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

2. Citadel of Alexandria
Eratosthenes
Eratosthenes lived in Alexandria in
the third century AD.
He was the director of the Alexandria on a map
Alexandrian library.

4. 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 of
elevation of the Sun would be 83° or 7° south of the zenith at the same time. He concluded, using geometry
of parallel lines, that the distance from Alexandria to Syene must be 7/360 of the total circumference of the
Earth. The distance between the cities was known from caravan travelling to be about 5,000 stadia. He
established 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 the
sun on the summer solstice.
Eratosthenes knew that on the summer solstice at local noon on the Tropic of Cancer, the Sun would appear
at 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

5. Technic to calculate the earth circumference
D = earth circumference
90 - a = distance to tropic of cancer (z)
Distance Syene →Ville X dans M
Dans le cas d’Erathosthenes 7 = 787.5
D = 40500 km
360 D

6. Syene is the name of Assouan. The distance is
5,000 stadia, 787,5 km.
It’s named Assouan or Swan nowadays.

7. Distance from Assouan to Montluçon
3666 km
We can use a compass to verify the true
position of the stick.
The approximate position of my school and of
Syene.
The distance between my school and Assouan
is 3666 km.

8. To know when occurs the solar
noon , we can place a stick at 90°
and measure the shadow ; the
time the shadow is the smaller is
the time of the solar noon.

9. 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 circumference
360*distance to the tropic / 65 = earth circumference
360*3666 / 65 = 20,304km.
Solar noon

10. Tower of Pise
Erathostene
We found about 20 thousands kilometers or the theorical one is
40 075kilometers, we can explain the differences since we have lots of
parameters like the sun angle which is changes all the days and varies
during the differents seasons or the distance to the tropic which is so
fare for a human we can’t have it under the hand like a sheet of paper
which are very difficult to have the true ones (real and a precisely
answer or number).