eratosthenes method
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A
Mr. SyracusePowerPoint Presentation
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Eratosthenes’ Method
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Eratosthenes of Cyrene276-194 B.C.E.
“β”
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The known world in 194 B.C.E.
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Ancient Library of Alexandria
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Modern Library of Alexandria
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Modern Library of Alexandria
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How big is the Earth?
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Look to the sun for the answer!
Earth
Sun
Well in Syene
Obelisk inAlexandria
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What Eratosthenes noticed
Sunlight was at an angle in Alexandria…
…And right overhead in Syene.
θ
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How could this be explained?
Center – O – the earth
θ
θ
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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.
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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!
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209 mPhoenician-Egyptian
196 mBabylonian-Persian
185 mAttic/Italic
176 mOlympic
157.5 mItinerary
Length (approximate)Stadium name
Ancient unit of measurement – the Stade
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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?