# Circumferemce Of Planet Earth . .



## Evagrius Ponticus (Dec 13, 2010)

Hello Friends,  

I've been trying for some time to completely understand how Eratosthenes was able to successfully measure the circumference of Planet Earth.  I've read his method several times but a complete understanding remains a tad beyond my reach.  

In the simplest terms, can anyone explain how he was able to determine what portion of a circle a segement of planet earth represents?  Thank You!

http://www.juliantrubin.com/bigten/eratosthenes.html


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## SydneyGeek (Dec 14, 2010)

Let's see...

Sun is directly overhead the Tropic of Cancer (Capricorn in Southern Hemisphere) at local noon on the summer solstice.
That makes the sun's rays go straight through the centre of the Earth, assuming it's a circle.
Next is to measure the angle of the sun where you are, at local noon on the solstice. Subtract from 90, and you get how many degrees you are away from the Tropic. The reason for that is that where parallel lines are cut by another straight line, the angle between the parallel and intersecting lines is the same. At the Tropic, it's 90 degrees. Where you are, it should be 90 degrees less the angle at the centre (of the earth). 
Eratosthenes got 7 degrees when he made the measurement. He then calculated the distance between Syene and Alexandria and multiplied it by 360/7 to get the answer. 
Does that help?

Denis


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## MrKowz (Dec 14, 2010)

SydneyGeek said:


> Let's see...
> 
> Sun is directly overhead the Tropic of Cancer (Capricorn in Southern Hemisphere) at local noon on the summer solstice.
> That makes the sun's rays go straight through the centre of the Earth, assuming it's a circle.
> ...


 
Did you write that off the top of your head!?  Very impressive!


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## Evagrius Ponticus (Dec 14, 2010)

Thanks Sydney - It does help - I will continue to work my way through it.  Measuring the angle of the sun is my next challenge


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## MrKowz (Dec 14, 2010)

Evagrius Ponticus said:


> Thanks Sydney - It does help - I will continue to work my way through it. Measuring the angle of the sun is my next challenge


 
Don't look directly at it... might sting a bit 

I think what you could do is put something with point perfectly vertical on a perfectly level surface.  Measure the distance from the base of the apparatus to the top.  Then look at the shadow.  Measure the distance from the center of the base to the tip of the shadow.  You can then use TAN to find the angle.


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## Atroxell (Dec 14, 2010)

Depending on how precise you want to get, you could use a protractor (or something similar) with a tube taped to it's flat side and a plumb line to measure the the sun's angle. When the tube is casting a circular shadow, then you have the correct angle.

That's how we did it in grammar school, once upon a long time ago...

Or borrow someone's sextant--eveyone has one, right?


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## Norie (Dec 14, 2010)

Eh, is the Earth a circle?

Isn't it some sort of ovoid, or geoid, or oddoid?


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## MrKowz (Dec 14, 2010)

Norie said:


> Eh, is the Earth a circle?
> 
> Isn't it some sort of ovoid, or geoid, or oddoid?


 
It is.  The spinning of the earth causes it to bulge out slightly at the equator due to centrilital force (think about a ball of dough and spinning it).  However, for all intensive purposes, we can consider it a sphere.


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## Norie (Dec 14, 2010)

'intensive' purposes?


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## Taul (Dec 14, 2010)

Norie said:


> Eh, is the Earth a circle?
> 
> Isn't it some sort of ovoid, or geoid, or oddoid?




no no no, only the sky is spheroid, the earth itself is flat, look out of the windows guys.

Whilst on the subject, gravity is a myth, the earth sucks!


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## MrKowz (Dec 14, 2010)

Paul-H said:


> no no no, only the sky is spheroid, the earth itself is flat, look out of the windows guys.
> 
> Whilst on the subject, gravity is a myth, the earth sucks!



You might like the Dark****** theory:

http://www.ed-cindy.com/gpage4.html


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## diddi (Dec 14, 2010)

the earth is about 21km shorter than it is wide, so multiply by pi gives somewhere near 65km difference in polar circumference over equatorial circumference.


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## Evagrius Ponticus (Dec 14, 2010)

MrKowz - now you tell me not to look at the sun directly - if you'd informed me of this little tid bit earlier I may still have functioning retnas 

Also, is it the spinning of the earth that creates the buldges on the sides or are the buldges created by the moon's gravitational force?


