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Eratosthenes, Over 2,000 Years Ago Has Estimated Earth’s Circumference

Eratosthenes|It was a time when our planet was the only world we could explore. Its true size was for the first time revealed by a simple but ingenious way by a man living in Egypt in the 3rd century BC
He was called Eratosthenes. He was an astronomer, historian, geographer, philosopher, theater critic, and mathematician. He was also the chief librarian of the great Library of Alexandria.


c. 276 BC – c. 195/194 BC

Eratosthenes was born around 276 BC. At Cyrene (Libya today). He made a series of discoveries and inventions, including a latitude and longitude system. He may have been the first to calculate the distance of the Earth from the Sun.

He created a map of the world based on the knowledge of the times, he was the initiator of the scientific chronology, and he set up the system for setting the date of events, reported from the date of the conquest of Troy.

One day, while reading a papyrus in the library, he found a curious note. “Far south in the last frontiers of Siena, one could see a remarkable thing on the longest day of the year. On June 21, the shadows of the columns of temples or a vertical stick are diminishing as they approach the afternoon.
At midday, the sun’s rays sink into the depths of a fountain, where it is the shadow in other days. And then, just in the afternoon, the columns have no shadow, and the Sun shines directly into the water of the pit. ”

Eratosthenes, however, was a scientist, and his contemplation of these common things would change the world. As Eratosthenes had the mood to experiment, to wonder if here, near Alexandria, a stick makes a shadow on the noon of June 21?

Then an idea came to Eratosthenes, he thought of using a gnomon, a vertical verge. When the sun was overhead in Alexandria at noon, Eratosthenes measured the angle between the stick and the sun’s rays. The angle was 7.2 °.


The Greeks believed that the Earth was round, and Alexandria was almost in the North direction of Syene so that the geometry of a circular section through the sphere showed that the distance between Alexandria and Syene was fifth of the Earth’s circumference.

Eratosthenes believed that the earth was spherical and knew that a circle had 360 °. Therefore, he divided 360 to 7.2. The result? His angle was fifty in a circle.



A man too skeptical might have said the Siena report was wrong. But it was a simple observation, why would anyone have lied about such a trivial aspect? Eratosthenes wondered how at one and the same moment a Siena stick could have no shadow and a stick in Alexandria, 800 km north to show a very clear shadow? The only answer was that the surface of the Earth is curved. Not only that, the higher the curvature, the greater the difference in the length of the shadows. The sun is so far that its rays are virtually parallel when they reach the Earth.


The sticks at different angles to the Sun will have different lengths of shadows. For the observed difference between the lengths of the shadows, the distance between Alexandria and Siena should be 7 degrees to the surface of the Earth. If you could imagine these sticks stretching to the center of the Earth, they would intersect at a 7-degree angle. Well, 7 degrees means about 50th part of the entire Earth’s circumference, 360 degrees.


Eratosthenes knew that a camel caravan would take 50 days to arrive from Alexandria to Syene, crossing 100 stadia a day. So the distance from Alexandria to Syene is 5000 stadium, which gives a circumference of Earth of 250,000 stadia.

How accurate is this number if we compare it with the results obtained from today’s calculations? The 250,000 stadia equate to 40,000-46,000 kilometers. With satellites that orbit around our planet, astronomers measured the polar pole circumference of the earth. The result? 40 008 kilometers.

So the calculations made by Eratosthenes more than 2,000 years ago are almost the same as the current ones, which is really astounding. What extraordinary precision if we think that this scientist only used a stick and geometric reasoning! Today’s astronomers also use this geometric method to measure distances outside of our solar system.

Note * The stadia is an old measure of length for the Greeks. Although the exact value varies from place to place, a stadium is believed to be between 160 and 185 meters.

If the stadia used by Eratosthenes had the value of 185 meters, it would result that the Earth’s circumference is 46,250 km, so with an error of ~ 15% of the actual value, now known. But if we assume that it used the Egyptian stadia (157 meters), it would reach a 39.250 km Earth circumference, with only a 2% error.


Some people find it extraordinary that Eratosthenes knew at that time that the earth was round. After all, hundreds of years ago even some scientists thought the earth was flat. The ancient Greeks have come to the conclusion that the earth is round after scientific observation.

But, about 500 years before Eratosthenes, a Jewish prophet wrote, “He [God] stands above the circle of the earth” (Isaiah 40:22). Isaiah was not a scientist. Then how did he know that the earth is round? This truth was revealed to him by divine inspiration.



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About Unknown

Le Minh Hieu is a national-level weightlifter and a Singapore Weightlifting sports performance coach. Hieu's biggest passion is helping everyone find confidence, happiness, and health through fitness.


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