Eratosthenes, a Greek philosopher measured the Earth's circumference based on the angle of Sun rays at two different points. Which cities were they?

The correct answer is Alexandria and Syene.

Key PointsEratosthenes' Measurement of Earth's Circumference

• Eratosthenes was a Greek philosopher, mathematician, and geographer who lived during the 3rd century BCE.
• He is best known for his remarkably accurate calculation of the Earth's circumference.
• Eratosthenes used the difference in the angle of the Sun's rays at two different locations to estimate the Earth's circumference.
• The two cities involved in his experiment were Alexandria and Syene (modern-day Aswan).
• In Syene, the Sun was directly overhead at noon during the summer solstice, casting no shadow. In Alexandria, a stick placed vertically in the ground cast a shadow, making an angle with the vertical.
• By measuring this angle and knowing the distance between the two cities, Eratosthenes was able to use simple geometry to calculate the Earth's circumference.

Additional Information

• Alexandria was an ancient city in Egypt, founded by Alexander the Great. It was one of the most important cultural and intellectual centers of the ancient world.
• Syene (modern-day Aswan) is located near the Tropic of Cancer. During the summer solstice, the Sun is directly overhead at noon.
• Geometry and Trigonometry: Eratosthenes' calculation was based on the principles of geometry and trigonometry. He assumed that the Earth was a sphere and used the formula for the circumference of a circle to arrive at his estimate.
• Historical Impact: Eratosthenes' measurement was remarkably accurate for his time. His estimate of the Earth's circumference was only about 10% off from the actual value, showcasing the advanced understanding of geometry and astronomy in ancient Greece.
• Legacy: Eratosthenes' work laid the foundation for future geographers and astronomers. His method of using geometric principles to solve real-world problems is still taught in schools today.