#### AndraiaZ

• 2
##### Mapping the Earth
« on: June 25, 2019, 04:50:56 PM »
Hi!

I did a bit of Research on the Flat Earth Theory in the last couple of months and in all that time I haven't got a good answer to a Question I think is one of the main Things I am skeptical about with that Theory.

It's about the Flat Earth Map. Maths tells us that you can't map out a sphere, there are Proofs for that, so no map of the earth is correct. The different maps obtained by projections (as claimed) all have one thing in common: They are distorted.
Some got correct angles and others correct lengths but they can't have both at the same time.

Now to my Question: If the earth is flat, we should have a map that has got both of those Attributes, in other words we should be able to have a perfect map of the earth without any distortion. Is there such a map?

If there is, I'm fully convinced that you're right, because the only way we could have a perfect map is when the earth is flat.

#### Acheron

• 1
##### Re: Mapping the Earth
« Reply #1 on: June 26, 2019, 07:14:14 AM »
It is true a sphere cannot be mapped to a flat plane. And you raise a fair point, if you could map a flat world with no distortion, where is said map?

If you look at the flat earth map all flat earthers use, the azimuthal equidistant projection, with lines of latitude & longitude to assist, you can see that the cells get wider and wider the further you move from the north pole. I must stress these are supposed to be SQUARES. That's the reason Australia looks twice as wide as it really is - because the map is distorted. And why is it distorted? Well, I'm sure you can come to that conclusion yourself.

#### iamcpc

• 832
##### Re: Mapping the Earth
« Reply #2 on: June 26, 2019, 01:19:41 PM »
Hi!

I did a bit of Research on the Flat Earth Theory in the last couple of months and in all that time I haven't got a good answer to a Question I think is one of the main Things I am skeptical about with that Theory.

It's about the Flat Earth Map. Maths tells us that you can't map out a sphere, there are Proofs for that, so no map of the earth is correct. The different maps obtained by projections (as claimed) all have one thing in common: They are distorted.
Some got correct angles and others correct lengths but they can't have both at the same time.

Now to my Question: If the earth is flat, we should have a map that has got both of those Attributes, in other words we should be able to have a perfect map of the earth without any distortion. Is there such a map?

If there is, I'm fully convinced that you're right, because the only way we could have a perfect map is when the earth is flat.

A big part of the problem is that there are at least a dozen different flat earth maps that I've come across and only one that I've found is supported by modern cartography, shipping, flight,  and travel data.

I've voiced my concerns with several of the flat earth maps but I have not been able to sway one person from adhering to their personal flat earth map.

https://www.bing.com/maps

• 219
• Belief does not make something a theory.
##### Re: Mapping the Earth
« Reply #3 on: June 26, 2019, 02:07:38 PM »

A big part of the problem is that there are at least a dozen different flat earth maps that I've come across and only one that I've found is supported by modern cartography, shipping, flight,  and travel data.

https://www.bing.com/maps

I'm sure you know this already, but that's not a flat earth map.  Bing maps uses the Mercator projection of a sphere earth.

https://docs.microsoft.com/en-us/bingmaps/articles/bing-maps-tile-system
Quote from: Tom Bishop
...circles do not exist and pi is not 3.14159...

Quote from: totallackey
Do you have any evidence of reality?

#### iamcpc

• 832
##### Re: Mapping the Earth
« Reply #4 on: June 26, 2019, 02:41:21 PM »

I'm sure you know this already, but that's not a flat earth map.  Bing maps uses the Mercator projection of a sphere earth.

https://docs.microsoft.com/en-us/bingmaps/articles/bing-maps-tile-system

When I use my eyes I can clearly see that Bing maps represents the earth as a flat plane. When I zoom all the way out i can plainly see a flat plane. There are many ways to draw a map in which the earth is shown as a flat plane.
By your logic there is no flat earth map. They are all projections of a sphere earth.

Take a look at this website:

Zoom all the way out. This website represents the earth as a sphere.

• 219
• Belief does not make something a theory.
##### Re: Mapping the Earth
« Reply #5 on: June 26, 2019, 03:28:26 PM »

When I use my eyes I can clearly see that Bing maps represents the earth as a flat plane. When I zoom all the way out i can plainly see a flat plane. There are many ways to draw a map in which the earth is shown as a flat plane.
By your logic there is no flat earth map. They are all projections of a sphere earth.

