How an Ancient Greek Measured the Size of Earth

An Ancient Greek named Eratosthenes (276-194 B.C) did something that was considered, at the time, impossible. He made the first recorded measurement of the circumference of the Earth.

Of course, Erasthenes had no expensive survey equipment, and most likely, he didn’t have lasers or satellites (or Google Earth). And he didn’t even put his own life at stake by going on a ship journey that would take the rest of his life to complete to circumnavigate the Earth.

He just did some out-of-the-box thinking, while in the Library of Alexandria. He read that there was a deep well in Syene (a city in southern Egypt) that would have its bottom completely lit by the noon sun one day a year. This implied that the sun must be directly overhead at that moment. He also observed that at the same time, vertical objects in Alexandria (directly north of Syene) cast a shadow. This meant that Alexandria received sunlight at a slightly different angle at the same time.

Eratosthenes realized that he could use this information to estimate the curvature of the earth.

He observed that the shadows at noon at that time of year (in Alexandria) made an angle that was one-fiftieth of an arc of a circle (or 7.2 degrees). By using geometry, he could prove that the circumference of Earth must be 50 times the distance between Alexandria and Syene.

The interesting thing is that while modern attempts to replicate these calculation differ in terms of the precise size of the angles, conversion rates between ancient and modern units of measurement, and the precise distance between the ancient cities, typical estimates put his calculation within only 3 percent of the actual value.

Eratosthenes’ calculation was a great improvement on previous knowledge, and his error was negligible. Even modern scientists were more off only a few decades ago about the size and age of the universe.

1,700 years after the Greek’s calculation, the famous Christopher Columbus made a mistake in his calculations, which was 25 percent short of the actual circumference of the earth. That was one of the main reasons Columbus thought he was in India, and not North America. Had Columbus known about Eratosthenes’ calculation, he would have avoided that mistake.

In business, people often assume that they need very sophisticated tools and large data sets to be able to assess risk, but a simple observation, like that of Eratosthenes can save you a lot of hassle. The “hard” way isn’t always the best way.

Source*: How to Measure Anything: Finding the Value of Intangibles in Business, Douglass W. Hubbard*

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