In the mid-20th century, we began launching satellites into
space that would help us determine the exact circumference of the Earth: 40,030
km. But over 2000 years earlier, a man in Ancient Greece came up with nearly
the exact same figure using just a stick and his brain. Following is a
transcript of the video.

How an ancient Greek mathematician calculated the Earth's
circumference. In the mid-20th century, we began launching satellites into
space that would help us determine the exact circumference of the Earth, 40,030
km. But over 2,000 years earlier in ancient Greece, a man arrived at nearly
that exact same figure by putting a stick in the ground.

That man was
Eratosthenes. A Greek mathematician and the head of the library at Alexandria.
Eratosthenes had heard that in Syene, a city south of Alexandria, no vertical
shadows were cast at noon on the summer solstice. The sun was directly
overhead.

He wondered if this were also true in Alexandria. So, on
June 21 he planted a stick directly in the ground and waited to see if a shadow
would be cast at noon.

It turns out there was actually one. And it measured about 7
degrees. Now, if the sun's rays are coming in at the same angle at the same
time of day, and a stick in Alexandria is casting a shadow while a stick in
Syene is not, it must mean that the Earth's surface is curved.

And Eratosthenes probably already knew that. The idea of a spherical Earth was floated around by Pythagoras around 500 BC and validated by Aristotle a couple centuries later.

If the Earth really was a sphere, Eratosthenes could use his
observations to estimate the circumference of the entire planet. Since the
difference in shadow length is 7 degrees in Alexandria and Syene, that means
the two cities are 7 degrees apart on Earth's 360-degrees surface.

Eratosthenes hired a man to pace the distance between the
two cities and learned they were 5,000 stadia apart, which is about 800
kilometers. He could then use simple proportions to find the Earth's
circumference — 7.2 degrees is 1/50 of 360 degrees, so 800 times 50 equals
40,000 kilometers. And just like that, a man 2200 years ago found the
circumference of our entire planet with just a stick and his brain.

"a stick and his brain" and geometry from Pythagoras. Great story!

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