Sindbad~EG File Manager

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\title{Eratosthenes Measures the Earth}
 

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That the earth was round has been known since at least 240 BCE,  when Eratosthenes
calculated its circumference.   His method used only the simplest mathematics, 
and will be explained here.   It depends on the fact that the Sun is sufficiently
far away from Earth that its rays arriving at Earth are essentially parallel, no matter
what part of Earth they strike:
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 The picture shows two rays of light, one landing at Alexandria, Egypt (where Euclid
 lived and worked),  and one landing at Syene, Egypt (modern-day Aswan).
 Syene is approximately due south of Alexandria,  and it happens to be located 
 on the Tropic of Cancer,  which means that at the summer solstice (June 21), the sun 
 is directly overhead at noon.  At that time and day,  the sun in Alexandria will 
 be a little south of the zenith, i.e.,  the shadow cast by a vertical stick will be short,
 but will point north.  
 
 Eratosthenes measured the angle between the sun's rays and the vertical in Alexandria, 
 and found 7 degrees and 12 minutes.   Since there are 360 degrees in a circle, that is 
 about $1/50$ of a circle.   
 If we imagine the two vertical lines at Alexandria and Syene meeting in the middle 
 of the earth, the angle between them will also be one-fiftieth of a circle.
Therefore, the circumference of the Earth is fifty times the distance between Syene and 
Alexandria.

To complete his calculation, Eratosthenes needed to measure the distance between Syene
and Alexandria, and multiply by 50.  He had some experience as a surveyor, and based 
on his knowledge of Egypt, he thought the distance was 5000 ``stadia''.  He inquired 
of traders about the time required to travel between the two cities by camel, to corroborate
this estimate.  

Historians argue about how long one station was.  Apparently there was a Greek station and 
and Egyptian stadion.  If he used the Egyptian definition, then his answer for the circumference
of the Earth was only off by 1.6\%.   Otherwise it was off by 16.3\%.   Either way,
it was pretty accurate for 240 BCE.

Eratosthenes worked at the Musaeum in Alexandria.  The Museum was not what we now think of 
as a ``museum''; it was a research center, where scholars lived and worked.  It had
lecture halls, meeting rooms, gardens, and apartments.  Associated with the 
Museum was the Library of Alexandria,  which archived the work of the entire Greek civilization.
The Library was burned (probably not just once, but several times, starting with a fire 
set by Julius Caesar in 42 BCE, and ending in final destruction with the Muslim invasion
of Egypt in 642.)   

Contrary to what you may have been taught in school,  the knowledge that the Earth is 
spherical (or nearly so) and not flat  was never lost, in spite of the destruction 
of the Musaeum and Library,  the fall of the Roman Empire,  the Plague, and the Dark Ages.
People always knew that the Earth was round.

When Columbus wanted funding for his expedition, he went first to the King of Portugal, 
who refused funding.  It is a myth that the King thought the Earth was flat and Columbus would sail off 
the edge;  instead, his advisors knew that the Earth was spherical, but too large for Columbus to 
make it to India in the tiny ships of that day.   What they didn't know, of course, was that 
North and South America lay within reach.   The Spanish royalty must have not had such good 
advice, and they were eager to compete with the Portugese, who had recently established trade
routes to the East around the southern tip of Africa,  so they did fund Columbus.




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