How math proves the world isn't flat.

There is an object in the sky that can be used to determine that the Earth is not flat using simple math.

Most flat earther's have chosen to believe the sun is roughly 3000 miles away and with some good reason. I don't think most of them understand why this particular number was chosen but some of them may.

Here is how FE'rs get 3000 miles. You see, if they assume the Earth is flat then you can just use the Pythagorean theorem to figure this out. It uses right triangles.

a^2 + b^2 = c^2

Where a and b are two sides of the right triangle adjacent to the right angle and c is the hypotenuse.

To do this they need 2 observers. The first observer will stand where the sun is directly overhead. The second observer will stand at some location away from the first observer where (at the same time) the sun is 45 degrees overhead which is exactly halfway between the horizon and directly overhead. Once these angles are measured then all you need is the distance between the observers to get the distance to the sun. When this is done the distance between the observers should be roughly 3000 miles which is coincidentally the same distance to the sun. To be more exact they should get 3112 miles.

With the information we have we don't even need to solve all of the theorem because we know that one of the angles (the angle to the sun for the second observer) is exactly 45 degrees. This means that a will equal b and that is all there is to it.

Because the FE'r assumes the earth is flat I will show you why they derive this number even though the earth is round. Look at this diagram.



The blue circle is earth while the yellow circle is the sun. The solid green line is the FE'rs mistaken flat horizon with the supplementary dashed green line being their view of the sun. The solid red line is the FE'rs mistaken flat horizon with the supplementary dashed red line being their view of the sun. The first observer is standing where the solid green line meets the surface of the earth while the second observer is standing where the solid red line meets the surface of the earth.

Since the earth is 24,901 miles in circumference the actual spot required for the second observer (red line) to get the sun to be 45 degrees above the horizon is about 1/8 of the circumference of the earth away from the first observer. This is precisely 3,112 miles away and as such they mistakenly perform the theorem and get these incorrect numbers.

I was confused about how they got 32 miles for diameter because the formula for diameter is D = 2(tan(.5) * distance) where D is diameter and .5 is the subtend angle of the sun.

Here is an explanation of the subtend angle

http://www.mathopenref.com/subtend.html

From this I get 3400 miles.

I think I know how they got the diameter.

They took the known diameter from round earth math and applied that by doing this:

RE diameter = 864,327 miles
RE distance = 93,000,000 miles
FE distance = 3,112 miles

864,327/93,000,000 = x/3,112

solve for x and you get 28.9 miles

So how does all this prove the earth isn't flat?

Well consider that the calculation of 32 miles is simply false. Using the correct equations and geometry I will agree that the distance should be roughly 3000 miles (3112 miles to be more precise). I think it is indisputable that if the earth was flat then the method used to derive 3112 miles is perfectly justified.

However, for the diameter the correct equation will produce a number of 3400 miles for the diameter (from above) which is obviously absurd.

The United States is roughly 3000 miles from coast to coast and if the sun was directly over the United States with that enormous diameter it would apparently be simply enormous. If you were in the middle of the country at noon it would cover the entire sky because its diameter would be just a little larger than the USA itself and being a mere 3000 miles overhead it would have to appear to be much larger than it actually is. With the observations of the sun and the deductions addressed here it is obvious, the size of the sun does not work with the distance that it must be if the earth was flat. Therefore, the earth is not flat.

The 3,000 miles figure is obtained when you do the measurement on 45 degrees latitudes. If you do the same measurement on the same day on different latitudes you will get different figures. Sun altitude on flat earth depends on where you measure it.

It doesn't have to be 45°. As long as the sun is directly overhead from the first observer the second observer could be anywhere 3112 miles away from the first observer. The sun just needs to be 45° from the horizon. The second observer could be at the equator or any point along the circle (made by a circle around the first observer, that circle has a radious of 3112 miles) around the first observer.

You can use this URL (http://aa.usno.navy.mil/data/docs/AltAz.php) to see the expected elevation of the sun on a particular day of the year for a given latitude and longitude. On March 22 (when the sun is directly above the equator), from 60° N the highest elevation of the sun will be 30.8°.

60° N is 4,170 miles to the equator. On a flat earth, the distance to the sun would be 2,486 miles.

