Cosmos - Eratosthenes calculates Earth's circumference

In the 3rd century BCE, Eratosthenes calculated the circumference of the Earth to high precision.
BicycleRepairMansays...

Measure the stick, and the shadow of the stick, and you get a triangle, in this case the sunlight hit the stick in Alexandria at a 7 degree angle.. so the triangle would be 90, 83 and 7 degrees.

so if the stick was 100cm tall, then the shadow would be 12.3 cm long, so thats 7 degrees angle between the imagined line from the top of the stick to the end of the shadow.

LEET Drawing:

Alexandria:
\\
\\\sunlight
\\\
\\\\

7 degrees
|\
| \
|_\
90 83

Syena:

||||
|||sunlight
||||
|||
0
|
|
|
|
no shadow..

In other words, assuming that the sunlight was parallel, the two sticks would join in the center of the earth at 7 degrees.(they were not parallel, as you would expect on a flat earth.)

honkeytonk73says...

You have got to love zealotry, book burning, and an aversion to scientific knowledge.. or more specifically knowledge that which is beyond or in contradiction with a supposed 'factual' religious/biblical reference.

Burn the books! Burn them! Heretic! Non-believer! Burn! Burn!

*sigh*

8132says...

No real use? Surely civilisation would have progressed at a faster pace if the early sailors did not fear the edge of the earth...

Eratosthenes was a genius >< Someone should put that on an IQ test. Ouch.

Quboidsays...

That is impressive. It does require a good understanding of the sun, I have no idea what people thought of it at the time. The shadow difference could be explained by the sun being much, much smaller and closer to earth, so that the rays aren't effectively parallel.
 
 
 O    <-- Sun  
 
 
 
  |        |\
_|____|\\_
 
 
There you go - different shadows on a flat earth. It requires a screwed up understanding of the sun, but if you think the world is flat, who knows what else you've got wrong (or maybe we've got wrong!! <_<)
Shame this took 2000 years to be accepted and even then it was resisted strongly by ... certain groups.

Lithicsays...

Errrm, feels very errendous to claim that Eratosthenes (ca 240 BC) 'discovered' that the earth was not flat when that fact had been a strong hypothesis since atleast ca 600 BC (and probebly as far back as 900 BC from memory) and Aristotle (ca 330 BC) provided quite compelling observational evidence for a spherical earth, Eratosthenes really mostly added to that.

So contrary to what is still sometimes a popular belief 'intellectuals' in the European (dont know enough about arabic/asian/south american etc to comment really) world have not believed the earth to be flat for atleast 2000 years and probebly longer.

Still Carl Sagan does have a purty voice, rawr.

BicycleRepairMansays...

Well, Eratosthenes calculated the circumference, which is more than just guessing its shape.

But still,information flow hasnt always been like it is now, to put it mildly. One reason I dig this story so much (apart from Sagan telling it) is that this little piece of information, a mere curiousity, could do so much if the right brain happens to come across it, this is why I love the internet so much, it really has potential to change the world, simply over the information flow, its so easy to get information nowadays..

Anyway, for the greater part of the last 3000 years, and certainly all the time before it, information flow sucked. Yes, people back this and this time figured it out, but its not like putting it on Youtube and everyone can cry OLD! three days later. No, most information just got stowed away and forgotten by everyone for hundreds of years before re-emerging, and wars were not being broadcast live on CNN either, news took weeks and months to reach more distant places, and the information had suffered through a heavy game of "telephone" before reaching the majority's ears.

This lack of effective communication prevented people from hearing about disease outbreaks, it created ignorant religions and left most people clueless. Hence you get times like the dark ages, where people thought the earth was flat, hundreds of years after these discoveries. It is readily apparent from an honest interpretation of the Qu'ran, for instance, that Muhammed thought the earth was flat as a pancake.

Lithicsays...

I gotta say BicycleRepairMan, I think you grossly underestimate the information flow and knowledge of both the ancient and the medieval world. A discovery like Aristotles evidence of a spherical earth (which was a lot more then just 'guessing' at its shape) would likely have been all over the hellenistic world within a few years.

And nothin I have ever read on the topic has said that the concept of a flat earth was ever wide spread during the 'dark' ages. In fact Klaus Anselm Vogel stated in his disseration from 1995 that "since the eighth century, no cosmographer worthy of note has called into question the sphericity of the Earth." (in german at http://webdoc.sub.gwdg.de/diss/2000/vogel/index.htm#inhalt).

I dont know much about Islamic history and I've never read the Qu'ran so wouldnt really feel comfortable commenting on that part though.

BicycleRepairMansays...

Yes, well I dont doubt the sincerity of "since the eighth century, no cosmographer worthy of note has called into question the sphericity of the Earth." but the problem is: surely a few well read historians, scientists etc was "in the know", but we all know how many books were read TO the illiterate masses, lets just say that they could all be counted on one finger, and one of them ends with "ible". The masses were kept in the dark. And occationally, some populist dictator or warlord of some kind would wipe out the few scholars there were.

The Qu'ran was written in the 7th century, btw, but as I tried saying, going backwards in time trying to put a date on when we knew what, is basically a hopeless task, because information didnt flow that good. its all well and good that we can dig up a book or piece of paper with some great thinker who knew much more than we'd expect from the timeline, but again, was it "Established" knowledge? Its sometimes difficult to know.

Take Darwin, next year there will be 150 years since he published "The Origin of Species by means of Natural Selection", yet half of America still dont fuckin get it, and its not even the dark ages(or so they tell me) And we DO have all this information flow, and most people can read, and so on. Just imagine how much more crippled progress was earlier.

Thats what I mean with information flow.

Lithicsays...

When you put it that way I can see your point. There is very little we can know about how the general public percieved things since the only people to write things down (and perserve them for us) was usually the educated elite.

The fact that people can't stay educated in this day and age is just sad.

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