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How did Eratosthenes measure the earth's circumference

  1. Aug 21, 2013 #1
    Hello everybody,
    Eratosthenes of Cyrene ( 276 BC– 195 BC) was a Greek mathematician, geographer, poet, astronomer, and music theorist.The interesting thing about his biography,is that he was able to measure the earth's circumference using only simple tools and good geometry .here is a video of Carl Sagan explains how he did it .

  2. jcsd
  3. Aug 21, 2013 #2
    If you can't follow his calculation, feel free to ask me.
    This is what wikipedia tells us:

    "Eratosthenes calculated the circumference of the Earth without leaving Egypt. Eratosthenes knew that, on the summer solstice, at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead (he had been told that the shadow of someone looking down a deep well would block the reflection of the Sun at noon). Using a gnomon, he measured the sun's angle of elevation at noon on the solstice in his hometown of Alexandria, and found it to be 1/50th of a circle (7°12') south of the zenith. He could have used a compass to measure the angle of the shadow cast. Assuming that the Earth was spherical (360°), and that Alexandria was due north of Syene, he concluded that the meridian arc distance from Alexandria to Syene must therefore be 1/50 = 7°12'/360°, and was therefore 1/50 of the total circumference of the Earth. His knowledge of the size of Egypt after many generations of surveying trips for the Pharaonic bookkeepers gave a distance between the cities of 5,000 stadia (about 500 geographical miles or 927.7 km). This distance was corroborated by inquiring about the time that it takes to travel from Syene to Alexandria by camel. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently debated. The common Attic stadion was about 185 m, which would imply a circumference of 46,620 km, which is off the actual circumference by 16.3%. However, if we assume that Eratosthenes used the "Egyptian stadion" of about 157.5 m, his measurement turns out to be 39,690 km, an error of 1.6%."
    Last edited: Aug 21, 2013
  4. Aug 21, 2013 #3


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    By the way, everybody "learns" in elementary school that Christopher Columbus differed from everyone else of his time because he believe the world was round while every one else believed it was flat. That, of course, is untrue. Every educated person (and, as far as geography is concerned that would include sea captains) knew the world was round and most knew the size from Erastosthene's calculation.

    Columbus was one of a minority of people of the time who believed Eratosthenes was wrong. Their reason was, essentially, a "stylistic" one- they refused to believe that half of the world was full of land (Europe, Africa, Asia) while the other half was empty ocean. Of course, they were wrong- and the other half of the world was full of "new lands".
  5. Aug 21, 2013 #4
    Just to clarify, Columbus didn't think Eratosthenes was wrong about the shape of the Earth, just the size. The funniest part is that in that false story, it's often claimed that Columbus "proved" that the Earth was round. I guess going a little further west than before and then returning just isn't possible on a flat Earth!
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