# Calculate the circumferance of the earth using Erathosthenes method.

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### 1 Answer

During the early time in the world, measuring large objects seem to be very hard; similar to the circumference of the earth which requires series of measurement to get it. However, Eratosthenes tried measuring the circumference without going around the world instead he used the lights and intelligent assumptions to measure the circumference of the earth.

Gathering the information from different travellers and experts, he came up with the following descriptions and assumptions.

1. The earth is spherical

2. At the summer solstice, the sun is directly overheard Alexandria.

3. The distance from Syene and Alexandria is 5000 stadia (1 stadium = 157.5 m)

He measured a shadow on Alexandria at noon to measure the sun’s angle and found out to be 7’12 or 7.2 degrees. Assuming that the earth is spherical, he concluded that the angle is 1/50 of the whole circle. Since he had a copy of the distance from Alexandria and Syene which is approximately 5040 stadia, by multiplying it by 50 he can get the circumference of the earth.

The solution can be written as: `(360^o)/(7.2^o) *(distance f rom Al exan dria t o Syen e)`

`(360^o)/(7.2^(o)) * (5000 stadia)`

`= 250000 stadia * ((157.5 meters)/(1 stadia)) * (( 1 kilometers)/(1000 meters))`

`= 39375 km = 40000 km ` ***

*** the measurement of stadia are varying. Other conversion says that 1 stadia = 185 m. Other historians are also saying that the distance from Alexandria and Syene is about 5040stadia not 5000 stadia.

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