The Big 90 Degree Triangle Bit

I"ve heard it said
"If the earth was flat, could i draw this 1000(?) mile trianlge with 90(?) degree corners on it mr genius flat head"
What the heck are these peolpe talking about, as surely this has never been done and is just a comment on geometry in general.

So does anyone know if this has been done on some smaller scale  or validated in some way?

I’m at the bar so it’s kind of hard to hear but I think this is the video. A flight computer with two 90 degree turns to end up at position one.



Edit:Apparently this thread was in Qand A, my bad.

On the surface of a sphere, an equal-sided triangle will have angles greater than 90°. At very small lengths, the difference will be undetectable, and since the Earth has hills and mountains small triangles will demonstrate nothing useful. At very long lengths, you could demonstrate the rotundity of the world this way, but it would be a surveying feat of epic proportions.

It is worth noting that on the Great Plains of the United States, when whole states were surveyed, they did indeed have to take into account the curvature of the Earth.

I"ve heard it said
"If the earth was flat, could i draw this 1000(?) mile trianlge with 90(?) degree corners on it mr genius flat head"
What the heck are these peolpe talking about, as surely this has never been done and is just a comment on geometry in general.

So does anyone know if this has been done on some smaller scale  or validated in some way?

Maybe some smart Aleck rudely asked "If the earth was flat, could you draw this 10,000 mile triangle with 90 degree corners on it?"
And of course your couldn't because any triangle on a flat surface must have angles totalling 180 degrees.

You might reply by asking this globe head to prove that he could draw a triangle with 10,000 km sides and each angle 90° on his Globe Earth.

I seriously doubt that he could.

I"ve heard it said
"If the earth was flat, could i draw this 1000(?) mile trianlge with 90(?) degree corners on it mr genius flat head"
What the heck are these peolpe talking about, as surely this has never been done and is just a comment on geometry in general.

So does anyone know if this has been done on some smaller scale  or validated in some way?

It has not been done on that scale. That scale is going from the equator, up to the pole, then back to the equator, then along the equator.

Each side is ~10 000 km long and all three angles are 90 degrees.

You can change the distance along the equator and still have the same fundamental problem. The 2 angles at the equator are 90 degrees. In order for that to be a triangle on a flat surface, the angle at the pole must be 0 degrees and thus you must be at the same point.

While it hasn't been done on that scale, it is done on a much smaller scale for surveying of large landmasses where you have an excess of the 180 degrees for the angle sum of a triangle.

However, you can indirectly do it with 2 such triangles joined together by looking at the sky.
The north and south celestial pole are just visible on the equator, and are always 180 degrees apart.
The fact that you can circle them means they must be some finite distance away and there must be a point on Earth below them.
So if you have 2 observation points along the equator, that allows you to construct 2 triangles (with their base along the equator touching) where the angle at the equator is 90 degrees, and the angle at the pole needs to be greater than 0 degrees.

I’m at the bar so it’s kind of hard to hear but I think this is the video. A flight computer with two 90 degree turns to end up at position one.



Edit:Apparently this thread was in Qand A, my bad.

So the computer says so?

Quote from: sokarul on February 08, 2020, 04:26:54 PM

I’m at the bar so it’s kind of hard to hear but I think this is the video. A flight computer with two 90 degree turns to end up at position one.



Edit:Apparently this thread was in Qand A, my bad.

So the computer says so?

And the plane can fly that route with its three 90° corners in the triangular course.
It would be a useless waste of fuel to prove what all navigators already know!

Quote from: sokarul on February 08, 2020, 04:26:54 PM

I’m at the bar so it’s kind of hard to hear but I think this is the video. A flight computer with two 90 degree turns to end up at position one.



Edit:Apparently this thread was in Qand A, my bad.

So the computer says so?

Yes, every modern commercial aircraft has one of these (or a similar model). The crew enter a route as part of the preparation and the computer gives them directions to follow that route. Typically the autopilot does most of the flying.

If you think for one second that these computers are fundamentally incapable of giving the correct headings to fly, then I suggest you stay on the ground and avoid all air travel.

I'm quite happy to put my trust in these flight computers, so if one of these demonstrably says you can fly a triangular course with 90 degree turns at every stage, then I believe that to be true.

Boy, I really had a senior moment when I said that an equal-sided triangle has 90° angles on a flat surface. I am embarrassed. Of course, it's 60° on a flat surface, and more on the surface of a sphere. 

Boy, I really had a senior moment when I said that an equal-sided triangle has 90° angles on a flat surface. I am embarrassed. Of course, it's 60° on a flat surface, and more on the surface of a sphere. 

I scratched my head and figured you were having an episode.
Probably should have sent a PM to see if your were having a stroke. 

Boy, I really had a senior moment when I said that an equal-sided triangle has 90° angles on a flat surface. I am embarrassed. Of course, it's 60° on a flat surface, and more on the surface of a sphere. 

