He made observations of the angle of the Sun with respect to zenith (overhead) at different latitudes which enabled him to accurately calculate the circumference of the Earth.

Question

BlackTom AI · Accepted Answer

Eratosthenes used observations of the Sun’s zenith angle at different locations to compute the Earth's circumference.

1. Relevant knowledge points and concepts
- The Sun’s rays are effectively parallel at Earth’s scale. A difference in the Sun’s zenith angle between two locations equals the angle subtended at the Earth’s center by the arc between them.
- Fraction of a full circle = central angle/360°. Circumference = (distance between locations) / (fraction of circle).
- Historical data: at Syene (Aswan) the Sun was overhead at local noon on the summer solstice; in Alexandria a shadow indicated an angle of about 7.2°.

2. Step-by-step reasoning
- Measure the angular difference: Alexandria’s Sun angle from zenith ≈ 7.2° relative to Syene (where angle = 0° that day).
- Convert angle to fraction of circle: 7.2°/360° = 1/50.

3. Calculations and intermediate steps
- If the distance between Syene and Alexandria = 5,000 stadia (Eratosthenes’ estimate), then Earth’s circumference = distance × (360° / 7.2°) = 5,000 stadia × 50 = 250,000 stadia.
- Converting to modern units depends on the stadion length, but this gives a value close to the true circumference (~40,000 km), demonstrating remarkable accuracy.

4. Why the correct answer is correct
- The method described (different zenith angles at different latitudes to infer Earth’s circumference) is the hallmark of Eratosthenes’ famous measurement around 240 BCE. No other listed figure applied this specific geometric method to measure Earth’s size.

5. Why other choices are incorrect
- Plato: ancient philosopher, not credited with measuring Earth’s circumference.
- Aristotle: made many natural-philosophy observations (argued for a spherical Earth) but did not perform this angular-distance circumference calculation.
- Aristarchus: worked on relative sizes and distances of the Sun and Moon and proposed a heliocentric idea, but did not calculate Earth’s circumference this way.

6. Conclusion
The correct answer is Eratosthenes, matching the provided answer.

He made observations of the angle of the Sun with respect to zenith (overhead) at different latitudes which enabled him to accurately calculate the circumference of the Earth.单项选择题

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