The sieve of Eratosthenes
Crossing out multiples systematically leaves the prime numbers: numbers greater than 1 with no smaller whole-number factors except 1.
06 / ANTIQUITY TO THE RENAISSANCE
Eratosthenes of Cyrene
You can measure a whole planet without travelling all the way around it. Measure one part, then find how many copies make a full turn.
Explore the mathematics ↓
01 / A PART AND THE WHOLE
Measure the Earth with a shadow
At noon on midsummer’s day, the sun stood straight above Syene: upright sticks cast no shadow. At the same moment in Alexandria, a stick cast a short one.
That little shadow angle is the key. Because sunlight is parallel, it tells you what slice of the whole Earth lies between the two cities.
Why does one stick cast a shadow and the other not?
At noon in Syene the sun is straight overhead. Drag City B along the Earth and watch its stick’s shadow.
Route from Syene to City B
=Copies to go all the way round
=Earth’s circumference
Eratosthenes’ own numbers
He reportedly measured 7.2° at Alexandria, one fiftieth of a full turn, and took the route to Syene as 5,000 stadia.
So the Earth is 50 × 5,000 = 250,000 stadia around. The exact length of his stadium is debated, so the lesson uses modern kilometres.
THE IDEAThe shadow angle at the stick equals the angle at Earth’s centre. If it is 1/50 of a full turn, the route is 1/50 of the way around the Earth.
The person behind the ideas
- Born in Cyrene, in present-day Libya; later worked in Alexandria.
- Directed the Library of Alexandria and studied geography, astronomy, and mathematics.
- Estimated Earth’s circumference using a measured distance and an angle from sunlight.
More of the mathematics
Mathematical geography
He connected distances, latitude, and a spherical Earth to the task of making maps.