TBH it's so unusual for anyone to own up to a mistake on this forum, it made my day 

Quote from: sokarul on February 08, 2020, 04:26:54 PM

I’m at the bar so it’s kind of hard to hear but I think this is the video. A flight computer with two 90 degree turns to end up at position one.



Edit:Apparently this thread was in Qand A, my bad.

So the computer says so?

Yes

To me this sound like theories of geometry...I acknowledge that the sky looks circular and maybe spherical. But can anyone cite an example of a larger than 180 degree triangle being drawn on the ground. Like maybe a particular instance used to teach the principal itself.

On the surface of a sphere, an equal-sided triangle will have angles greater than 90°. At very small lengths, the difference will be undetectable, and since the Earth has hills and mountains small triangles will demonstrate nothing useful. At very long lengths, you could demonstrate the rotundity of the world this way, but it would be a surveying feat of epic proportions.

It is worth noting that on the Great Plains of the United States, when whole states were surveyed, they did indeed have to take into account the curvature of the Earth.

Do you know any of the details, i would like to look at the facts that note how they took into account the curvature of the earth.

Try looking up Geodetic Survey.

I"ve heard it said
"If the earth was flat, could i draw this 1000(?) mile trianlge with 90(?) degree corners on it mr genius flat head"
What the heck are these peolpe talking about, as surely this has never been done and is just a comment on geometry in general.

So does anyone know if this has been done on some smaller scale  or validated in some way?

yes, it has been done. We call it as "the europe is flat". Here it was:

https://www.theflatearthsociety.org/forum/index.php?topic=66387.0

Some Links are seemingly broken. They were valid at that time but  it seems needed to be updated.

so much so that if you select 4 cities to form a rectangle when you place them at the corners on europe, the diagonal distance is the same as the diagonal of the rectangle. there is no circular length in any way. The reason for this is that all distances are known correctly because Europe is an advanced civilization. Maps are inconsistent in australia, america and africa because the dimensions could not be confirmed. but in europe all dimensions have been checked and perfectly compatible with the flat map.

You can check it whenever wherever you want in Europe.

To me this sound like theories of geometry...I acknowledge that the sky looks circular and maybe spherical. But can anyone cite an example of a larger than 180 degree triangle being drawn on the ground. Like maybe a particular instance used to teach the principal itself.

This is easy enough to see on a globe. On the earth itself it's still true, but far more subtle at scales a person can work in (see later in this post for why).

Start at the North Pole and follow the Prime Meridian due south to the Equator.

At the Equator, take a 90° turn to the west and travel 90° along the Equator to the 90° West meridian.

At the 90° Meridian, take a 90° turn to the north and follow the 90° West meridian to the north pole.

You will approach the pole 90° from the direction you followed when starting out, closing the spherical triangle that has three 90° interior angles for a sum of 270°.



In general, the sum of the interior angles of spherical triangles is

S = 180° (1 + 4a/A)

S is the sum of the interior angles, a is the area enclosed by the triangle, and A is the surface area of the sphere.

In the example above, the area of the triangle is 1/4 the area of the northern hemisphere (this should be obvious from inspection), so it's 1/8 the area of the whole sphere.

S = 180° (1 + 4(1/8))
 = 180° (1 + 1/2)
 = 180° (1.5)
 = 270°, as expected.

Since the surface area, A, of a sphere with radius R is
A = 4 pi R²

then, for the earth, with R = 4000 miles approximately,

A = 4 pi (4000 mi)²
 = 4 pi 16,000,000 mi²
A = 201,061,930 mi² (call it 200 million square miles).

How big would a surveyed triangle have to be to cause the interior angles to add up to 181°?

181° = 180° (1 + a/200,000,000 mi²)
181° - 180° = 180° x a/200,000,000 mi²
1° / 180° = a/200,000,000  mi²
200,000,000  mi² / 180 = a

a = 1,111,111  mi², about twice the area of Alaska. If this were an equilateral spherical triangle, the sides would be roughly 1600 miles long!

That's how big your survey would have to be to produce a 1° excess interior angle, so seeing this "on the ground" will not be easy even though it's real, and there.

Land surveys have much higher precision than 1°, and, as a result, when the area being surveyed exceeds 100 square miles or so, plane surveying (which approximates a limited area as being a plane) may not be accurate enough for some purposes, and much more complex geodetic surveying (which makes no such approximation, at the expense of much more difficult data reduction) is required.

 

It is ridiculous to claim that the corners of the triangle are ninety degrees. this is only so on paper about a so called curved earth. you can practically never prove it.

To me this sound like theories of geometry...I acknowledge that the sky looks circular and maybe spherical. But can anyone cite an example of a larger than 180 degree triangle being drawn on the ground. Like maybe a particular instance used to teach the principal itself.

