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Flat Earth?


gerrydandridge
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15 hours ago, La Colombe said:

That would make three. How does one wander lowly anyway?  And in what way can a cloud be thus described? I don't get it. 

 

1 hour ago, Sheldon said:

Anything's better than more ramblings about flat bloody earth - except, maybe, Under Milk Wood.

An acquired taste that particular milk.

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So we have a mathematical description of our hypothesis:

Maths2.png.39f442e47046d362df8c162248736719.png

y = h tan(atan(x/h) + 1) - x

y = the dependent variable: how far you will have to continue moving away your current location, which has a certain angle up to the sun, until the angle is reduced by 1 degree.

x = the independent variable - something entirely down to the experimenter: where an observation of the angle up to sun is taken - measured from the point O where the sun is vertical in the sky.

And the height of the sun above this point, h.  This is unknown, but what we can do is make predictions about how big y will be at a given x based on how high the sun is.

The result is a graph like this:

Maths3.thumb.png.314cb1e77de34a7af25a21195697d218.png 

Each line is a prediction of how far you will have to move on the flat earth until the angle up to the sun is reduced by 1 degree if the sun is the presumed height above the earth.

This is exactly point 3 in the Rochester University outline:

3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations.

We are predicting what new observations will be like, if the hypothesis and the height of the sun above the sky presumed is true.

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Of course a flat earth isn't the only hypothesis we could develop.  There are as many hypotheses as we have the imagination to think up; and without experimental data they are equally valid, no matter how barmy or reasonable.

So what was Eratosthenes' hypothesis - well we've become across this earlier:

  1. The earth is a sphere.
  2. Light rays travel in straight lines
  3. Light rays are parallel coming from the distant sun

With these assumptions we would get a diagram like this:

Maths4.thumb.png.fc353989ddef7ed2f3725435feb0562b.png

Now Paul, if the earth has a certain circumference what is the relationship between x and y involving the circumference C.

What is the relationship between where you are on the sphere, a distance x from O, where the angle up to the sun is θ, and the point a further y along the surface of the earth where the angle has reduced to θ-1.

In the past you've claimed the angles shown on a flat earth and a spherical one are the same.  Fancy actually doing the maths and seeing if this is the case?

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