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## diddi (Dec 14, 2010)

the moon does not orbit the earth equatorially, so it is not responsible the ovoid deformation on the earth. it is the rotation which causes this.  moon causes tides, though, and also the earth as it orbits the sun exhibits 'nutation' which is tiny wobbling in the mathematically predicted orbit due to the gravitational pulling of the moon.


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## Atroxell (Dec 15, 2010)

In any event, the spheroid shape of the Earth is negligible for most applications of the distance between two geographic points. It only becomes relevant when you are measuring large distances.

Most of my point-to-point measurements are less that 150 miles, so I don't think that the egg-shaped Earth issue is relevant.

P.S. If the sky is spheroid, then you support my idea that the moon landing was faked. The moon and stars would then have to be a two dimensional images overlaid on a black background (which of course, blocks out our view of Lands of The Gods.) Or are the moon and stars just DARK SUCKERS????? Oh, I am so losing sleep tonight...


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## Sandeep Warrier (Dec 15, 2010)

The Dark ****** Theory is really funny 

Enjoyed it a lot.


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## Sandeep Warrier (Dec 15, 2010)

If you would open a drawer  very slowly you will notice that the light goes into the drawer (this  you can see happen). You cannot see the dark leave the drawer. Continue  to open the drawer and light will continue to enter the drawer; however,  you will not see any dark leave the drawer. Therefore, dark is faster  than light.


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## Taul (Dec 15, 2010)

yes, dark is very fast, it's about the same speed as Schrödinger's cat


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## Evagrius Ponticus (Dec 15, 2010)

Thanks for the explanation Diddi, well done. If it is true that the moon is escaping earth's orbit at roughly 1 inch per year, and I have no reason to doubt this position, and it is also true that the moon's gravitational force is what stabilized the earth on it's 24 degree tilt and controls the speed of earth's rotation so that a day is 24 hours, then at what point will the moon be far enough from earth so that earth's tilt will become unpredictable and the length of each day will increase? Which is more likely to occur first, the complete escape of the moon from earth's orbit or the exhaustion of the sun's energy source? I am only asking so I can plan ahead!


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## MrKowz (Dec 15, 2010)

Evagrius Ponticus said:


> Thanks for the explanation Diddi, well done. If it is true that the moon is escaping earth's orbit at roughly 1 inch per year, and I have no reason to doubt this position, and it is also true that the moon's gravitational force is what stabilized the earth on it's 24 degree tilt and controls the speed of earth's rotation so that a day is 24 hours, then at what point will the moon be far enough from earth so that earth's tilt will become unpredictable and the length of each day will increase? Which is more likely to occur first, the complete escape of the moon from earth's orbit or the exhaustion of the sun's energy source? I am only asking so I can plan ahead!


 
I don't think you have anything to worry about for the next 2.3 billion years or so.


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## Evagrius Ponticus (Dec 15, 2010)

2.3 Billion Eh, I suppose that's enough time  I wonder what this board will look like then - will they still be using Excel?


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## MrKowz (Dec 15, 2010)

Nah, everyone will have a computer chip in their brain, hunting for Sarah Conner.


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## Sandeep Warrier (Dec 15, 2010)

Evagrius Ponticus said:


> Thanks for the explanation Diddi, well done. If it is true that the moon is escaping earth's orbit at roughly 1 inch per year, and I have no reason to doubt this position, and it is also true that the moon's gravitational force is what stabilized the earth on it's 24 degree tilt and controls the speed of earth's rotation so that a day is 24 hours, then at what point will the moon be far enough from earth so that earth's tilt will become unpredictable and the length of each day will increase? Which is more likely to occur first, the complete escape of the moon from earth's orbit or the exhaustion of the sun's energy source? I am only asking so I can plan ahead!



The Sun will be around for the next 5 billion years... so no worries there 

Though after some time, we may actually be within the Sun (not for another 3 billion years or so.... so lots of time to plan ahead )


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## diddi (Dec 15, 2010)

Evagrius Ponticus said:


> I wonder what this board will look like then - will they still be using Excel?



I expect that we shall discover that the board is run by mice and that the all the cyber-dolphins will have left cyber-earth saying 'so long and thanks for all the cyber-fish'


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## Evagrius Ponticus (Dec 15, 2010)

Hmmm, you are right, I think they estimate that the sun will be around for another 5 billion years or so, but since the sun gets 10% hotter every 1 billion years, we may have moved our unruly species to another home by then Maybe some distant planet where the laws of physics work like Road Runner Cartoons 

Also Sandeep - you may have a valid point about dark being faster than light.  Based on observations, the universe is expanding at an increasing rate, and that in defiance of gravity, and scientists don't seem to know how or why it is expanding, so they have called the force that is expanding the Universe "Dark Energy."  It could be expanding faster than the speed of light . . .I suppose . .