Take a look at this website:

Zoom all the way out. This website represents the earth as a sphere.

Microsoft clearly states in it's documentation that it is a flat projection of a sphere.  Bing maps isn't representing Earth as a flat plane as you suggest.

Quote
By your logic there is no flat earth map. They are all projections of a sphere earth.

Well, my logic isn't a factor here.  I made no blanket claim that all flat earth maps are projections of a sphere earth.  I was simply displaying what Microsoft states about the one map you believe is the most plausible flat earth map.
Quote from: Tom Bishop
...circles do not exist and pi is not 3.14159...

Quote from: totallackey
Do you have any evidence of reality?

#### iamcpc

• 832
##### Re: Mapping the Earth
« Reply #6 on: June 26, 2019, 07:40:44 PM »
Bing maps isn't representing Earth as a flat plane as you suggest.

If bing maps are not representing the earth as a flat plane then what shape are they representing the earth as? It's not a sphere. I already demonstrated what an interactive sphere earth map looks like and it didn't look like bing maps.

It sure is not a pyramid or a cube or a cylinder either.

Well, my logic isn't a factor here.  I made no blanket claim that all flat earth maps are projections of a sphere earth.  I was simply displaying what Microsoft states about the one map you believe is the most plausible flat earth map.

Oh. Well then my original statement still stands. Any map of the entire earth that is printed on paper (or could be printed on paper) represents the earth (regardless of the shape of that earth) as a flat plane.
« Last Edit: June 26, 2019, 07:50:53 PM by iamcpc »

#### ICanScienceThat

• 328
##### Re: Mapping the Earth
« Reply #7 on: June 26, 2019, 08:36:53 PM »
Forgive me if my comments seem offensive, but is iamcpc even a FE?
This is classic Poe, right?

Sorry... the moderators will hate that. Let me explain.
I had the impression already that iamcpc isn't a FE. IIRC, I've seen them chiming in from various points of view.

iamcpc has already stated that the scale of bing maps changes as you scroll North/South. This indicates they clearly understand the the projection isn't "flat". I mean it's flat, sure, but it's clearly a projection onto flat. If you printed it on paper that sliding scale wouldn't happen, and iamcpc clearly shows it.

So... is this a joke? or... what?
« Last Edit: June 26, 2019, 08:39:20 PM by ICanScienceThat »

#### iamcpc

• 832
##### Re: Mapping the Earth
« Reply #8 on: June 26, 2019, 09:10:05 PM »
Forgive me if my comments seem offensive, but is iamcpc even a FE?
This is classic Poe, right?

Sorry... the moderators will hate that. Let me explain.
I had the impression already that iamcpc isn't a FE. IIRC, I've seen them chiming in from various points of view.

iamcpc has already stated that the scale of bing maps changes as you scroll North/South. This indicates they clearly understand the the projection isn't "flat". I mean it's flat, sure, but it's clearly a projection onto flat. If you printed it on paper that sliding scale wouldn't happen, and iamcpc clearly shows it.

So... is this a joke? or... what?

I guess I don't understand the question.

Is an interactive map with a scale that changes a joke? I don't think so.
Is my belief that the most accurate flat earth map that I've seen resembles Bing maps? I don't think so.

When you ask if i'm FE I don't know what that means. Could you please elaborate?

If, by FE, you mean do I believe 100% that we have proven the earth to be flat then: no. I'm not.

If, by FE, you mean that I honestly believe there is real evidence, and logical arguments which supports the idea that the earth is flat (or some flattish shape)  as well as real evidence and logical arguments which weaken the round earth model then: Yes I am

It's not black and white. You don't have to 100% know the earth is flat or 100% know the earth is round. You could  be 80-20 Flat earth. You could be 60-40 flat earth. It's not just strongly agree or strongly disagree. There are areas in the middle.

I could think there is a very real possibility backed by evidence and logic which supports the idea that the earth could be flat but have an issue with some of the more common flat earth models having issues reconciling with observations I've personally made.

I found this map https://www.zmescience.com/other/design-other/accurate-map-design-11022016/ which does NOT have an interactive changing scale but it does not have a north so I don't know how to verify if it's accurate.

