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# COMENIUS - Experience d'Eratosthene

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Exposé réalisé par un groupe d'étudiant français à partir de la webquest : "ERATOS EXPERIMENT"

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### COMENIUS - Experience d'Eratosthene

1. 1. Citadel of Alexandria Eratosthenes Eratosthenes lived in Alexandria inthe third century AD. He was the director of the Alexandria on a mapAlexandrian library.
2. 2. Sometimes, we watch only sailing of the boat in the sea. It’s evidence that the Earth might be spherical.Using a vertical stick and measuring the cast shadow, that in his hometown of Alexandria, the angle ofelevation of the Sun would be 83° or 7° south of the zenith at the same time. He concluded, using geometryof parallel lines, that the distance from Alexandria to Syene must be 7/360 of the total circumference of theEarth. The distance between the cities was known from caravan travelling to be about 5,000 stadia. Heestablished a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia.Eratosthenes explains the information with the evidence, stadia per degree, and the angle of elevation of thesun on the summer solstice.Eratosthenes knew that on the summer solstice at local noon on the Tropic of Cancer, the Sun would appearat the zenith, directly overhead. He also knew, from using a vertical stick and measuring the cast shadow.The formula used by Erasthenes is :angle of the sun distance to Tropic of Cancer----------------------- = -----------------------------------360° Earth circumference
3. 3. Technic to calculate the earth circumference D = earth circumference90 - a = distance to tropic of cancer (z)Distance Syene →Ville X dans MDans le cas d’Erathosthenes 7 = 787.5 D = 40500 km 360 D
4. 4. Syene is the name of Assouan. The distance is5,000 stadia, 787,5 km. It’s named Assouan or Swan nowadays.
5. 5. Distance from Assouan to Montluçon 3666 kmWe can use a compass to verify the trueposition of the stick.The approximate position of my school and ofSyene.The distance between my school and Assouanis 3666 km.
6. 6. To know when occurs the solarnoon , we can place a stick at 90°and measure the shadow ; thetime the shadow is the smaller isthe time of the solar noon.
7. 7. The measure of the angle of the shadow is 65°. We can use the formula of Eratosthenes: angle of the sun / 360°65/360 = distance to the tropic / earth circumference360*distance to the tropic / 65 = earth circumference360*3666 / 65 = 20,304km. Solar noon
8. 8. Tower of Pise ErathosteneWe found about 20 thousands kilometers or the theorical one is40 075kilometers, we can explain the differences since we have lots ofparameters like the sun angle which is changes all the days and variesduring the differents seasons or the distance to the tropic which is sofare for a human we can’t have it under the hand like a sheet of paperwhich are very difficult to have the true ones (real and a preciselyanswer or number).