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## Sandeep Warrier (Dec 16, 2010)

Evagrius Ponticus said:


> Also Sandeep - you may have a valid point about dark being faster than light.  Based on observations, the universe is expanding at an increasing rate, and that in defiance of gravity, and scientists don't seem to know how or why it is expanding, so they have called the force that is expanding the Universe "Dark Energy."  It could be expanding faster than the speed of light . . .I suppose . .



Actually scientist havent been able to figure out the amount of matter present in the universe. According to current theory (or at least the ones prevalent 6 years ago when I did my Masters) there are 3 possible endings for the Universe depending on something called Critical Density (Ω)..

1. If the amount of matter is more than Ω then in time gravity will take over causing the universe to collapse.
2. If the amount of matter equals Ω then in time the acceleration and gravity will balance each other and the universe will just be.
3. If the amount of matter is lesser than Ω then the universe will continue to expand forever...... This, if I recollect correctly, is the current proposed fate, since scientists say that dark energy exerts negative pressure, which counters the attractive force of gravity.




Evagrius Ponticus said:


> Maybe some distant planet where the laws of physics work like Road Runner Cartoons



*Cartoon Laws of Physics* ​
*Cartoon Law I:* Any body suspended in space will remain in space until made aware of its situation.

Daffy Duck steps off a cliff, expecting further pastureland.  He loiters in midair, soliloquizing flippantly, until he chances to look down.  At this point, the familiar principle of 32 feet per second per second takes over.

*Cartoon Law II:* Any body in motion will tend to remain in motion until solid matter intervenes suddenly.

Whether shot from a cannon or in hot pursuit on foot, cartoon characters are so absolute in their momentum that only a telephone pole or an outsize boulder retards their forward motion absolutely.  Sir Isaac Newton called this sudden termination of motion the stooge's surcease.

*Cartoon Law III:* Any body passing through solid matter will leave a perforation conforming to its perimeter.

Also called the silhouette of passage, this phenomenon is the specialty of victims of directed-pressure explosions and of reckless cowards who are so eager to escape that they exit directly through the wall of a house, leaving a cookie-cutout-perfect hole.  The threat of skunks or matrimony often catalyzes this reaction.

*Cartoon Law IV:* The time required for an object to fall twenty stories is greater than or equal to the time it takes for whoever knocked it off the ledge to spiral down twenty flights to attempt to capture it unbroken. Such an object is inevitably priceless, the attempt to capture it inevitably unsuccessful.

*Cartoon Law V:* All principles of gravity are negated by fear.

Psychic forces are sufficient in most bodies for a shock to propel them directly away from the earth's surface.  A spooky noise or an adversary's signature sound will induce motion upward, usually to the cradle of a chandelier, a treetop, or the crest of a flagpole.  The feet of a character who is running or the wheels of a speeding auto need never touch the ground, especially when in flight.

*Cartoon Law VI:* As speed increases, objects can be in several places at once.

This is particularly true of tooth-and-claw fights, in which a character's head may be glimpsed emerging from the cloud of altercation at several places simultaneously.  This effect is common as well among bodies that are spinning or being throttled.  A `wacky' character has the option of self-replication only at manic high speeds and may ricochet off walls to achieve the velocity required.

*Cartoon Law VII:* Certain bodies can pass through solid walls painted to resemble tunnel entrances; others cannot.

This trompe l'oeil inconsistency has baffled generations, but at least it is known that whoever paints an entrance on a wall's surface to trick an opponent will be unable to pursue him into this theoretical space.  The painter is flattened against the wall when he attempts to follow into the painting.  This is ultimately a problem of art, not of science.

*Cartoon Law VIII:* Any violent rearrangement of feline matter is impermanent.

Cartoon cats possess even more deaths than the traditional nine lives might comfortably afford.  They can be decimated, spliced, splayed, accordion-pleated, spindled, or disassembled, but they cannot be destroyed.  After a few moments of blinking self pity, they reinflate, elongate, snap back, or solidify.

*Corollary:*  A cat will assume the shape of its container.

*Cartoon Law IX:* Everything falls faster than an anvil.

