing for both his time and our time, he met a sad end. It is widely thought that he starved himself after going blind and was no longer able to do any work. His legacy continues on though, leaving his mark in science forever.

Who was Eratosthenes?

Eratosthenes was born about 276 B.C. in modern-day Libya, but was at the time Cyrene, Greece. He had the chance to study in Athens, which was a big deal at the time, and used it as a way to study poetry, scientific writing, study the skies, and work on his math.

Because he was so amazing in so many different fields of study, Eratosthenes was able to nab the attention of the ruler of Egypt at the time, Ptolemy III. The ruler thought he was impressive and asked him to go to Alexandria, Egypt to help teach his own son and to be a librarian.

The Great Library of Alexandria

The library of the university in Alexandria, or as it has also been known, the Ancient Library of Alexandria, Royal Library of Alexandria, and the Library of Alexandria, is one of the most important libraries in history. Ptolemy III, as well as his father and son, pushed for the success of the library. The library had gardens, lecture halls, as well as a massive number of books.

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Through the library, Eratosthenes was able to study at his leisure as well as talk about ideas with other scholars. Having an endless number of facts at his fingertips let him look at things in new ways including things such as how the sunlight fell onto the ground.

Counting by Columns

After having hung around in Alexandria for a while, Eratosthenes started looking at how the sunrays went completely vertical at noon during the summer solstice. Having the information to compare, he found that in Syene, a place south of where he was, there were no shadows at high noon, but in Alexandria, at the same time of day, he saw the shadows from the library’s columns.

Syene had most likely been recorded as having no shadows before he noticed. As he was awesome at math, Eratosthenes was able to measure the circumference of the Earth based on the shadows.

Getting Down to Numbers

Eratosthenes, in his greatness, measured how long the shadow of an obelisk was on the summer solstice at high noon. From his measurements, the sun was about seven degrees, give or take, from being straight overhead. Since the Earth was round, the more it was curved, the bigger the shadow there would be.

Therefore, since we know that Syene was at zero since there were no shadows, he knew that Syene was seven degrees from Alexandria. He then took the physical distance between the two places in the units they used at the time, which were called stadia.

The Haziness of Stadia

The tricky part about stadia was that there wasn’t a universal system, like the metric system. So stadia meant different things to different people. And there weren’t really distance markers to know what the exact distance between the two places were, so Eratosthenes had to count it himself.

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There is no certain answer for how he measured the distance. It was too long ago to know, but there are a couple of theories. One is that he paid someone to walk in between the two towns and count his steps. The other is that he counted how long it would take a camel to travel from one location to the other. Either way, he guessed the distance to be 5,000 stadia between the two locations.

Not a Bad Guess

Based off of his numbers, Eratosthenes thought the Earth’s circumference was about 250,000 stadia. The downside is still that stadia was not a consistent measurement, so it is hard to know how far off he was, but it is believed that his number was anywhere from .5% to 17% off from the real number.

You might be thinking that 17% is a big difference, but think about the lack of modern tools he had. Really though, they think that he most likely used the Egyptian stadia, which meant that he was less than 1% off from the actual number. There had been other attempts at guessing the Earth’s size, but his was by far the best.

His Legacy

While his work on the Earth’s size probably was his biggest claim to fame in his day, it was not the only thing that he accomplished. For mathematicians, he is the father of the Sieve of Eratosthenes which is a simple way to find prime numbers.

Eratosthenes also created a new way of mapping out the world. He drew in lines from north to south and east to west, which was the first recorded use of longitude and latitude lines.

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