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Imagine trying to measure the circumference of Earth without satellites, GPS or modern technology.
That's what Eratosthenes, a Greek mathematician and scholar, attempted more than 2,000 years ago.
☀️ The Amazing Observation
Eratosthenes knew that around noon on the summer solstice, the Sun was almost directly overhead at Syene in ancient Egypt. A vertical object there produced little or no shadow.
But at the same time in Alexandria, a vertical object produced a shadow.
Eratosthenes realised that this difference was caused by the curvature of Earth.
By measuring the shadow in Alexandria, he calculated an angle of approximately 7.2°.
A complete circle is 360°.
So:
7.2° ÷ 360° = 1/50
This meant that the distance between Alexandria and Syene represented approximately 1/50 of Earth's circumference.
🧮 The Calculation
The formula is:
Earth's Circumference = (360° ÷ Measured Angle) × Distance Between the Two Locations
Using an angle of 7.2° and an approximate distance of 800 km:
Earth's Circumference = (360° ÷ 7.2°) × 800
= 50 × 800
= 40,000 km
The modern equatorial circumference of Earth is approximately 40,075 km.
That's remarkably close!
🤯 Why Is This So Amazing?
Eratosthenes didn't measure Earth directly.
He measured something as simple as a shadow and used mathematics to estimate the size of an entire planet.
His idea can be summarised simply:
Shadow → Angle → Earth's curvature → Earth's circumference
⚠️ An Important Historical Point
Ancient accounts also report Eratosthenes' result as 250,000 stadia. However, the exact length of the ancient unit called a stadion is uncertain, so converting that number into kilometres is not exact.
The angle-and-distance method gives us a simple and clear way to understand the mathematics behind his famous idea.
🌍 The Big Lesson
More than 2,000 years ago, Eratosthenes showed that we don't always need advanced technology to solve enormous problems.
A simple shadow, careful observation and mathematics were enough to estimate the size of Earth.