You can use this URL (http://aa.usno.navy.mil/data/docs/AltAz.php) to see the expected elevation of the sun on a particular day of the year for a given latitude and longitude. On March 22 (when the sun is directly above the equator), from 60° N the highest elevation of the sun will be 30.8°.

60° N is 4.170 miles to the equator. On a flat earth, the distance to the sun would be 2,486 miles.

Yes, of course you can't go higher than 45° N. That isn't the point. You would obviously have to do this when the sun allows you to. This goes without saying.

Quote from: Cartesian on October 06, 2013, 01:22:15 AM

You can use this URL (http://aa.usno.navy.mil/data/docs/AltAz.php) to see the expected elevation of the sun on a particular day of the year for a given latitude and longitude. On March 22 (when the sun is directly above the equator), from 60° N the highest elevation of the sun will be 30.8°.

60° N is 4.170 miles to the equator. On a flat earth, the distance to the sun would be 2,486 miles.

Yes, of course you can't go higher than 45° N. That isn't the point. You would obviously have to do this when the sun allows you to. This goes without saying.

Same date, at 10° N (695 mi to the equator) the highest elevation will be 80.8°, the distance to the sun would be 4,291 miles. So:

10° = 4,291 miles
45° = 3,112 miles
60° = 2,486 miles

I thought your point was that maths prove the earth isn't flat.

No Cartesian, you seem to be thinking about this in the wrong way. When the sun is over the equator, it is only directly over the equator at one point. You seem to be thinking about doing this experiment by restricting the second observer by only allowing them to go directly north or south away from the first observer. In reality observer 2 can walk away from observer 1 in any direction until the sun is 45 degrees from the horizon.

My point is that maths prove the earth isn't flat given that the distance measurement is sound, which I believe it is. If it is a     correct distance then the calculated diameter should be 3400 miles which is just plainly false since the suns distance from earth is obviously larger than the sun's diameter.

I don't think you see where I am getting at.

Choose one latitude, on the 22nd of March any point in that latitude will have solar noon at the same UTC/GMT time. And then get four observers at different longitudes; one at the equator just to confirm that the sun is really overhead, one at 10° N, one at 45° N and one at 60° N. The elevation degree of the sun depends on which observer you ask. The same sun cannot be at different places at the same time can it?

10° = 4,291 miles
45° = 3,112 miles
60° = 2,486 miles

Sorry, I overlooked the fact that you said the calculated diameter of the sun should be 3,400 miles but I still fail to see where you get this figure from.

I was confused about how they got 32 miles for diameter because the formula for diameter is D = 2(tan(.5) * distance) where D is diameter and .5 is the subtend angle of the sun.

Here is an explanation of the subtend angle

http://www.mathopenref.com/subtend.html

From this I get 3400 miles.

This is because you are hopeless at mathematics.

Below is a calculator. Set side 'a' as 3000 and angle 'B' as 0.54.

http://www.endmemo.com/geometry/isotriangle.php
It is widely agreed that the sun is 32 arc minutes or 0.54 degrees wide as viewed from earth.

At this point the sun comes out as around 28 miles across.

Where you get 3400 miles as a diameter from I have no idea.

You are incorrect aeven and so am I. We don't use formulas for an iscoseles triangle to compute this. Our methods for distance do not obtain the distance to the edges of the sun.

We use basic pythagorean trigonometry where the tan(an angle) = opposite side/adjacent side

I made one small error so our subtend angle should be half of the subtend. So half of .54 is .27 so that is the angle we will work with.

The adjacent side will be 3112.

So the formula is tan(.27) = R/3112 where R is the radius of the sun.

Unfortunately I also made another huge mistake and had my calculator set on radians instead of degrees. This produced a drastically incorrect number.

This gives us about 14.6 miles for R which can be multiplied by 2 to give us the diameter.

This gives 28.4 miles.

My original error was to use .5 as the subtend angle because we should be using half of that angle to use this trig properly and of course using the wrong setting on my calculators

My argument can be disregarded as I have made a huge mistake.

This thread could still be useful to help educate people on how these numbers were calculated.

