Distances

I thought I'd make a thread about this, since everyone has been complaining about distances recently. The distances below the equator in FET are different from the ones in RET. Here's some calculations:

The length of a line of latitude below the equator:

y=445.277963x+40,075.016686

Where y is the answer and x is the degree of the line (this is all in km, since we are an international forum).

Distances:



r₁ is the first radius (centered at the north pole).
θ₁ is the first longitude.

r₂ is the second radius.
θ₂ is the second longitude.

d is the distance.

Note: thanks to momentia

if you make your first equation:
y=-x445.277963+40,075.016686

This should extend your line lengths into the domain of the northern hemisphere.

Your distance formula doesn't work:
say we want the distance from from a point to itself at radius r1 > 0:
d² = (y(|a-b|/180))²+(r1+r2)²
This means:
d² = (r1+r2)² = (2r1)² > 0

if you make your first equation:
y=-x445.277963+40,075.016686

This should extend your line lengths into the domain of the northern hemisphere.

True. I hadn't really put much thought into distances above the equator, because they already have proper measurements. Thanks.

Your distance formula doesn't work:
say we want the distance from from a point to itself at radius r1 > 0:
d² = (y(|a-b|/180))²+(r1+r2)²
This means:
d² = (r1+r2)² = (2r1)² > 0

Hmm. You're right. I think it only works if the angle of the two radii is obtuse. I'll have to test that.

EDIT:
I figured what's wrong. For places that aren't on the other side of the Earth, the (r₁+r₂) should have a - instead of a +.

I thought I'd make a thread about this, since everyone has been complaining about distances recently.

The distance debate is not new. Its been going on for years. Lurk Moar.

The distances below the equator in FET are different from the ones in RET.

Actually the distances everywhere except for on the equator are all wrong. The scale is just backwards between north and south. But since there are no FE maps that have a proper account for observed and measured distances, FE has yet to make a claim. Judging from the few very basic maps/sketches that have been presented its pretty easy to tell they are wrong based on comparing the size of the continents to each other. there need not be any further investigation on distances untill a map is presented.

Simple distance measurements are among the most basic major hoels in FE ideas. They are a bad place to argue from if your are a FE proponent. The current observed supface of the planet only works on a sphere.

Quote from: Tausami on November 17, 2011, 02:33:04 PM

I thought I'd make a thread about this, since everyone has been complaining about distances recently.

The distance debate is not new. Its been going on for years. Lurk Moar.

Quote from: Tausami on November 17, 2011, 02:33:04 PM

The distances below the equator in FET are different from the ones in RET.

Actually the distances everywhere except for on the equator are all wrong. The scale is just backwards between north and south. But since there are no FE maps that have a proper account for observed and measured distances, FE has yet to make a claim. Judging from the few very basic maps/sketches that have been presented its pretty easy to tell they are wrong based on comparing the size of the continents to each other. there need not be any further investigation on distances untill a map is presented.

Simple distance measurements are among the most basic major hoels in FE ideas. They are a bad place to argue from if your are a FE proponent. The current observed supface of the planet only works on a sphere.

1) I meant, more than usual.
2) No, they aren't. It gets smaller as you get closer to the North Pole on RET, too.
3) The distances are wrong in RET.

Can you tell us how using the Zetetic Method you arrived at these formulae? Did you personally measure all the distances all over the Earth and verify that your formula is correct? Please provide your data here and then submit it for peer review. Thanks.

If were going to reference this thread, we might as well get a better FE distance formula:


r₁ is the first radius (centered at the north pole).
θ₁ is the first longitude.

r₂ is the second radius.
θ₂ is the second longitude.

d is the distance.

If were going to reference this thread, we might as well get a better FE distance formula:


r₁ is the first radius (centered at the north pole).
θ₁ is the first longitude.

r₂ is the second radius.
θ₂ is the second longitude.

d is the distance.

Why is that better?

Can you tell us how using the Zetetic Method you arrived at these formulae? Did you personally measure all the distances all over the Earth and verify that your formula is correct? Please provide your data here and then submit it for peer review. Thanks.

I used the Pythagorean theorem, which I've personally verified to be true.

If you take measured distances from between points around the world, you find that they match the RET distances, not the FET ones. It would appear that your distance model is inaccurate.

Quote from: ClockTower on December 15, 2011, 08:14:01 PM

Can you tell us how using the Zetetic Method you arrived at these formulae? Did you personally measure all the distances all over the Earth and verify that your formula is correct? Please provide your data here and then submit it for peer review. Thanks.

I used the Pythagorean theorem, which I've personally verified to be true.

Please tell us how you used PT to get your formulae. Again, please provide your data here and then submit it for peer review. Surely you've used the Zetetic Method to reach your conclusion, right? Thanks.