It's hard to talk about maps when people claim for any map that it's just a projection of a sphere therefore does not count as a flat earth map.
« Last Edit: June 26, 2019, 09:27:11 PM by iamcpc »

#### ICanScienceThat

• 328
##### Re: Mapping the Earth
« Reply #9 on: June 26, 2019, 09:44:40 PM »
Is an interactive map with a scale that changes a joke? I don't think so.
Is my belief that the most accurate flat earth map that I've seen resembles Bing maps? I don't think so.

When you ask if i'm FE I don't know what that means. Could you please elaborate?

If, by FE, you mean do I believe 100% that we have proven the earth to be flat then: no. I'm not.

If, by FE, you mean that I honestly believe there is real evidence, and logical arguments which supports the idea that the earth is flat (or some flattish shape)  as well as real evidence and logical arguments which weaken the round earth model then: Yes I am
Everything you wrote there is great, and I respect it all.

Let's talk about the bing map and your presentation of it. Is it "flat"? Sure, insofar as it is 2 dimensional, yeah it's flat. But could this be a representation of what the Earth is really like? You pointed out the dynamic scale, so I'm forced to say the representation is clearly a distortion of reality, and you clearly understand that. So I'm led to the most obvious conclusion that the suggestion that this map is the best "flat earth map" was meant to be cheeky.

If not, then consider... if the map must dynamically change scale, then it could NOT be the same as a physical, static object. (I'm assuming we can agree that the Earth isn't dynamically scaling.)

So can we agree that the bing map is the projection of some higher dimensional shape onto a 2D plane? This projection has caused significant distortions as indicated by the dynamic scale. Agreed?

In that case, I would suggest that we can now agree the Earth cannot look like this. What are the possibilities that remain?

a) You were being cheeky all along, and I've fallen into your trap.
b) You hadn't really thought about it before, but now you realize this map doesn't meet the criteria of a "flat earth map".
c) You still don't understand why the bing map cannot be the "flat earth map" we're looking for.

If you want to go with c), there are 2 possibilities:
c1) You possess an understanding of an abstract type of geometry that I am failing to consider
c2) You don't respect the same rules of 2D geometry and 3D geometry that I do.

It's hard to talk about maps when people claim for any map that it's just a projection of a sphere therefore does not count as a flat earth map.
I think that's a pretty good summation of exactly what I'm claiming. Are you suggesting that a projection of a sphere CAN qualify as a flat earth map? Or perhaps you are suggesting that the same map could be BOTH a projection from a sphere and an accurate presentation of the flat Earth?

#### iamcpc

• 832
##### Re: Mapping the Earth
« Reply #10 on: June 26, 2019, 09:56:34 PM »
If not, then consider... if the map must dynamically change scale, then it could NOT be the same as a physical, static object. (I'm assuming we can agree that the Earth isn't dynamically scaling.)

So can we agree that the bing map is the projection of some higher dimensional shape onto a 2D plane? This projection has caused significant distortions as indicated by the dynamic scale. Agreed?

No. I don't agree. Just because a map has a scale which changes does not mean that the earth is a sphere. The earth could be more shaped like a dinner plate or some other shape which is more "flat" than a sphere and have an interactive scale.

In that case, I would suggest that we can now agree the Earth cannot look like this. What are the possibilities that remain?

This is a moot point. Any map I present can just be claimed to be a projection of a sphere therefore a round earth map. The map with the interactive scale you claim to be a projection of a sphere could also be a projection of an oblate spheroid correct? What about an ellipsoid?

I think that's a pretty good summation of exactly what I'm claiming. Are you suggesting that a projection of a sphere CAN qualify as a flat earth map? Or perhaps you are suggesting that the same map could be BOTH a projection from a sphere and an accurate presentation of the flat Earth?

We have a different definition of a flat earth map. You define a flat earth map as a map of the earth in which the earth is represented as a flat plane in which the map is also a projection of a flat plane.
by your definition there is no flat earth map.

My definition of a flat earth map is a map which represents the earth as a flat plane which can be verified as accurate.

#### ICanScienceThat

• 328
##### Re: Mapping the Earth
« Reply #11 on: June 26, 2019, 10:03:18 PM »
If not, then consider... if the map must dynamically change scale, then it could NOT be the same as a physical, static object. (I'm assuming we can agree that the Earth isn't dynamically scaling.)

