Triple Right Triangle

I'm not sure if this has been discussed in depth, but I'm curious as to how this would even begin to work on a flat Earth.



Granted, I'm not entirely sure if this has been demonstrated by a person on the Earth, but given the resources and time, it wouldn't be all too difficult.

I'm proposing that someone should try this out on our planet, to determine once and for all the answer to the question that is heatedly debated on this site.

Granted, I'm not entirely sure if this has been demonstrated by a person on the Earth, but given the resources and time, it wouldn't be all too difficult.

I strongly disagree.  You do realize that each of those lines is half the distance from the north to south pole, right?

I do. I certainly was not suggesting that the journey was to be made on foot, by any means. 

Why don't you try it on earth? Walk 300 yards, turn 90 degrees, walk 300 more, turn 90 degrees and walk another 300 yards. If you aren't where you started, RE theory is the one that has questions to answer.

There is no reason the same shape can't be scaled down. And its a ball so you can start anywhere. In a field near your house if you like. All lines of latitude bisect those of longitude at 90 degrees after all.


Zetetic reasoning if ever I saw it, that a round earth is absolute tripe.

You can't scale this down unless you scale down the earth, we all agree I think that on a small area the curvature of the earth does not really matter

You can't scale this down unless you scale down the earth, we all agree I think that on a small area the curvature of the earth does not really matter

Of course you can. Walk a smaller triangle.

There are lots of reasons it can't be scaled down. There becomes a problem at shorter distances because the curvature of the Earth is not readily directly observable from any point of reference. The reason the triangle on the diagram example in the OP is so large, is that the triple right triangle relies on curvature of a spherical object to do what it does.

In short, asking me to do this by walking 300 yards is absolutely just as ridiculous as asking me to draw a triple right triangle on a piece of paper. It simply can't be done if spherical curvature is not present, which on our planet, would make it only possible over huge distances.

There are lots of reasons it can't be scaled down. There becomes a problem at shorter distances because the curvature of the Earth is not readily directly observable from any point of reference. The reason the triangle on the diagram example in the OP is so large, is that the triple right triangle relies on curvature of a spherical object to do what it does.

In short, asking me to do this by walking 300 yards is absolutely just as ridiculous as asking me to draw a triple right triangle on a piece of paper. It simply can't be done if spherical curvature is not present, which on our planet, would make it only possible over huge distances.

Do you agree my smaller blue triangle is also correct?
That all lines of latitude bisect all lines of longitude at 90 degrees?
That earth is a ball so you could in effect start anywhere?

All of a sudden, flat earth theory starts to make a lot of sense.

Your smaller triangle poses a few problems.
1. We're talking about the Earth here. That's still a pretty large triangle.
2. Your fictional 2nd equator line looks more parabolic than straight.

Your smaller triangle poses a few problems.
1. We're talking about the Earth here. That's still a pretty large triangle.
2. Your fictional 2nd equator line looks more parabolic than straight.

1. Make the triangle 300 yards. You still get the same shape on a ball.
2. I think you know what a line of latitude looks like. And you know they bisect at 90 degrees. No matter how far from the starting point. Even 300 yards.

Unsettling isn't it? The earth is flat.

You could start anywhere as long as you move a long enough distance and not just a few hundred meters as you are requesting, for that small distance (relative to earth) the plane and the sphere behave the same and you know that I suppose

Why do I need a long distance? I just showed you. Lines of latitude always bisect at 90 degrees on a round earth. And a line of latitude can be 300 yards away. They are imaginary parallel rings running around the earth.

I know I'm right. So do you. Why are you asking about a distance I can't test when the theory should hold true for one I can test?

The distance has to be long enough that the curvature of the spherical object is enough to make the tip of the triangle intersect at 90 degrees. This is not possible over such a short distance because as g el said, at such a distance, the sphere-section would act as a plane. Again, I challenge you to draw a triple right triangle on a piece of paper.

Right now you're not proving the Earth is flat, you're proving that you have a basic misunderstanding of non-Euclidean geometry.

Why do I need a long distance? I just showed you. Lines of latitude always bisect at 90 degrees on a round earth. And a line of latitude can be 300 yards away. They are imaginary parallel rings running around the earth.

I know I'm right. So do you. Why are you asking about a distance I can't test when the theory should hold true for one I can test?

You know what you are saying doesn't make sense because the line you are traveling on in your diagram (the blue line) is not a straight line on a round earth. This is why you need to go all the way to the equator so that the lines traveled after doing 45° turns are always straight lines.

