Eratosthenes and the Measurement of Earth's Circumference
Who Was Eratosthenes?
Eratosthenes (276–194 BC) was a Greek mathematician, geographer, and astronomer. Known as the "Father of Geography," he is most famous for being the first person to calculate the Earth's circumference with remarkable accuracy over 2,000 years ago.
The Brilliant Idea
Eratosthenes lived in Alexandria, Egypt, and had access to a wealth of knowledge. He learned that at noon on the summer solstice in the city of Syene (modern-day Aswan), the Sun was directly overhead, casting no shadow. However, in Alexandria, which is north of Syene, objects still cast shadows at the same time.
This observation gave him an idea: by measuring the angle of the shadow in Alexandria and knowing the distance between the two cities, he could calculate the Earth's circumference using simple geometry.
The Math Behind the Measurement
Eratosthenes measured the angle of the shadow in Alexandria at noon, which was about 7.2 degrees. He reasoned that this angle was equivalent to 1/50th of a full circle (360 degrees). He then used the following relationship:
Circumference of Earth (C) = Distance between cities (D) × (360° ÷ Angle)
The distance between Syene and Alexandria was approximately 800 kilometers. Plugging in the values:
C = 800 km × (360° ÷ 7.2°)
C = 800 km × 50
C = 40,000 km
Eratosthenes concluded that the Earth's circumference was about 40,000 kilometers, which is incredibly close to modern measurements!
Impact of Eratosthenes' Discovery
This calculation was groundbreaking for its time and demonstrated the power of observation and geometry. It established that the Earth is a sphere and provided a foundation for future explorers and scientists.
Conclusion
Eratosthenes' ingenious use of shadows and basic geometry not only calculated the Earth's size but also inspired countless discoveries in geography, astronomy, and mathematics. His work remains a testament to human curiosity and intellect.