[Jane]

Hi! First post on this particular branch of the site, though I've been hanging around the sister site for a while longer. This seems to be the place to come for actual answers.

Or Southern Hemiplane, depending where you put the centre at. Whichever way, on a Flat Earth it would be a circle with a circumference at, for example, the equator. Under regular FET, it's just part of a larger disk, but it's still a circle.
Of course, it doesn't need to be an exact circle, but a circle's the best-case scenario.

Now we get onto maths. I'm studying it, and there's something known as the 'Isoperimetric Inequality'. I can give you a proof of that if you really want, but it's fairly long, and pretty advanced: unless every mathematician is knowingly in on the conspiracy, however, it should be worth noting it has been around since the 19th century (rigorously proven), and known generally for much longer. You're more than welcome to look it up, there are several proofs online.
Essentially, it's a relationship between the boundary of a shape, and its volume: but we only need to worry about the two-dimensional case. That is, with a flat shape, with perimeter, and area.
The inequality provides a bound: the area of a shape can be no larger than a certain function of area. The inequality is:

L² >= 4pi*A

Where L is the length of the perimeter, A is the area. Equality holds only with a circle: what this means is, as we know the length of the equator, we can calculate the largest possible size of the hemiplane contained within it on a flat Earth. Strictly speaking we just need to calculate the area of a circle with that circumference, but it's nicer to use the inequality form as it shows explicitly we're concerned with an upper bound.
The equator has length of approximately 40,000km. Plug that into the inequality, we find:

A <= 127323954.5km²

Or around 0.13 billion (the American kind).
Just for fun, we can also note that's also approximately the area of a circle with said circumference (rounding errors aside).

Anyway, that gives us the largest possible area for the inner hemiplane. For comparison's sake, that's little more than the area of Afro-Eurasia: one supercontinent which mostly takes up a third of the northern hemiplane. It's also about half the area of what we'd expect on a spherical Earth, after a hasty calculation (and while the Earth is not perfectly spherical, I rounded the FE number up and the RE number down). Even if there's some concave/vexity, that's one hell of an error bar.

So, can we blame this all on the conspiracy? Is every number we've been given wrong? Are you suggesting not one cartographer, pilot or anyone has noticed that the distances, calculated by Round Earth numbers, fall drastically short? If anyone wants to work out the speeds at which planes would have to be travelling under FET given the area of the necessary hemiplane, you're welcome to; might be too short to keep lift, I don't know offhand.
Or is all of maths just wrong?

[Pongo]

How did you determine the length of the equator?

[Ghost of V]

BiJane, I presume? Like I asked before, why are you assuming that the Earth disc is a perfect circle?

[Jane]

How did you determine the length of the equator?

I used an existing, known measurement based on the fact that, if the true value was radically different (as it seems to need to be), then such things as the distance to said equator will also shift greatly, and you've still got plenty of issues that really should've been noticed by now.
If you want, I'll calculate the size of the equator you'd need, assuming the best case scenario of a perfect circle?

I make that about 56000km, so you've got error bars of over a third given what the assumed length is.

As I said initially:

So, can we blame this all on the conspiracy? Is every number we've been given wrong? Are you suggesting not one cartographer, pilot or anyone has noticed that the distances, calculated by Round Earth numbers, fall drastically short? If anyone wants to work out the speeds at which planes would have to be travelling under FET given the area of the necessary hemiplane, you're welcome to; might be too short to keep lift, I don't know offhand.
Or is all of maths just wrong?

You can say the numbers are wrong, but that doesn't explain how such a huge incongruity hasn't been noticed: especially given, according to this site, there's no Flat Earth conspiracy, just a space travel one.

why are you assuming that the Earth disc is a perfect circle?

Assume it's not if you want: that makes the numbers worse. I explained this in the main post: the circle is the best case scenario. If you're saying it's convex/cave instead, I can happily give you a degree of roundness which would explain the measurements, but you won't like it.

[Ghost of V]

Assume it's not if you want: that makes the numbers worse. I explained this in the main post: the circle is the best case scenario. If you're saying it's convex/cave instead, I can happily give you a degree of roundness which would explain the measurements, but you won't like it.

I'm not saying what it is specifically, but I know it's not a perfect circle. Clearly the flight times add up on a flat Earth, since I've been on a plane (and I assume you have as well). All I know is that it's not a perfect circle. You can assume whatever you want, but when you base math around assumptions (because you lack the knowledge on the true shape of the Earth) then this is theory crafting at best and not evidence or a refutation of anything.

[Jane]

I'm not saying what it is specifically, but I know it's not a perfect circle. Clearly the flight times add up on a flat Earth, since I've been on a plane (and I assume you have as well). All I know is that it's not a perfect circle. You can assume whatever you want, but when you base math around assumptions (because you lack the knowledge on the true shape of the Earth) then this is theory crafting at best and not evidence or a refutation of anything.