*Cartoon Law X:* For every vengeance there is an equal and opposite revengeance.

This is the one law of animated cartoon motion that also applies to the physical world at large.  For that reason, we need the relief of watching it happen to a duck instead.

*Cartoon Law Amendment A:* A sharp object will always propel a character upward.

When poked (usually in the buttocks) with a sharp object (usually a pin), a character will defy gravity by shooting straight up, with great velocity.

*Cartoon Law Amendment B:* The laws of object permanence are nullified for "cool" characters.

Characters who are intended to be "cool" can make previously nonexistent objects appear from behind their backs at will.  For instance, the Road Runner can materialize signs to express himself without speaking.

*Cartoon Law Amendment C:* Explosive weapons cannot cause fatal injuries. They merely turn characters temporarily black and smoky.

*Cartoon Law Amendment D:* Gravity is transmitted by slow-moving waves of large wavelengths.

Their operation can be witnessed by observing the behavior of a canine suspended over a large vertical drop.  Its feet will begin to fall first, causing its legs to stretch.  As the wave reaches its torso, that part will begin to fall, causing the neck to stretch.  As the head begins to fall, tension is released and the canine will resume its regular proportions until such time as it strikes the ground.

*Cartoon Law Amendment E:* Dynamite is spontaneously generated in "C-spaces" (spaces in which cartoon laws hold).

The process is analogous to steady-state theories of the universe which postulated that the tensions involved in maintaining a space would cause the creation of hydrogen from nothing.  Dynamite quanta are quite large (stick sized) and unstable (lit).  Such quanta are attracted to psychic forces generated by feelings of distress in "cool" characters (see Amendment B, which may be a special case of this law), who are able to use said quanta to their advantage.  One may imagine C-spaces where all matter and energy result from primal masses of dynamite exploding.  A big bang indeed.


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## Evagrius Ponticus (Dec 16, 2010)

Good Show Sandeep! My wife yelled at me for laughing so loud   That's just good stuff! I think I will cut and paste the laws and send to my co-workers tomorrow 

But I understood that they have estimated Dark energy to compose roughly 70% of the universe, dark matter roughly 25% of the universe, and the remaining composite of roughly 5% to be ordinary matter. Is that not the case? Also, if the universe continues to expand as is the case, those ratios will change, correct?


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## snowblizz (Dec 16, 2010)

Evagrius Ponticus said:


> But I understood that they have estimated Dark energy to compose roughly 70% of the universe, dark matter roughly 25% of the universe, and the remaining composite of roughly 5% to be ordinary matter. Is that not the case? Also, if the universe continues to expand as is the case, those ratios will change, correct?


No, there will be more "space" in between them. I think that is what is referred to as the Big Freeze, because it'll get really cold without any energy what so ever.

Anyway everyone knows the world is held up by four elephants riding a turtle. So I don't see what this supposed "shape" has to do with anything.


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## Sandeep Warrier (Dec 16, 2010)

Nopes. The ratio will not change because, per basic laws of physics, the total amount of mass and energy in the universe remains constant. So, even if new matter is being created continuously (via quantum effects), equal amount of matter will disappear somewhere else and the end result of amount of enery+mass is the same.

The "Big Freeze" occurs when, due to continous expansion, the universe becomes so big and the galaxies/stars have such vast distances between them (much much much larger than the current distances) that light is heavily red shifted = very low energy = no heat = cold.

Additionally, after some amount of time, all stars will have exhausted their fuel and so no new star will be born. (The Sun is at least a 2nd generation star, if not a 3rd generation star). This will contribute to the freezing of the universe.

However, it is possible that scientists are completely wrong about what dark energy actually is and it may turn out that we have more matter than Ω, the end result being the universe will collapse - probably leading to another big bang (which is what I believe will happen in the end).


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## SuperFerret (Dec 16, 2010)

snowblizz said:


> Anyway everyone knows the world is held up by four elephants riding a turtle.


 
Terry Pratchett fan Snowblizz?


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## snowblizz (Dec 16, 2010)

SuperFerret said:


> Terry Pratchett fan Snowblizz?


Haha, not yet! But I'm planning on being.

I've heard a lot about it over the years but never really picked any of the books up. And just last week I happened to catch a filmatisation (sic?) of some of his work(s). I can't say which books it concerned but I realised the man's a genius and that I really need to read these. I was laughing so hard.