It could, hypothetically, work at such a small distance if you're very precise.  Longer distances would be better, but unless each line covers a quarter of the sphere's circumference you wouldn't get a triple right triangle, just a triangle with an interior angle of greater than one hundred eighty degrees.

This is because the smaller the distance on a sphere, the closer to planar the surface between points is.  So the smaller the distance on the Earth, the smaller the total interior angle of the triangle, down to one hundred eighty degrees, or very near to it.

It could, hypothetically, work at such a small distance if you're very precise.

this guy gets it.

I always find comments like

you're proving that you have a basic misunderstanding of non-Euclidean geometry.

particularly annoying when something so obvious to me is completely missed by the person I am addressing and they in some way think its my education that is lacking.

Quote from: Pyrolizard on September 15, 2013, 11:18:13 AM

It could, hypothetically, work at such a small distance if you're very precise.

this guy gets it.

I always find comments like

Quote from: th3rm0m3t3r0 on September 15, 2013, 11:09:44 AM

you're proving that you have a basic misunderstanding of non-Euclidean geometry.

particularly annoying when something so obvious to me is completely missed by the person I am addressing and they in some way think its my education that is lacking.

It can't work at a small distance. The blue line is not a straight line. Obviously.

Quote from: Ævan on September 15, 2013, 11:47:31 AM

Quote from: Pyrolizard on September 15, 2013, 11:18:13 AM

It could, hypothetically, work at such a small distance if you're very precise.

this guy gets it.

I always find comments like

Quote from: th3rm0m3t3r0 on September 15, 2013, 11:09:44 AM

you're proving that you have a basic misunderstanding of non-Euclidean geometry.

particularly annoying when something so obvious to me is completely missed by the person I am addressing and they in some way think its my education that is lacking.

It can't work at a small distance. The blue line is not a straight line. Obviously.

Like I said, it could work if you're very precise and the lines would all be straight, but you wouldn't get a triple right triangle.  Just one that has an interior angle measurably larger than would be on a plane.  The larger the distance, the less precise you need to be.

That also means you would have to be ludicrously accurate at six hundred yards a leg.  As in, within hundredths of a degree.  A much larger distance is still necessary to rule out human or tool error.

Quote from: rottingroom on September 15, 2013, 11:50:51 AM

Quote from: Ævan on September 15, 2013, 11:47:31 AM

Quote from: Pyrolizard on September 15, 2013, 11:18:13 AM

It could, hypothetically, work at such a small distance if you're very precise.

this guy gets it.

I always find comments like

Quote from: th3rm0m3t3r0 on September 15, 2013, 11:09:44 AM

you're proving that you have a basic misunderstanding of non-Euclidean geometry.

particularly annoying when something so obvious to me is completely missed by the person I am addressing and they in some way think its my education that is lacking.

It can't work at a small distance. The blue line is not a straight line. Obviously.

Like I said, it could work if you're very precise and the lines would all be straight, but you wouldn't get a triple right triangle.  Just one that has an interior angle measurably larger than would be on a plane.  The larger the distance, the less precise you need to be.

That also means you would have to be ludicrously accurate at six hundred yards a leg.  As in, within hundredths of a degree.  A much larger distance is still necessary to rule out human or tool error.

The point of the idea is to use right angles.

Quote from: Ævan on September 15, 2013, 11:47:31 AM

Quote from: Pyrolizard on September 15, 2013, 11:18:13 AM

It could, hypothetically, work at such a small distance if you're very precise.

this guy gets it.

I always find comments like

Quote from: th3rm0m3t3r0 on September 15, 2013, 11:09:44 AM

you're proving that you have a basic misunderstanding of non-Euclidean geometry.

particularly annoying when something so obvious to me is completely missed by the person I am addressing and they in some way think its my education that is lacking.

It can't work at a small distance. The blue line is not a straight line. Obviously.

It should a would work on a smaller distance. Get a globe and trace with your finger a smaller triangle following say the 10 degree line of latitude. I don't want to keep tooing and froing with it does work, it doesn't work.

It does. you need to do some research and come back when you are ready to debate.

Below the same conundrum is actually a riddle using 10 miles as the distance.
http://www.cut-the-knot.org/triangle/pythpar/NonEuclid.shtml

And of course being a sphere you can start anywhere. So do this experiment yourself and tell me if you end up where you started. If you don't the earth is flat.

Quote from: Pyrolizard on September 15, 2013, 12:02:32 PM

Quote from: rottingroom on September 15, 2013, 11:50:51 AM

Quote from: Ævan on September 15, 2013, 11:47:31 AM

Quote from: Pyrolizard on September 15, 2013, 11:18:13 AM

It could, hypothetically, work at such a small distance if you're very precise.

this guy gets it.

