CDS (II) 2024 General Knowledge · Question 76 of 120

Correct — A, Alexandria and Syene. Eratosthenes was chief librarian at Alexandria in the third century BCE, and the measurement he is remembered for used two Egyptian towns roughly on the same meridian. At Syene, the modern Aswan, the noon Sun at the summer solstice stood directly overhead: rods threw no shadow and sunlight reached the bottom of a well. On the same day at Alexandria, far to the north, a vertical rod did cast a shadow, and Eratosthenes measured the angle at about 7.2 degrees. Seven point two is a fiftieth of a full circle, so the arc between the two towns had to be a fiftieth of the Earth's circumference. Multiplying the known distance between them by fifty gave him roughly 250,000 stadia. What makes the method beautiful is how little it needs — one angle, one distance, and the assumption that the Sun is far enough away for its rays to arrive parallel.

• (b)Syene and Troy — Keeps the right southern town but replaces the observing station with a city in Asia Minor that has no part in the story and lies far off the meridian.
• (c)Alexandria and Troy — Keeps Alexandria and drops the essential town. The whole method depends on Syene, where the solstice Sun was overhead and there was no shadow to measure.
• (d)Alexandria and Thebes — Thebes, modern Luxor, lies in Upper Egypt but not on the Tropic; the zero-shadow observation belongs to Syene, near which the Tropic of Cancer then ran.

That the Earth is a sphere was argued in Greek natural philosophy well before it was measured — Aristotle reasoned it from the round shadow the Earth throws on the Moon during an eclipse and from the way the stars shift as one travels north or south. Eratosthenes, who lived from about 276 to about 195 BCE and ran the Library at Alexandria, turned the question into arithmetic. He is also credited with a system of latitude and longitude, a map of the known world, and the sieve for finding prime numbers that still carries his name.

The item is pure recall, but the recall sticks better if you carry the geometry with it. Syene mattered because the Tropic of Cancer ran close to it in that era, which is what made the solstice Sun stand overhead there. Alexandria mattered because it was north of Syene and nearly on the same meridian, so the angle between the two places was a difference in latitude and nothing else. Troy and Thebes are put in as plausible-sounding classical names. On the printed stem: the paper reads ‘Eratosthenes, a Greek philosopher measured’, with the second comma missing, and describes him as a philosopher where most accounts call him a mathematician and geographer as well. Neither slip touches what is being asked.

• Eratosthenes lived from about 276 to about 195 BCE and became chief librarian of the Library of Alexandria.
• At noon on the summer solstice the Sun cast no shadow at Syene, the modern Aswan, and shone to the bottom of a well there.
• At Alexandria on the same day the shadow angle was about 7.2 degrees, which is one fiftieth of a full circle.
• Multiplying by fifty gave a circumference of roughly 250,000 stadia.
• The method assumes the Sun's rays arrive parallel and that the two towns lie on the same meridian.

• Naming Athens or Rome as the observing station; the observation was made at Alexandria in Egypt.
• Forgetting that Syene is the ancient name of Aswan, which is how the town appears on a modern map.
• Assuming the measurement needed a known distance to the Sun. It needed only the angle and the ground distance.

As a one-line recall of the two cities, or as a question on who first measured the Earth's circumference and how.

• practice — not a real PYQ

  Syene, the town where the solstice Sun stood overhead in Eratosthenes' measurement, is known today by which name?

  • (a)Aswan
  • (b)Luxor
  • (c)Cairo
  • (d)Alexandria

  Answer(a) Aswan — in Upper Egypt, close to where the Tropic of Cancer ran in Eratosthenes' time.

• practice — not a real PYQ

  The shadow angle Eratosthenes measured at Alexandria was about 7.2 degrees. What fraction of a full circle is that?

  • (a)One twelfth
  • (b)One twentieth
  • (c)One fiftieth
  • (d)One hundredth

  Answer(c) One fiftieth — 360 divided by 7.2 is 50, which is why he multiplied the distance between the two towns by fifty.