Tag Archives: geometry

How he did it

Just to recap from the last couple of posts: First, Eratosthenes guessed the Earth was round like a ball. Second, he knew that at noon on the Summer solstice, the Sun shone directly overhead in the town of Syene, which was 5,000 stadia south of Eratosthenes.

Third, Eratosthenes guessed the Sun was really big—huge, even. He noticed that shadows cast by the Sun are all parallel, so all the Sun’s rays must be parallel, too. Parallel means 2 or more lines that never touch—they stay the same distance from each other. Think train tracks.

SO, Eratosthenes—in Alexandria, 5,000 stadia north of Syene—put a stick (like the gnomon of a sundial) in the ground and made sure it was plumb. That stick was pointing down to the center of the Earth. If Earth is round, the well in Syene and Eratosthenes’ stick won’t be parallel, right? They’ll be at an angle to each other. Eratosthenes didn’t know exactly how many degrees that angle was, but in Alexandria at noon on June 21st, his stick cast a shadow.

There weren’t any shadows in Syene, because the Sun was directly overhead. He measured the stick, he measured the shadow, and used those measurements to draw an angle. The angle turned out to be a little over 7 degrees, or 1/50 of a circle.

Eratosthenes knew the distance from Alexandria to Syene was 5,000 stadia. He multiplied 5,000 by 50 to get the circumference of the Earth—250,000 stadia. In modern measurements that works out to be 28,738.418 miles or 46,250 kilometers.

The actual polar circumference of Earth is about 24,860 miles or just a bit over 40 thousand kilometers. The stadion Eratosthenes used may have been a little different from the standard unit. But even today, right now, if you search the internet for the circumference of the Earth, you won’t get just one answer.

Eratosthenes was a genius who used what he knew and observed, along with what he guessed at, to calculate something that no one knew—and he did it pretty accurately.

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Plumb

A plumb line or plumb bob.

Last post I rattled on about how the well at Syene was plumb.

‘Plumb’ means straight up-and-down. Builders used to use a plumb line—a string with a weight tied onto it—to check that their walls were straight up-and-down. A plumb line will always point to the center of the Earth. Nowadays they use a spirit level. Builders who dug wells made sure that the hole they dug was plumb—pointing directly toward the Earth’s center.

Why was it so important to Eratosthenes that the well at Syene (a town located on the Tropic of Cancer) was pointing directly at the Earth’s center at noon on June 21st—the Summer solstice?

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Eratosthenes


Head-Librarian Eratosthenes explains to a student how to laminate a dust jacket.

In an earlier post, I hinted about how over 2,000 years ago somebody calculated the circumference (how big around) of the Earth. This guy did it using only a well, a protractor and a stick (okay, maybe instead of a stick he used a column, but you could use a stick and get the same result).

I’m talking about Eratosthenes, the head librarian at the Great Library of Alexandria. Alexandria is an ancient city in Egypt, located where the Nile River flows into the Mediterranean Sea. Many scholars lived in Alexandria—like Ctesibius, who perfected the water-clock.

Back to the beginning of The Western Civ User’s Guide to Time & Space