Once again, I'm not relying on it being a perfect circle in any way, shape or form.
If it is a 2-D shape, the isoperimetric inequality I gave holds: that is, the largest possible area (still way too small) is given by a perfect circle. if it's not a perfect circle, your area shrinks even more. Just gets better for me.
If it is a 3-D shape, you've just successfully argued for RET.

[Ghost of V]

But you are relying on the assumption that it is circular, no?

[Jane]

But you are relying on the assumption that it is circular, no?

Once again, I'm not relying on it being a perfect circle in any way, shape or form.

[Ghost of V]

That doesn't really answer my question, but ok.

Also, 2D shape? You realize that true 2D shapes do not exist in three dimensional space, right?

[Jane]

That doesn't really answer my question, but ok.

How does it not?
I only need a 2D shape.

Also, 2D shape? You realize that true 2D shapes do not exist in three dimensional space, right?

Approximation. There's room for some error, sure: but not quite as much as we observe.

[Tom Bishop]

Vauxhall is correct. What reason is there to believe that the FE is circular rather than oval?

[Jane]

Vauxhall is correct. What reason is there to believe that the FE is circular rather than oval?

As I said, that doesn't matter. We're talking about the equator, but beyond that, if the interior is any shape other than that a circle, the area within will be smaller. that's what the Inequality proves.
Suppose it's an oval, a heptagon, a splodge, whatever you want. There is no 2-D shape that can hold more area than a perfect circle: and even a perfect circle doesn't give anywhere near enough.

[Ghost of V]

There is no 2-D shape that can hold more area than a perfect circle

This is demonstrably false.

Also, like I've said, we live in a 3 dimensional universe. I really don't understand the point you're trying to make.

[Jane]

There is no 2-D shape that can hold more area than a perfect circle

This is demonstrably false.

If it's demonstrably false, would you care to demonstrate? Draw a shape: then draw a circle with the same perimeter. The circle will have more area. That's the Isoperimetric Inequality.

Also, like I've said, we live in a 3 dimensional universe. I really don't understand the point you're trying to make.

And as I said, that's rather irrelevant. We're not dealing with surface area and hills and valleys etc: we're dealing with the distances from point to point. Your only way to sneak in more area would be to introduce more concave/vexity, and if you do that you've left FET far behind.

[Ghost of V]

Firstly, area is irrelevant. Which is why this thread is mostly pointless...


Here's a diagram:



You don't know the true shape of the Earth. If you're operating under the assumption that it is a circle, something similar to a circle, a perfect circle, or a 2D shape (despite the fact that we live in a 3D universe) then you're going to get incorrect results.

You can't base math on an assumption and then assume you've proved something. That's unscientific, Jane.

[Jane]

Firstly, area is irrelevant.

Would you care to say why? If the FE area is dramatically smaller than what we observe, that seems to be quite a problem.

Here's a diagram:

Please try to note the 'same perimeter' fact I have been using in every single post.

You don't know the true shape of the Earth. If you're operating under the assumption that it is a circle, something similar to a circle, a perfect circle, or a 2D shape (despite the fact that we live in a 3D universe) then you're going to get incorrect results.

I'm working on the basis that the surface is approximately flat, under your worldview. If it is not approximately flat, it is either concave, or convex. Which is it? Neither can exactly be called FET. Again, texture like mountains and hills and valleys isn't relevant: you need much larger geographical features. That is, convex behaviour, or concave behaviour.
I'm tired of repeating myself. Do you feel willing to respond to basically any point I've made?

[Ghost of V]

Do you feel willing to respond to basically any point I've made?

I have responded to all your points. Is this how you normally conduct debate?


I am not very good at math, you know this. I hardly know what formulas you have going on in the OP, but I know one thing for sure... basing math on assumed information is going to get results that skew in your favor. You can't disprove anything without first figuring out the true shape of the Earth and taking legitimate measurements... which you haven't done.

[Jane]

I have responded to all your points. Is this how you normally conduct debate?

You have not. At best you've constructed straw men (see: your obviously different perimeter shapes). This is exactly why you're blocked on the other site. In order, now:

• Why is area irrelevant?
• Is the Earth concave or convex, and if not how do you find the radically greater area than is possible on an approximately flat surface?

basing math on assumed information is going to get results that skew in your favor. You can't disprove anything without first figuring out the true shape of the Earth and taking legitimate measurements... which you haven't done.

Once again, I'm focusing on the equator, not the Earth. if it is a 2-D or approximately 2-D shape, we do not get the area we have.
Or, if you're instead taking the decision that the measurements are wrong, how? Many maps etc predate, for example, space travel, and distances are repeatedly verified by literally anyone who has any travelling to do. Are you taking the position every measured distance is false?

[Ghost of V]

Are you taking the position every measured distance is false?

I thought that was obvious?

[Jane]

Are you taking the position every measured distance is false?

I thought that was obvious?

If you aren't going to take the time to respond to my points, why do you post? Once more:

Or, if you're instead taking the decision that the measurements are wrong, how? Many maps etc predate, for example, space travel, and distances are repeatedly verified by literally anyone who has any travelling to do.