I hadn't really put much thought into distances above the equator, because they already have proper measurements.

I used the Pythagorean theorem, which I've personally verified to be true.

Hmm, so RET just happens to be correct above the equator, but their math is incorrect.

According to your profile, you live above the equator (British).

So how do you know your personal verification of the pythagorean theorem wasn't a fluke?

Quote from: momentia on December 16, 2011, 02:10:38 AM

If were going to reference this thread, we might as well get a better FE distance formula:


r₁ is the first radius (centered at the north pole).
θ₁ is the first longitude.

r₂ is the second radius.
θ₂ is the second longitude.

d is the distance.

Why is that better?

Since it would theoretically work with the given FET, unlike Tausami's.
It is the law of cosines, but with both sides square-rooted.

Quote

I hadn't really put much thought into distances above the equator, because they already have proper measurements.

Quote

I used the Pythagorean theorem, which I've personally verified to be true.

Hmm, so RET just happens to be correct above the equator, but their math is incorrect.

According to your profile, you live above the equator (British).

So how do you know your personal verification of the pythagorean theorem wasn't a fluke?

I'm actually American, I just prefer British English to American English.

Anyway, here's a list of 96 proofs of the Pythagorean Theorem. If you can find an error, I'd be delighted.
http://www.cut-the-knot.org/pythagoras/index.shtml

Quote from: Tausami on December 16, 2011, 02:54:24 AM

Quote from: ClockTower on December 15, 2011, 08:14:01 PM

Can you tell us how using the Zetetic Method you arrived at these formulae? Did you personally measure all the distances all over the Earth and verify that your formula is correct? Please provide your data here and then submit it for peer review. Thanks.

I used the Pythagorean theorem, which I've personally verified to be true.

Please tell us how you used PT to get your formulae. Again, please provide your data here and then submit it for peer review. Surely you've used the Zetetic Method to reach your conclusion, right? Thanks.

Alright. I'll post it all in another post, because it'll take me a while.

Anyway, here's a list of 96 proofs of the Pythagorean Theorem. If you can find an error, I'd be delighted.
http://www.cut-the-knot.org/pythagoras/index.shtml

You misunderstand. You don't have to convince me that PT is valid. You're the one saying a multitude of other theories are invalid, yet they somehow manage to yield the "proper measurements" in half of the world (your own words). They all have just as many proofs. What convinces you that PT is special, especially considering that your verification of it was performed in the same half of the world that would have proved all the other theories correct which you deny?

Circumference formula:

I took the length of the Equator, 40,075.016686, and divided it by the difference in degrees N between the North Pole and the Equator, 90. The answer was 445.277963. This is the base length. Thus, y=-445.277963x+40,075.016686. It's important to note that it uses degrees North. For instance, the Tropic of Capricorn is 23 degrees South, which is -23 degrees north.

Formula 1 (other side of Earth):

This one is fairly simple. The (y(|a-b|/180)) finds the latitudinal distance. What's actually happening is that you're taking the opposite of the longitude of the one place (if the latitude is 45 degrees East, you're using  45 degrees West) and using the circumference formula to find the distance from that point (which we'll call Point 1) to the second place, if they're at the same latitude. The |r₁+r₂| finds the distance from the first place to point 1, and then the Pythagorean Theorem is used to find the distance because the points make a right angle. I can make a diagram if you'd like.

Formula 2 (same side)

This one is the same as the other, but instead of using |r₁+r₂|, which find the distance by going over the North Pole, it uses |r₁-r₂|, which just finds the distance between the two degrees. Again, I can make a diagram if you want.

Quote from: Tausami on December 16, 2011, 04:45:06 PM

Anyway, here's a list of 96 proofs of the Pythagorean Theorem. If you can find an error, I'd be delighted.
http://www.cut-the-knot.org/pythagoras/index.shtml

You misunderstand. You don't have to convince me that PT is valid. You're the one saying a multitude of other theories are invalid, yet they somehow manage to yield the "proper measurements" in half of the world (your own words). They all have just as many proofs. What convinces you that PT is special, especially considering that your verification of it was performed in the same half of the world that would have proved all the other theories correct which you deny?

You understand what the Pythagorean Theorem is, right? It finds the hypotenuse of a right angle when the other two sides are known. It has absolutely nothing to do with FET or RET.

Circumference formula:

I took the length of the Equator, 40,075.016686, and divided it by the difference in degrees N between the North Pole and the Equator, 90. The answer was 445.277963. This is the base length. Thus, y=-445.277963x+40,075.016686. It's important to note that it uses degrees North. For instance, the Tropic of Capricorn is 23 degrees South, which is -23 degrees north.