There is an object in the sky that can be used to determine that the Earth is not flat using simple math.

Most flat earther's have chosen to believe the sun is roughly 3000 miles away and with some good reason. I don't think most of them understand why this particular number was chosen but some of them may.

Here is how FE'rs get 3000 miles. You see, if they assume the Earth is flat then you can just use the Pythagorean theorem to figure this out. It uses right triangles.

a^2 + b^2 = c^2

Where a and b are two sides of the right triangle adjacent to the right angle and c is the hypotenuse.

To do this they need 2 observers. The first observer will stand where the sun is directly overhead. The second observer will stand at some location away from the first observer where (at the same time) the sun is 45 degrees overhead which is exactly halfway between the horizon and directly overhead. Once these angles are measured then all you need is the distance between the observers to get the distance to the sun. When this is done the distance between the observers should be roughly 3000 miles which is coincidentally the same distance to the sun. To be more exact they should get 3112 miles.

With the information we have we don't even need to solve all of the theorem because we know that one of the angles (the angle to the sun for the second observer) is exactly 45 degrees. This means that a will equal b and that is all there is to it.

Because the FE'r assumes the earth is flat I will show you why they derive this number even though the earth is round. Look at this diagram.



The blue circle is earth while the yellow circle is the sun. The solid green line is the FE'rs mistaken flat horizon with the supplementary dashed green line being their view of the sun. The solid red line is the FE'rs mistaken flat horizon with the supplementary dashed red line being their view of the sun. The first observer is standing where the solid green line meets the surface of the earth while the second observer is standing where the solid red line meets the surface of the earth.

Since the earth is 24,901 miles in circumference the actual spot required for the second observer (red line) to get the sun to be 45 degrees above the horizon is about 1/8 of the circumference of the earth away from the first observer. This is precisely 3,112 miles away and as such they mistakenly perform the theorem and get these incorrect numbers.

I was confused about how they got 32 miles for diameter because the formula for diameter is D = 2(tan(.5) * distance) where D is diameter and .5 is the subtend angle of the sun.

Here is an explanation of the subtend angle

http://www.mathopenref.com/subtend.html

From this I get 3400 miles.

I think I know how they got the diameter.

They took the known diameter from round earth math and applied that by doing this:

RE diameter = 864,327 miles
RE distance = 93,000,000 miles
FE distance = 3,112 miles

864,327/93,000,000 = x/3,112

solve for x and you get 28.9 miles

So how does all this prove the earth isn't flat?

Well consider that the calculation of 32 miles is simply false. Using the correct equations and geometry I will agree that the distance should be roughly 3000 miles (3112 miles to be more precise). I think it is indisputable that if the earth was flat then the method used to derive 3112 miles is perfectly justified.

However, for the diameter the correct equation will produce a number of 3400 miles for the diameter (from above) which is obviously absurd.

The United States is roughly 3000 miles from coast to coast and if the sun was directly over the United States with that enormous diameter it would apparently be simply enormous. If you were in the middle of the country at noon it would cover the entire sky because its diameter would be just a little larger than the USA itself and being a mere 3000 miles overhead it would have to appear to be much larger than it actually is. With the observations of the sun and the deductions addressed here it is obvious, the size of the sun does not work with the distance that it must be if the earth was flat. Therefore, the earth is not flat.

This whole experiment seems like a bunch of hooey. Wouldnt they angle mesured be ambigous concerning there mesuring something up in the sky

Why would you think its hooey. Trigonometry is exactly how we measured the round earth numbers that you agree with.

Even if you could find a "magic bullet" argument to disprove a flat-earth, it does nothing to prove a round one. When you've demonstrated that the world is round, then we'll believe you.

Even if you could find a "magic bullet" argument to disprove a flat-earth, it does nothing to prove a round one. When you've demonstrated that the world is round, then we'll believe you.

There are plenty that prove it to be round. That wasn't the purpose of this failed thread

Even if you could find a "magic bullet" argument to disprove a flat-earth, it does nothing to prove a round one. When you've demonstrated that the world is round, then we'll believe you.

If we can prove the earth is not flat, we don't even need to prove the earth is round. This society is not called The Not a Globe Society, it's The Flat Earth Society.