I always find comments like

Quote from: th3rm0m3t3r0 on September 15, 2013, 11:09:44 AM

you're proving that you have a basic misunderstanding of non-Euclidean geometry.

particularly annoying when something so obvious to me is completely missed by the person I am addressing and they in some way think its my education that is lacking.

It can't work at a small distance. The blue line is not a straight line. Obviously.

Like I said, it could work if you're very precise and the lines would all be straight, but you wouldn't get a triple right triangle.  Just one that has an interior angle measurably larger than would be on a plane.  The larger the distance, the less precise you need to be.

That also means you would have to be ludicrously accurate at six hundred yards a leg.  As in, within hundredths of a degree.  A much larger distance is still necessary to rule out human or tool error.

The point of the idea is to use right angles.

And the point of my statement is that, even if you don't travel the necessary distance to get a triangle with three right angles, you can still get a triangle with interior angles that are impossible on a flat Earth.

It's to make the entire experiment less expensive and time consuming, and still bare out the results that can prove one way or another.  I'm not saying it should be done at six hundred yards for each side, that's ridiculous, unless we can measure to the nanometer the results will be effectively the same as on a plane.  I'm just saying that you need not travel tens of thousands of miles to get conclusive results.

Quote from: rottingroom on September 15, 2013, 12:04:22 PM

Quote from: Pyrolizard on September 15, 2013, 12:02:32 PM

Quote from: rottingroom on September 15, 2013, 11:50:51 AM

Quote from: Ævan on September 15, 2013, 11:47:31 AM

Quote from: Pyrolizard on September 15, 2013, 11:18:13 AM

It could, hypothetically, work at such a small distance if you're very precise.

this guy gets it.

I always find comments like

Quote from: th3rm0m3t3r0 on September 15, 2013, 11:09:44 AM

you're proving that you have a basic misunderstanding of non-Euclidean geometry.

particularly annoying when something so obvious to me is completely missed by the person I am addressing and they in some way think its my education that is lacking.

It can't work at a small distance. The blue line is not a straight line. Obviously.

Like I said, it could work if you're very precise and the lines would all be straight, but you wouldn't get a triple right triangle.  Just one that has an interior angle measurably larger than would be on a plane.  The larger the distance, the less precise you need to be.

That also means you would have to be ludicrously accurate at six hundred yards a leg.  As in, within hundredths of a degree.  A much larger distance is still necessary to rule out human or tool error.

The point of the idea is to use right angles.

And the point of my statement is that, even if you don't travel the necessary distance to get a triangle with three right angles, you can still get a triangle with interior angles that are impossible on a flat Earth.

It's to make the entire experiment less expensive and time consuming, and still bare out the results that can prove one way or another.  I'm not saying it should be done at six hundred yards for each side, that's ridiculous, unless we can measure to the nanometer the results will be effectively the same as on a plane.  I'm just saying that you need not travel tens of thousands of miles to get conclusive results.

What is this nanometer rubbish? If you can't tell the difference between 60 degrees and 90 degrees in a 300 yard sided triangle, you are seriously inept.

Are you deliberately not reading the thread, he obviously said it will not be right angles at this small area, the inconsistency with a plane will come because the sum of angles will be more than 180

Quote from: Pyrolizard on September 15, 2013, 12:13:39 PM

And the point of my statement is that, even if you don't travel the necessary distance to get a triangle with three right angles, you can still get a triangle with interior angles that are impossible on a flat Earth.

It's to make the entire experiment less expensive and time consuming, and still bare out the results that can prove one way or another.  I'm not saying it should be done at six hundred yards for each side, that's ridiculous, unless we can measure to the nanometer the results will be effectively the same as on a plane.  I'm just saying that you need not travel tens of thousands of miles to get conclusive results.

What is this nanometer rubbish? If you can't tell the difference between 60 degrees and 90 degrees in a 300 yard sided triangle, you are seriously inept.

Aevan, it's been explained why you wouldn't get ninety degrees at such a small distance multiple times.  See here:

It could, hypothetically, work at such a small distance if you're very precise.  Longer distances would be better, but unless each line covers a quarter of the sphere's circumference you wouldn't get a triple right triangle, just a triangle with an interior angle of greater than one hundred eighty degrees.

This is because the smaller the distance on a sphere, the closer to planar the surface between points is.  So the smaller the distance on the Earth, the smaller the total interior angle of the triangle, down to one hundred eighty degrees, or very near to it.