Formula 1 (other side of Earth):

This one is fairly simple. The (y(|a-b|/180)) finds the latitudinal distance. What's actually happening is that you're taking the opposite of the longitude of the one place (if the latitude is 45 degrees East, you're using  45 degrees West) and using the circumference formula to find the distance from that point (which we'll call Point 1) to the second place, if they're at the same latitude. The |r₁+r₂| finds the distance from the first place to point 1, and then the Pythagorean Theorem is used to find the distance because the points make a right angle. I can make a diagram if you'd like.

Formula 2 (same side)

This one is the same as the other, but instead of using |r₁+r₂|, which find the distance by going over the North Pole, it uses |r₁-r₂|, which just finds the distance between the two degrees. Again, I can make a diagram if you want.

Please tell us when and how you measured the length of the Equator. I find your thought experiment interesting but totally unjustified. Again, I remind you of our request that you provide your reasoning that your technique is correct. Have you for example measured even one distance in the Southern Hemidisk?

Quote from: Tausami on December 16, 2011, 05:11:07 PM

Circumference formula:

I took the length of the Equator, 40,075.016686, and divided it by the difference in degrees N between the North Pole and the Equator, 90. The answer was 445.277963. This is the base length. Thus, y=-445.277963x+40,075.016686. It's important to note that it uses degrees North. For instance, the Tropic of Capricorn is 23 degrees South, which is -23 degrees north.

Formula 1 (other side of Earth):

This one is fairly simple. The (y(|a-b|/180)) finds the latitudinal distance. What's actually happening is that you're taking the opposite of the longitude of the one place (if the latitude is 45 degrees East, you're using  45 degrees West) and using the circumference formula to find the distance from that point (which we'll call Point 1) to the second place, if they're at the same latitude. The |r₁+r₂| finds the distance from the first place to point 1, and then the Pythagorean Theorem is used to find the distance because the points make a right angle. I can make a diagram if you'd like.

Formula 2 (same side)

This one is the same as the other, but instead of using |r₁+r₂|, which find the distance by going over the North Pole, it uses |r₁-r₂|, which just finds the distance between the two degrees. Again, I can make a diagram if you want.

Please tell us when and how you measured the length of the Equator. I find your thought experiment interesting but totally unjustified. Again, I remind you of our request that you provide your reasoning that your technique is correct. Have you for example measured even one distance in the Southern Hemidisk?

It works for the model. I'm unable to determine whether or not it's actually accurate at the present time, but when I get out of college I'm planning to circumnavigate, so I can test it then.

It works for the model. I'm unable to determine whether or not it's actually accurate at the present time, but when I get out of college I'm planning to circumnavigate, so I can test it then.

So it's nothing more than your fantasy. Thanks--for nothing.

Quote from: Tausami on December 16, 2011, 05:42:28 PM

It works for the model. I'm unable to determine whether or not it's actually accurate at the present time, but when I get out of college I'm planning to circumnavigate, so I can test it then.

So it's nothing more than your fantasy. Thanks--for nothing.

Yeah. Basically, a lot of people were talking about distances (there were >10 threads about it in as many days, and one of them is still going on) and a consistent theme was that they were asking for a model of the distances, so I decided to give them one. I have no proof one way or another as to whether or not it's accurate, but it is long as the map is.

Quote from: ClockTower on December 16, 2011, 05:43:38 PM

Quote from: Tausami on December 16, 2011, 05:42:28 PM

It works for the model. I'm unable to determine whether or not it's actually accurate at the present time, but when I get out of college I'm planning to circumnavigate, so I can test it then.

So it's nothing more than your fantasy. Thanks--for nothing.

Yeah. Basically, a lot of people were talking about distances (there were >10 threads about it in as many days, and one of them is still going on) and a consistent theme was that they were asking for a model of the distances, so I decided to give them one. I have no proof one way or another as to whether or not it's accurate, but it is long as the map is.

Please label your fantasies, like the map and the distance formulae, as such. You disappoint.

Quote from: Tausami on December 16, 2011, 05:46:42 PM

Quote from: ClockTower on December 16, 2011, 05:43:38 PM

Quote from: Tausami on December 16, 2011, 05:42:28 PM

It works for the model. I'm unable to determine whether or not it's actually accurate at the present time, but when I get out of college I'm planning to circumnavigate, so I can test it then.

So it's nothing more than your fantasy. Thanks--for nothing.

Yeah. Basically, a lot of people were talking about distances (there were >10 threads about it in as many days, and one of them is still going on) and a consistent theme was that they were asking for a model of the distances, so I decided to give them one. I have no proof one way or another as to whether or not it's accurate, but it is long as the map is.

