Eratosthenes' Measurement Cities Explained

The question asks about the specific locations used by the ancient Greek scholar Eratosthenes to calculate the Earth's circumference. He cleverly used the difference in the angle of the Sun's rays at two different locations on the same day.

Understanding Eratosthenes' Method

Eratosthenes' measurement technique was based on a simple observation and geometric principles:

• He knew that on the summer solstice, at noon in Syene (modern Aswan, Egypt), the Sun was directly overhead. This meant that sunlight shone straight down into deep wells without casting any shadows.
• At the same time (noon on the summer solstice), in Alexandria, which was located directly north of Syene, the Sun was not directly overhead.
• Eratosthenes observed that vertical objects in Alexandria cast a shadow at this time.
• He measured the angle of this shadow in Alexandria. Using geometry, he deduced this angle represented the difference in latitude between the two cities relative to the Earth's center.
• Knowing the approximate distance between Alexandria and Syene, he could then scale this angle up to estimate the full circumference of the Earth.

The Key Cities Used

The two cities Eratosthenes used for his groundbreaking measurement were:

• Syene (modern Aswan)
• Alexandria

These two cities were chosen because they lay roughly on the same line of longitude, and Eratosthenes had information about the Sun's position relative to the vertical in both locations simultaneously.

Why Alexandria and Syene?

The choice of Alexandria and Syene was critical:

• Syene's location near the Tropic of Cancer meant the Sun could be directly overhead at noon on the summer solstice.
• Alexandria's position to the north allowed for a measurable shadow at the same time, providing the necessary angle difference.

This comparison allowed Eratosthenes to calculate the angle difference, which was approximately 7.2 degrees, or 1/50th of a full circle (360 degrees). By multiplying the distance between the cities by 50, he arrived at his estimate for the Earth's circumference.