Eratosthenes: The Ancient Genius Who Measured the Earth’s Circumference

In the 3rd century BCE, when much of the world was still shrouded in mystery, there was one man who dared to think differently about the shape and size of the Earth. That man was Eratosthenes of Cyrene, a Greek mathematician, geographer, and astronomer who became famous for his remarkably accurate calculation of the Earth’s circumference. Using nothing more than a few simple measurements, basic geometry, and the sun’s rays, Eratosthenes achieved what many considered impossible at the time. His groundbreaking work not only helped lay the foundations for modern geography but also proved that with ingenuity and observation, even the most profound mysteries of nature can be understood.

The Challenge of Measuring the Earth

Long before Eratosthenes, ancient cultures had speculated about the shape of the Earth. Some believed it to be flat, while others suggested that it might be a giant sphere. But how could anyone measure something so vast and seemingly beyond reach?

The task would require both curiosity and a keen understanding of natural phenomena, and that’s where Eratosthenes came in. Around 240 BCE, while working as the chief librarian at the Library of Alexandria, Eratosthenes learned that in the Egyptian city of Syene (modern-day Aswan), at noon on the summer solstice, vertical objects cast no shadow. However, in Alexandria, located to the north of Syene, objects cast a shadow at the same time. This curious observation sparked an idea—an idea that would change the course of history.

Eratosthenes’ Method

Eratosthenes realized that the difference in the length of the shadows was due to the curvature of the Earth. If the Earth were flat, the sun’s rays would strike both cities at the same angle. But since they didn’t, the Earth must be round. He deduced that by measuring the angle of the shadow in Alexandria, he could calculate the distance between the two cities, and from there, the Earth’s circumference.

The steps Eratosthenes followed were both simple and ingenious:

1. Measure the angle of the shadow:

   To understand how Eratosthenes measured the angle of the shadow, it’s essential to grasp the basic concept behind the Earth’s curvature. The Earth is a sphere, and the sun’s rays hit different locations at different angles, depending on their position relative to the Earth’s surface.

   Step-by-Step Process:

   1. Choosing the Right Time and Place: Eratosthenes chose the summer solstice, the day when the Sun is directly overhead at the Tropic of Cancer. This timing was crucial because at noon, the Sun would be at its highest point in the sky for both Alexandria and Syene, but it would not be directly overhead in Alexandria.
   2. Measuring the Shadow in Alexandria: In Alexandria, Eratosthenes placed a vertical stick (gnomon) in the ground and observed the shadow it cast at noon. The shadow was not zero, as it would have been in Syene, but rather had a measurable length. Eratosthenes carefully measured the length of this shadow.
   3. Understanding the Shadow’s Angle: Eratosthenes used the length of the shadow and the height of the stick to calculate the angle of the Sun’s rays. By applying basic geometry, specifically the principles of similar triangles, he could calculate the angle formed between the stick and the rays of sunlight. This angle turned out to be approximately 7.2 degrees.
   4. Interpreting the Angle: The key insight was that this angle represented the curvature of the Earth between Alexandria and Syene. If the Earth were flat, the Sun’s rays would hit both cities at the same angle, and no shadow would have been cast in Alexandria while there was none in Syene. However, since the shadow did exist, Eratosthenes concluded that the angle of 7.2 degrees reflected the difference in the angle of the Sun’s rays due to the Earth’s curvature.
   5. Relating the Angle to the Earth’s Circumference: Eratosthenes realized that the angle of 7.2 degrees was a fraction of a complete circle. Since a full circle has 360 degrees, 7.2 degrees is 1/50th of a circle (because 360 ÷ 7.2 = 50). Therefore, the distance between Alexandria and Syene (about 800 kilometers) represented 1/50th of the Earth’s total circumference.
2. Calculate the distance between the two cities: Eratosthenes then used the known distance between the two cities—about 800 kilometers (500 miles)—which was provided by travelers and merchants.
3. Apply geometry: With this angle and distance in hand, Eratosthenes could calculate the Earth’s total circumference by multiplying the distance between Alexandria and Syene by 50 (since 7.2 degrees is 1/50th of 360 degrees).

The result? Eratosthenes calculated that the Earth’s circumference was approximately 39,375 kilometers (24,662 miles), a figure remarkably close to the actual measurement of 40,075 kilometers (24,901 miles) that we know today.

Results and Impact

Eratosthenes’ calculation was not just a theoretical exercise—it was an astonishing achievement. The accuracy of his measurement was unprecedented for its time, and it proved that the Earth could be understood through logical reasoning, observation, and mathematical principles.

But beyond the precision of his method, Eratosthenes’ work also showed the power of scientific inquiry. He didn’t rely on complex tools or instruments; instead, he used everyday observations and basic geometry to make an extraordinary discovery. His method was elegant in its simplicity, relying on the straightforward principle that the Earth’s curve causes the sun’s rays to hit different locations at slightly different angles.

Legacy

Eratosthenes’ method was ingenious in its simplicity. He didn’t have access to modern technology or measuring instruments, but through careful observation and a basic understanding of geometry, he was able to solve one of the greatest scientific challenges of the ancient world.

He confirm that the Earth was a sphere, but it also laid the groundwork for future explorers and scientists to understand the world around them more accurately. His work influenced generations of scholars, including those who worked on later developments in geography, astronomy, and mathematics.

Today, Eratosthenes is remembered as one of the great minds of ancient Greece, and his method for calculating the Earth’s circumference remains a testament to the ingenuity of the human spirit. His ability to combine observation with mathematics has inspired countless scientists throughout history, showing that even the most profound mysteries can be solved through curiosity, careful thought, and a bit of imagination.