Please label your fantasies, like the map and the distance formulae, as such. You disappoint.

No reason to. The RE'ers will dismiss it as one of my eccentric fantasies regardless of whether or not I tell you to.

Quote from: zarg on December 16, 2011, 04:53:33 PM

Quote from: Tausami on December 16, 2011, 04:45:06 PM

Anyway, here's a list of 96 proofs of the Pythagorean Theorem. If you can find an error, I'd be delighted.
http://www.cut-the-knot.org/pythagoras/index.shtml

You misunderstand. You don't have to convince me that PT is valid. You're the one saying a multitude of other theories are invalid, yet they somehow manage to yield the "proper measurements" in half of the world (your own words). They all have just as many proofs. What convinces you that PT is special, especially considering that your verification of it was performed in the same half of the world that would have proved all the other theories correct which you deny?

You understand what the Pythagorean Theorem is, right? It finds the hypotenuse of a right angle when the other two sides are known. It has absolutely nothing to do with FET or RET.

Same goes for all mathematical facts which are used to prove Earth is round (or at the very least that your distances are wrong). In order to believe in your FE model, you must disregard those. But you accept PT. I ask again: What makes PT special?

Quote from: Tausami on December 16, 2011, 05:12:47 PM

Quote from: zarg on December 16, 2011, 04:53:33 PM

Quote from: Tausami on December 16, 2011, 04:45:06 PM

Anyway, here's a list of 96 proofs of the Pythagorean Theorem. If you can find an error, I'd be delighted.
http://www.cut-the-knot.org/pythagoras/index.shtml

You misunderstand. You don't have to convince me that PT is valid. You're the one saying a multitude of other theories are invalid, yet they somehow manage to yield the "proper measurements" in half of the world (your own words). They all have just as many proofs. What convinces you that PT is special, especially considering that your verification of it was performed in the same half of the world that would have proved all the other theories correct which you deny?

You understand what the Pythagorean Theorem is, right? It finds the hypotenuse of a right angle when the other two sides are known. It has absolutely nothing to do with FET or RET.

Same goes for all mathematical facts which are used to prove Earth is round (or at the very least that your distances are wrong). In order to believe in your FE model, you must disregard those. But you accept PT. I ask again: What makes PT special?

That's not true. I'm not sure which proofs you're talking about, but they're all actually quite easy to disprove without resorting to saying geometry is wrong. We're just messing with you when we talk about that.

Quote

Same goes for all mathematical facts which are used to prove Earth is round (or at the very least that your distances are wrong). In order to believe in your FE model, you must disregard those. But you accept PT. I ask again: What makes PT special?

That's not true. I'm not sure which proofs you're talking about, but they're all actually quite easy to disprove without resorting to saying geometry is wrong. We're just messing with you when we talk about that.

Do you realize how much you just contradicted yourself? I say "in order to believe in your model you must disregard [these proofs]", you say "that's not true", but then proceed to disregard the proofs! And if you don't know which proofs I'm talking about, how can you say they're easy to disprove?!

Quote from: Tausami on December 16, 2011, 06:33:14 PM

Quote

Same goes for all mathematical facts which are used to prove Earth is round (or at the very least that your distances are wrong). In order to believe in your FE model, you must disregard those. But you accept PT. I ask again: What makes PT special?

That's not true. I'm not sure which proofs you're talking about, but they're all actually quite easy to disprove without resorting to saying geometry is wrong. We're just messing with you when we talk about that.

Do you realize how much you just contradicted yourself? I say "in order to believe in your model you must disregard [these proofs]", you say "that's not true", but then proceed to disregard the proofs! And if you don't know which proofs I'm talking about, how can you say they're easy to disprove?!

I can disprove every one. I'm just not sure which one specifically you're talking about, because you never specified.

zarg, perhaps you should start a new thread and explain in depth what you mean. This thread is purely theoretical.

Anyways, from what I can tell, Tausami's formula is wrong, and a real one can be found here:
http://www.theflatearthsociety.org/forum/index.php?topic=51811.msg1279699#msg1279699

Tausami, drawing a picture of your formula would probably be enough to convince you that it doesn't even theoretically work.

I can disprove every one.

Except Pythagorean Theorem. For the third time, what makes it special?

momentia, my whole point is fully explained in my first post. There is nothing "in depth" about it.

Quote from: Tausami on December 16, 2011, 06:49:41 PM

I can disprove every one.

Except Pythagorean Theorem. For the third time, what makes it special?

momentia, my whole point is fully explained in my first post. There is nothing "in depth" about it.

The Pythagorean Theorem isn't a proof of the Earth being round. Did you think I meant mathematical proofs?