Question 1

Did Eratosthenes really measure the Earth?

Accepted Answer

Yes — and the measurement was remarkably good, achieved with geometry, a well and the distance between two cities, around **240 BC**.

**The observation he started from.** In Syene — modern Aswan — at noon on the summer solstice, the sun was reported to shine directly down a deep well, casting no shadow. The sun was therefore **directly overhead** at that moment.

**The measurement.** On the same date in Alexandria, some distance north, Eratosthenes measured the shadow cast by a vertical object and found the sun was about **7.2 degrees** from vertical.

**The reasoning.** If the Earth is a sphere and the sun's rays arrive effectively parallel, the angular difference between the two locations equals the angle they subtend at the Earth's centre. **7.2 degrees is one fiftieth of a circle.** Therefore the distance between Alexandria and Syene is one fiftieth of the Earth's circumference.

Multiplying that distance by fifty gives the circumference of the Earth.

**How accurate was it?** He expressed the result in **stadia**, and the difficulty is that the length of a stadion is uncertain and varied. Depending on which value is assumed, his result is either within a few percent of the modern figure or off by around fifteen percent. **The uncertainty is in our knowledge of his units**, not in his method — which is exact.

**The sources of error in his data** were real: the distance between the cities was estimated, possibly from the time taken by camel caravans or by professional pacers; Syene is not precisely on the Tropic of Cancer; and the two cities are not on exactly the same meridian. These errors partly cancelled.

**What it demonstrates.** That the Earth was **known to be spherical** in the ancient world, and its size approximately known — which is why the persistent belief that people before Columbus thought the Earth was flat is false. Educated opinion had accepted sphericity since the Greeks.

**He also** measured the tilt of the Earth's axis, produced a sieve for finding prime numbers still taught today, attempted a chronology of history, and served as chief librarian at Alexandria.

Question 2

Was Columbus trying to prove the Earth was round?

Accepted Answer

No. That the Earth is a sphere had been established knowledge among educated Europeans for nearly two thousand years before Columbus sailed, and nobody he petitioned believed otherwise. The ancient

Question 3

Who was Ibn al-Haytham?

Accepted Answer

An eleventh-century scholar whose work on optics overturned the accepted theory of vision and who is described by many historians as having practised something close to the modern scientific method

Question 4

Who was Hypatia of Alexandria?

Accepted Answer

Hypatia was a mathematician, astronomer and philosopher who taught in Alexandria around AD 400, and one of the few women scholars of the ancient world whose reputation is securely documented by

Question 5

Did Pythagoras discover Pythagoras' theorem?

Accepted Answer

Almost certainly not. The relationship was known and used for over a thousand years before he was born, across several civilisations. The prior evidence: Babylonian mathematics. The clay tablet

Question 6

Did Archimedes really shout Eureka in the bath?

Accepted Answer

Almost certainly not as told — the story appears two centuries after his death, in a source not otherwise noted for rigour, and the physics as described does not work well. The story. Hiero II of

Question 7

Who was Eunice Foote?

Accepted Answer

An American scientist and campaigner who, in 1856, demonstrated experimentally that carbon dioxide traps heat — three years before the work usually credited with founding climate science, and then

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