How Eratosthenes calculated the Earth's circumference

Summary

In ancient Greece, Eratosthenes, head of the Library of Alexandria, ingeniously calculated Earth's circumference using a stick and observations of shadows during the summer solstice. He noted a 7° difference in shadow angles between Alexandria and Syene, cities 5,000 stadia apart. By assuming Earth's spherical shape, he applied simple proportions, equating 7.2 degrees to 1/50th of 360°, to estimate Earth's circumference at approximately 40,000 km, remarkably close to modern measurements.

Takeaways

• 🚀 In the mid-20th century, satellites were launched to determine the Earth's circumference, which was found to be approximately 40,000 km.
• 🏺 Over 2,000 years earlier, the Greek mathematician Eratosthenes estimated the Earth's circumference using a simple experiment.
• 🌞 Eratosthenes observed that at noon on the summer solstice, a stick in Syene (modern-day Aswan) cast no shadow, indicating the sun was directly overhead.
• 📍 He also noted that in Alexandria, a stick cast a shadow at noon on the same day, measuring about 7°.
• 🌐 Understanding the Earth's curvature, Eratosthenes deduced that the difference in shadow angles meant the Earth's surface was curved.
• 📚 Building on the spherical Earth theory proposed by Pythagoras and validated by Aristotle, Eratosthenes used his observations to calculate the Earth's size.
• 📏 He had the distance between Alexandria and Syene measured, finding it to be 5,000 stadia (approximately 800 km).
• 🧮 Eratosthenes applied simple proportions to calculate the Earth's circumference, using the 7° difference and the measured distance.
• 🌍 He estimated the Earth's circumference to be 40,000 km, remarkably close to the modern value.
• 🧠 Eratosthenes' method showcased the power of observation, critical thinking, and mathematical reasoning in ancient times.

Q & A

Who was Eratosthenes and what was his role in ancient Greece?

Eratosthenes was a Greek mathematician and the head of the Library of Alexandria in ancient Greece.

What was the significance of the observation made in Syene during the summer solstice?

In Syene, no vertical shadows were cast at noon on the summer solstice, indicating the sun was directly overhead.

What did Eratosthenes observe in Alexandria on the same day?

In Alexandria, Eratosthenes observed a shadow at noon on the summer solstice, which measured about 7°.

How did the difference in shadows between Syene and Alexandria indicate the Earth's curvature?

The difference in shadows indicated that the Earth's surface is curved, as the sun's rays were coming in at the same angle but creating different shadow lengths in the two locations.

What was the significance of the 7° difference in shadow length observed by Eratosthenes?

The 7° difference in shadow length meant that the two cities were 7° apart on the Earth's 360° surface.

How did Eratosthenes measure the distance between Alexandria and Syene?

Eratosthenes hired a man to pace the distance between the two cities, which was found to be 5,000 stadia, or approximately 800 km.

What method did Eratosthenes use to calculate the Earth's circumference?

Eratosthenes used simple proportions, considering that 7.2° is 1/50th of 360°, and then multiplied the distance between the two cities by 50 to find the Earth's circumference.

What was the estimated circumference of the Earth calculated by Eratosthenes?

Eratosthenes estimated the Earth's circumference to be approximately 40,000 km.

How did Eratosthenes' method compare to modern satellite measurements?

Eratosthenes' method of calculating the Earth's circumference was remarkably close to modern satellite measurements, which determine the Earth's circumference to be about 40,075 km.

What earlier theories supported the idea of a spherical Earth before Eratosthenes' calculations?

The idea of a spherical Earth was proposed by Pythagoras around 500 BC and later validated by Aristotle.