In the mid-20th century, satellite shipments into space have helped scientists to calculate the magnitude of the Earth's circumference accurately, which is 40,030 km. However, about 2,000 years ago, a Greek scientist actually managed to measure the circumference of the earth using only a rod and brilliant brain. His name is Eratosthenes.

Eratosthenes as Era. He was a mathematician and head of libraries in the city of Alexandria, Greece at the time. One day, Era heard from a friend that in the city of Syene, south of the city of Alexandria, there was no sun shadow at noon when there was a "solstice" event.

What does it mean if in the city of Syene there is no sun shadow? That is, the sun was laying just above the city.
Era daydreams, "If in the city of Syene there is currently no sun shadow, is it in Alexandria too?"

Era took a stick and set it on the ground. Apparently formed a shadow of the sun on a stick that is established by him. Once measured, the angle is about 7.2 degrees.

If sunlight radiates to earth at the same angle at the same time, and the wand in Alexandria has a 7.2-degree shadow while the rod in Syene has no shadow at all, meaning the earth's surface must be curved.


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Illustration of a stick with a shadow (in Alexandria) and without shadow (in Syene)

In the days of Mr. Era, there was already a discussion of the idea that the earth was a sphere. This idea was made by Pythagoras (500 BC) which was later proved by Aristotle centuries later. Thus, if true the earth is spherical.

Mr. Era should be able to use his observations to measure the circumference of the earth. Era then asked someone to measure the distance between the cities of Alexandria and Syene. From there he learned that these two cities were separated as far as 5,000 stadia (about 800 km).


Due to the long margin of shadow in the city of Alexandria and Syene 7.2 degrees, the two cities are separated as far as 7.2 degrees on the earth's surface which is a full circle (360 degrees).

Mr. Era then can use a simple comparison to measure the circumference of the earth, that 7.2 degrees are about 1/50 times the total circumference of the earth.

If two separate towns are 7.2 degrees the distance is 800 km, the total circumference of the Earth with a 360-degree angle is 800 km × 50 = 40,000 km.


And it's that simple, Mr. Era, over 2000 years ago, discovered the magnitude of the circumference of the earth using only a stick. Compare with the results of accurate modern measurement (40,030 km), only 30km disagree only.


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