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## JamesW (Dec 16, 2010)

The TV programs he did are total rubbish compared to the books.

Colour of Magic and Light Fantastic are his first 2, they will get you in touch with most of the main characters.

My favourite one is Thief of Time. Never laughed so much reading a book..


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## SuperFerret (Dec 16, 2010)

My brother was the one that got me into them, I used to hear him howling with laughter in the early hours because he'd start reading one before going to sleep and be inable to put it down! 

I have to say my favorite so far was colour of magic, but I do have plans to read more when I get chance!


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## Sandeep Warrier (Dec 16, 2010)

snowblizz said:


> Anyway everyone knows the world is held up by four elephants riding a turtle. So I don't see what this supposed "shape" has to do with anything.



There is actually a Hindu creation myth where the Earth is held up by 4 elephants who stand on the back of a tortoise; and this entire setup is enclosed within a giant snake (not literally within it, but the snake goes around so as to form a circle).


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## Expiry (Dec 16, 2010)

Evagrius Ponticus said:


> Hello Friends,
> 
> I've been trying for some time to completely understand how Eratosthenes was able to successfully measure the circumference of Planet Earth.  I've read his method several times but a complete understanding remains a tad beyond my reach.
> 
> ...



I think if you had a tape measure that was big enough to physically measure the circumference of the earth, the result would be completely different to any answer that has been produced through a 'succesful' theory.

I also suspect that if you measured the circumference of the earth on 100 different days, you would get 100 different answers.

I therefore summise that you could apply any theory to measure the circumference of the earth and as long as you make a few assumptions and use enough long words to make it sound like you know what you're talking about, no-one's going to argue too much.


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## Evagrius Ponticus (Dec 16, 2010)

So then Sandeep - are you of the opinion that the Big Bang is an eternally reoccurring phenomenon? It collapses on itself, then expands, then collapses again, and then repeats to infinity? I have heard this theory . .


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## Michael M (Dec 16, 2010)

Umm, just jumping in here....
The earth is an Oblate Spheroid, or, Pear shaped but not as extreme...
Now you know when things go wrong....they go "Pear Shaped"


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## diddi (Dec 16, 2010)

just jumping in as well... to the water.  hows your place going now the floods gone down.


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## Sandeep Warrier (Dec 16, 2010)

Evagrius Ponticus said:


> So then Sandeep - are you of the opinion that the Big Bang is an eternally reoccurring phenomenon? It collapses on itself, then expands, then collapses again, and then repeats to infinity? I have heard this theory . .



Yup. I firmly believe in this (call it a gut feeling).


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## Michael M (Dec 16, 2010)

Hey Diddi
Yeah,everything's good. Harvest started again on Tuesday.
Wheat gone from $200 / tonne to $10 / tonne feed wheat, but I imagine you all know that down your way.
Hope you all came out OK too.....Have a safe and merry......ugh, I hate saying that !!


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## diddi (Dec 16, 2010)

@michael m

yeh we lost a lot of fruit to brown rot amoungst others, and the wheat and canola is no good in the western districts


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## JamesW (Dec 17, 2010)

'Big Bang'??  I was under the impression the Universe was sneezed out of the nose of a being called the Great Green Arkleseizure. 

Douglas Adams anyone?


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## snowblizz (Dec 17, 2010)

JamesW said:


> The TV programs he did are total rubbish compared to the books.
> 
> Colour of Magic and Light Fantastic are his first 2, they will get you in touch with most of the main characters.
> 
> My favourite one is Thief of Time. Never laughed so much reading a book..


Wow. Well then I *really* do have something to look forward to don't I.

And I guess that is partly why I now decided I really most take a look at this, since I am fully aware that translating a book into the medium of film/tv is generally regarded as poor. If I enjoyed the adaptation this much, imagine how good I will find the books!

I think the point where they got me was when they encountered the circum-fence of the world. You mean circumference? No, it is an actual fence.
Not verbatim, but close enough. Still makes me chuckle when I think about it now.



JamesW said:


> 'Big Bang'??


The Big Bang Theory? No that's another good show, I think we were discussing that in another thread already. Which started on an equally different topic. 



sandeep.warrier said:


> There is actually a Hindu creation myth  where the Earth is held up by 4 elephants who stand on the back of a  tortoise; and this entire setup is enclosed within a giant snake (not  literally within it, but the snake goes around so as to form a  circle).


I would imagine that is where Pratchett borrowed the idea from.


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