So can we agree that the bing map is the projection of some higher dimensional shape onto a 2D plane? This projection has caused significant distortions as indicated by the dynamic scale. Agreed?

No. I don't agree. Just because a map has a scale which changes does not mean that the earth is a sphere. The earth could be more shaped like a dinner plate or some other shape which is more "flat" than a sphere and have an interactive scale.

In that case, I would suggest that we can now agree the Earth cannot look like this. What are the possibilities that remain?

This is a moot point. Any map I present can just be claimed to be a projection of a sphere therefore a round earth map. The map with the interactive scale you claim to be a projection of a sphere could also be a projection of an oblate spheroid correct? What about an ellipsoid?

I think that's a pretty good summation of exactly what I'm claiming. Are you suggesting that a projection of a sphere CAN qualify as a flat earth map? Or perhaps you are suggesting that the same map could be BOTH a projection from a sphere and an accurate presentation of the flat Earth?

We have a different definition of a flat earth map. You define a flat earth map as a map of the earth in which the earth is represented as a flat plane in which the map is also a projection of a flat plane.
by your definition there is no flat earth map.

My definition of a flat earth map is a map which represents the earth as a flat plane which can be verified as accurate.

If I understand you correctly, you are suggesting that the Bing map could be a distortion from a flat shape into it's current flat shape. Right?
I agree. It could. But here we agree that it is significantly distorted, right?

Can we please have a map that is not distorted this badly? Something that represents a God's eye view of the Earth as it really is?

I'd be happy to take the Bing map and un-distort it for you to show you what that looks like. Have you ever seen that? Do you want to?

#### iamcpc

• 832
##### Re: Mapping the Earth
« Reply #12 on: June 26, 2019, 10:16:00 PM »

If I understand you correctly, you are suggesting that the Bing map could be a distortion from a flat shape into it's current flat shape. Right?
I agree. It could. But here we agree that it is significantly distorted, right?

Can we please have a map that is not distorted this badly? Something that represents a God's eye view of the Earth as it really is?

I'd be happy to take the Bing map and un-distort it for you to show you what that looks like. Have you ever seen that? Do you want to?

If you don't like the distorted map then why on earth is it used so commonly and widely for just about everything??

If i'm able to take a map with an interactive scale and use it to accurately navigate hundreds of thousands of square miles on the earth i'm pretty happy with the map.  I've seen 2d map of the earth without an interactive scale which I had linked previously in this thread and I didn't like it because it didn't line up well with the cardinal directions.

#### ICanScienceThat

• 328
##### Re: Mapping the Earth
« Reply #13 on: June 26, 2019, 10:25:54 PM »
If you don't like the distorted map then why on earth is it used so commonly and widely for just about everything??

If i'm able to take a map with an interactive scale and use it to accurately navigate hundreds of thousands of square miles on the earth i'm pretty happy with the map.  I've seen 2d map of the earth without an interactive scale which I had linked previously in this thread and I didn't like it because it didn't line up well with the cardinal directions.
The question is truly one of, "Is it possible that the Earth is flat?" If the Earth is a sphere, there is no possible way to draw an undistorted 2D map of it. If the Earth is flat, an undistorted 2D map should be no problem. So present us such an undistorted 2D map, and we have our answer. Lacking such a map, we can continue to conclude that the Earth simply is not flat.

And again, it seems CERTAIN that you know exactly why we're having this discussion. You know that an undistorted 2D map is KEY to the flat Earth question.

I posit once more that it seems extremely unlikely that you are seriously proposing a distorted map as any sort of validation that the Earth could truly be flat. I have the distinct feeling of a fishhook in my cheek.

#### spherical

• 214
##### Re: Mapping the Earth
« Reply #14 on: June 26, 2019, 10:43:01 PM »
Google maps tend to be more accurate for regular people observation.
Even if you get your spinning globe at the corner of the room and observe details with a magnifier, you will see no difference if the map was flatten or not.
In small angles it is very difficult to notice differences.
Google does that, when you zoom in, it tend to flat since there is no gain in keeping the roundness.
If you zoom out, it tend to become more and more round, but it is just for the sake of it, you don't have any real use for a whole planet view as a map, other than just curiosity to locate something or to learn a little bit more.