It is based upon the portion of ground covered. If you cover 1/8th of the surface of Earth, you end up with an angle excess of 90 degrees.
In order to have a 1 degreee excess you will need to cover ~0.14% of the surface of Earth.
That doesn't sound like much, but as Earth has a surface area of roughly 500 million square km, you would need to cover roughly 700 000 km^2. That is a very large triangle.

yes, it has been done. We call it as "the europe is flat". Here it was:

You mean you used a horribly inaccurate method of determining distance so have no idea if Earth is flat or not?

Do you remember this:

Where we used 4 cities and distances you said were accurate to show they don't work on a FE?

Quote from: magellanclavichord on February 08, 2020, 04:48:50 PM

On the surface of a sphere, an equal-sided triangle will have angles greater than 90°. At very small lengths, the difference will be undetectable, and since the Earth has hills and mountains small triangles will demonstrate nothing useful. At very long lengths, you could demonstrate the rotundity of the world this way, but it would be a surveying feat of epic proportions.

It is worth noting that on the Great Plains of the United States, when whole states were surveyed, they did indeed have to take into account the curvature of the Earth.

Do you know any of the details, i would like to look at the facts that note how they took into account the curvature of the earth.

As noted in my later post, I was having a senior moment (or perhaps a stroke, as Bullwinkle suggested). 

Please substitute 60° (the correct number) for the 90° I unaccountably wrote.

Some of the posts above explain how a curved surface results in different numbers. Euclidean geometry is also called plane geometry because it is the geometry of a flat surface, and Jack Black showed how if you place one vertex at the pole and the opposite side on the equator, you get 90°.

It is ridiculous to claim that the corners of the triangle are ninety degrees. this is only so on paper about a so called curved earth. you can practically never prove it.

Do you really think turning from due south to due west isn't 90°, turning from due west to due north isn't 90°, and the 90° W meridian doesn't form a 90° angle with the Prime Meridian at the poles? What angles do you think they are? Do you think you can prove it?

Have you looked at your own globe? Do you have a globe? Can you borrow one? Owning a globe might help you understand some quite basic concepts.

Here is another example, this time over greater distances:

No, I am claiming that the air route distances cannot fit on any flat surface.

For example take the international airports at Johannesburg (JNB), Dubai (DBX), Beijing (PEK) and Sydney (SYD).
The nominal distances between these airports (from Great Circle Mapper) is:

		DBX		PEK		SYD
JNB		6,390 km		11,699 km		11,045 km
DBX		xxx		5,857 km		12,039 km
PEK		xxx		xxx		8,934 km

Now if we take the Johannesburg (JNB) to Sydney (Syd) flight (11,119 km) as a baseline we can use
      the routes JNB to SYD, JNB to DXB and JNB to DXB to calculate the location of Dubai, relative to Johannesburg and Sydney and use
      the routes JNB to SYD, JNB to PEK and SYD to PEK to calculate the location of Beijing, relative to Johannesburg and Sydney.
Then the distance from Dubai to Beijing can be calculated or scaled off a diagram - I did both.

This shown here:

JNB-DBX-PEK-SYD Flat Air Routes
This distance from Dubai to Beijing is 7,591 km^[1] as calculated in Excel for a flat surface. But the actual air route distance from Dubai to Beijing is not 7,591 km but 5,857 km.

So the real earth flight distances do not fit on any flat surface.

Now the distances I have used are just the nominal distances and real flight distances would all be a little longer.

Here is the Emirates Airlines route for Dubai to Beijing:


[1] Note that the 7608 km from Dubai to Beijing shown on the diagram is slightly high and it should be 7,591 km.

Thx for all the info guys. I'm gonna look at all of this.

My preliminary search turned up mostly services for sale as opposed to data. Anyone know if i can access data from large scale surveys and what search terms i'd use...?

 Thank you for the link,  Wise

It is ridiculous to claim that the corners of the triangle are ninety degrees. this is only so on paper about a so called curved earth. you can practically never prove it.

Sure, "It is ridiculous to claim that the corners of the triangle are ninety degrees" on a flat surface.
But it is quite reasonable to claim that the corners of a triangle with sides each 10,010 km are each very close to 90°
if the Earth is a Globe with an average circumference of 40,040 km - as it is known to be.

I"ve heard it said
"If the earth was flat, could i draw this 1000(?) mile trianlge with 90(?) degree corners on it mr genius flat head"
What the heck are these peolpe talking about, as surely this has never been done and is just a comment on geometry in general.

So does anyone know if this has been done on some smaller scale  or validated in some way?

The big portion of Geodesy is triangulation. The use of angles / triangles and the related geometry.

We didn't need all those space imagery to know the shape and the size of our planet.
It was measured long before space flights.

See the https://en.wikipedia.org/wiki/Triangulation_(surveying)
Google for "geodetic triangulation" for more.

Thx guys...Get around to this soon

Wise link looks legit

Wise link looks legit

Really? How would you know because most of his links are broken?

Wise link looks legit

Which one and how so?