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Eratosthenes’ Method

Eratosthenes of Cyrene276-194 B.C.E.

“β”

The known world in 194 B.C.E.

Ancient Library of Alexandria

Modern Library of Alexandria

Modern Library of Alexandria

How big is the Earth?

Look to the sun for the answer!

Earth

Sun

Well in Syene

Obelisk inAlexandria

What Eratosthenes noticed

Sunlight was at an angle in Alexandria…

…And right overhead in Syene.

θ

How could this be explained?

Center – O – the earth

θ

θ

We can get a simple formula!

θ360°

DistanceCircumference=

Part of a circle in relationto the whole circle…

…Part of the circumference in relationto the whole circumference.

So how big is the earth?

• Eratosthenes figured out that θ was 7.2°

• He knew the distance was 5,000 stadia

• Just plug and chug to find the circumference!

209 mPhoenician-Egyptian

196 mBabylonian-Persian

185 mAttic/Italic

176 mOlympic

157.5 mItinerary

Length (approximate)Stadium name

Ancient unit of measurement – the Stade

Why was he a little bit off?

• The two cities are not directly north or south of each other.

• The distances couldn’t be accurately measured.

• The angle couldn’t be accurately measured.

• He got about 39,690 km. How far off is that?