Google gain points by that, since you can actually see the poles in almost real geometry, and the lands of higher latitudes.
Microsoft tend to be lazy on the programming for real time scaling, they keep the map as the Mercator projection - some navigators like the mercator since it represent a spaced time longitude, but fails on distances.  Spaced time is good for navigation observing the sky, Sun, stars, etc, but it doesn't mean exactly "clock time", since distances become shorter, it seems you are traveling faster, what is not true.  If you measure wind speed and knots of water movement, it doesn't match the traveled time, but they use a table for latitude compensation that fixes that, they are not stupid.

For the common person, observing the Mercator map makes a wrong impression of the planet, but a great part of the "common persons" can not even think in 3D or in a spherical navigation, most of them not even left the city they're born, so...

My own young age education used the Mercator map, and it polarized my mind in a wrong way.  It took few years of my youth to correct it, mostly close to the poles.  Then, and only then, everything about the solar projections, seasons and eclipses start to make better sense, and then I move out from the bag of "common persons".

Interesting that there is no need to use Mercator projection for Mars map, for example, but it is done like that, and I think they do it for "compatibility" of what "common person" is used on the Mercator map of Earth.  Even so, I think it is ridiculous. Fortunately we have GoogleEarth with Mars 3D database, what solves the issue easy.

There is a lot of people already working for the Human trip to Mars, it is a good plan, there are many thousands of people, companies, universities (including us) studying all kinds of subjects, everything you can imagine and more, just to avoid surprises once on Mars.  In 20~40 years we will have people there, researching, living, expanding environmental habitats, increasing the living conditions for more and more people moving to Mars.  There is even a research about animal embryos to be transported to Mars and grew up there, some as food, some as pets, some tests involve low oxygen levels.  FEs would continue to say it is just fake pictures and images from NASA, unfortunately, for them.

https://youtu.be/8QtXFLL7Y2g

• 219
• Belief does not make something a theory.
##### Re: Mapping the Earth
« Reply #15 on: June 27, 2019, 02:23:22 PM »
No. I don't agree. Just because a map has a scale which changes does not mean that the earth is a sphere. The earth could be more shaped like a dinner plate or some other shape which is more "flat" than a sphere and have an interactive scale.

Are you completely ignoring the fact that Microsoft is using a projection created from a spherical map?
Quote from: Microsoft
To simplify the calculations, we use the spherical form of this projection, not the ellipsoidal form. Since the projection is used only for map display, and not for displaying numeric coordinates, we donâ€™t need the extra precision of an ellipsoidal projection. The spherical projection causes approximately 0.33% scale distortion in the Y direction, which is not visually noticeable.

My definition of a flat earth map is a map which represents the earth as a flat plane which can be verified as accurate.

Do you consider the Mercator projection which Bing uses accurate?

https://thetruesize.com/#?borders=1~!MTc4OTI0NTI.NDAzNTc1MQ*MzYwMDAwMDA(MA
Quote from: Tom Bishop
...circles do not exist and pi is not 3.14159...

Quote from: totallackey
Do you have any evidence of reality?

#### phyllo

• 9
##### Re: Mapping the Earth
« Reply #16 on: June 27, 2019, 03:35:31 PM »
I'm chiming in on this as a cartographer/geographer.

To reiterate what sperical, ICanScienceThat, Bad Puppy are saying (and I hope I'm not misrepresenting their thoughts):

If the earth is flat, or flatish (in imacpc's words), then a projection is not necessary to represent the earth.  A simple scaled drawing would be the most accurate representation of the world on a flat surface.  Just as an architectural drawing is a scaled drawing of the layout of a house and does not have any projection applied to it.  And the scale would not change from north to south or east to west and the shapes of land masses.  All the angles and distances between objects would all be correct.  And all the objects (the land masses) would not be distorted in any way.

However, if the earth is not flat and is, say, close to a sphere, then to represent that shape on a 2D surface one must use some sort of projection.  And all projections will distort some aspect of the original shape.  So you can have accurate angles, accurate distances, accurate shapes.  But you can not have all three on the same map.  So you choose your projection based upon the purpose of the map.  If navigation is important then the Mercator projection is one of the preferred projections.  But it does distort the surface areas of the continents, as mentioned above.

All this gets back to the original OP question: "Is there such a map?" (i.e. "a perfect map of the earth without any distortion")

And the answer is that there is not such a map of the FE world.  Which does seem odd since a scale drawing of a 2D surface should be pretty straightforward over the course of human history.

On the difference between a sphere, an oblate spheroid, and an ellipsoid in discussions of the earth.
While it's true that in the RE world the earth is not a perfect sphere, it is so close that in everyday language the term 'sphere' is perfectly adequate.  The diameter of the earth at the equator is approximately 12,756 km and the diameter from North to South pole is approximately 12,714 km.  A difference of 42 km, or 0.3%!  Although those distances are necessary to know for many applications, for most people and in most instances that difference of 42 km has no practical meaning and we can talk of the earth as being a sphere.  But technically it is an oblate spheroid. which is just a type of ellipsoid.

#### iamcpc

• 832
##### Re: Mapping the Earth
« Reply #17 on: June 27, 2019, 03:45:45 PM »
The question is truly one of, "Is it possible that the Earth is flat?" If the Earth is a sphere, there is no possible way to draw an undistorted 2D map of it. If the Earth is flat, an undistorted 2D map should be no problem. So present us such an undistorted 2D map, and we have our answer. Lacking such a map, we can continue to conclude that the Earth simply is not flat.

Here is an undistorted 2D map of the earth. By your logic the earth must be flat. I believe you are incorrect to make assumptions about the shape of the earth based on a map. The earth could be flat or a sphere or an oblate spheroid and we could draw a map of it.

I posit once more that it seems extremely unlikely that you are seriously proposing a distorted map as any sort of validation that the Earth could truly be flat. I have the distinct feeling of a fishhook in my cheek.

I'm not. I've made several statements like the one below indicating that you can't infer the shape of the earth because a map has an interactive scale:

No. I don't agree. Just because a map has a scale which changes does not mean that the earth is a sphere. The earth could be more shaped like a dinner plate or some other shape which is more "flat" than a sphere and have an interactive scale.

Here I am making the point that just because a map is distorted does not mean the earth is a sphere. It could be an ellipsoid. It could be a long FLAT ellipsoid. It could be a dinner plate where the edges cause distortion when projected onto a 2D image. It could be any number of shapes.

You sir are the one who says look a distorted map! The earth is a sphere! Yet, when presented with a map with no distortion you won't flip 180 degrees and say look! a map with no distortion! The earth is flat!

I'm telling you that I believe that both ways of thinking are false.

« Last Edit: June 27, 2019, 03:53:29 PM by iamcpc »

• 219
• Belief does not make something a theory.
##### Re: Mapping the Earth
« Reply #18 on: June 27, 2019, 04:03:20 PM »

Here is an undistorted 2D map of the earth. By your logic the earth must be flat. I believe you are incorrect to make assumptions about the shape of the earth based on a map. The earth could be flat or a sphere or an oblate spheroid and we could draw a map of it.

Do you really believe this is an undistorted 2D map of the earth?  Do people always forget about water, and distances when they look for a map where the size of of the bodies correspond to measurements?  How about simple things like the distance between Iceland and Norway being almost 1/4 the distance between Australia and Antarctica?  Is it an infinite repeating plane, or are you suggesting that the earth is a rectangle?

Are you just trolling now?
Quote from: Tom Bishop
...circles do not exist and pi is not 3.14159...

Quote from: totallackey
Do you have any evidence of reality?

#### Tim Alphabeaver

• 218
• That's no beaver
##### Re: Mapping the Earth
« Reply #19 on: June 27, 2019, 04:07:52 PM »
Here is an undistorted 2D map of the earth. By your logic the earth must be flat. I believe you are incorrect to make assumptions about the shape of the earth based on a map. The earth could be flat or a sphere or an oblate spheroid and we could draw a map of it.

Your map gets distances obviously wrong, though. South Africa isn't ~50x further away from Antarctica than South America. This is because the map is distorted.
There is only one way that you can get a map that gets all distances, shapes etc. correct, and that's on the surface of a sphere. Therefore, the Earth is a sphere. If you tried to accurately represent the Earth on a long ellipsoid, or a dinner plate, or in fact any other shape, it would be distorted.

The point is that the sphere is the only shape that can produce a non-distorted map in this particular case. The argument isn't that distorted map == sphere.

Quote
If you don't like the distorted map then why on earth is it used so commonly and widely for just about everything??
Because phones and flat maps are much easier to carry around than spheres.
**I move away from the infinite flat plane to breathe in