It can't work at a small distance. The blue line is not a straight line. Obviously.

Draw a line on a ball and then look at it from a different angle. It will appear curved. That, afterall, is why it's possible to make a triple-right triangle on a sphere.

Quote from: rottingroom on September 15, 2013, 11:50:51 AM

It can't work at a small distance. The blue line is not a straight line. Obviously.

Draw a line on a ball and then look at it from a different angle. It will appear curved. That, afterall, is why it's possible to make a triple-right triangle on a sphere.

Exactly. AEVOHEEN's suggestion is to go down to whatever angle from the north pole and then head west following lines of latitude. Well if you follow THAT line you won't make a straight line. For instance, the line of latitude at 30° N is not a straight line on a sphere. It is a curved line as you will notice if you looked at it from an angle perpendicular to 30° N. This is precisely why flight routes and shipping routes do not go straight from east to west or vice-versa and instead seem to take a curve. That curved route is actually the straight route. 

We are trying to make a triangle with right angles. The lines must be straight.

Quote from: rottingroom on September 15, 2013, 11:50:51 AM

Quote from: Ævan on September 15, 2013, 11:47:31 AM

Quote from: Pyrolizard on September 15, 2013, 11:18:13 AM

It could, hypothetically, work at such a small distance if you're very precise.

this guy gets it.

I always find comments like

Quote from: th3rm0m3t3r0 on September 15, 2013, 11:09:44 AM

you're proving that you have a basic misunderstanding of non-Euclidean geometry.

particularly annoying when something so obvious to me is completely missed by the person I am addressing and they in some way think its my education that is lacking.

It can't work at a small distance. The blue line is not a straight line. Obviously.

It should a would work on a smaller distance. Get a globe and trace with your finger a smaller triangle following say the 10 degree line of latitude. I don't want to keep tooing and froing with it does work, it doesn't work.

It does. you need to do some research and come back when you are ready to debate.

Below the same conundrum is actually a riddle using 10 miles as the distance.
http://www.cut-the-knot.org/triangle/pythpar/NonEuclid.shtml

And of course being a sphere you can start anywhere. So do this experiment yourself and tell me if you end up where you started. If you don't the earth is flat.

are you visually impaired? the lines in this picture are not straight lines. If you change your perspective for each line to be directly on top you will notice that they are all curved.

This has been pointed out before, but I want to remind it since some people seem to ignore it... You can NOT make a triple right triangle on a smaller scale. You can make triangles where each angle is >60 degrees but unless you travel a fair distance it will be less than 1 degree more. Learn some geometry before you argue on this topic (but geometry is science so you can't trust it...)

This has been pointed out before, but I want to remind it since some people seem to ignore it... You can NOT make a triple right triangle on a smaller scale. You can make triangles where each angle is >60 degrees but unless you travel a fair distance it will be less than 1 degree more. Learn some geometry before you argue on this topic (but geometry is science so you can't trust it...)

Being as I am the only person to have provided a source (as usual) and all I have from round earthers is hot air and bluster, I'm at the point where I get bored and wander off. Maybe one of you would actually like to examine the link I gave where a man travels in a triangle 10 miles by 10 miles and ends up where he started.

Below the same conundrum is actually a riddle using 10 miles as the distance.
http://www.cut-the-knot.org/triangle/pythpar/NonEuclid.shtml

I will then back that up with a further source to cement the fact that I am right and that you are all talk and no show.

east  (st)
n.
1.  Abbr. E
a.  The cardinal point on the mariner's compass 90° clockwise from due north and directly opposite west.

Combine my two sources. Digest the information. Conclude earth is flat. Good evening gentleman, its getting late.

Quote from: LockRay on September 15, 2013, 12:51:18 PM

This has been pointed out before, but I want to remind it since some people seem to ignore it... You can NOT make a triple right triangle on a smaller scale. You can make triangles where each angle is >60 degrees but unless you travel a fair distance it will be less than 1 degree more. Learn some geometry before you argue on this topic (but geometry is science so you can't trust it...)

Being as I am the only person to have provided a source (as usual) and all I have from round earthers is hot air and bluster, I'm at the point where I get bored and wander off. Maybe one of you would actually like to examine the link I gave where a man travels in a triangle 10 miles by 10 miles and ends up where he started.

Quote from: Ævan on September 15, 2013, 12:07:41 PM

Below the same conundrum is actually a riddle using 10 miles as the distance.
http://www.cut-the-knot.org/triangle/pythpar/NonEuclid.shtml

I will then back that up with a further source to cement the fact that I am right and that you are all talk and no show.

Quote from: http://www.thefreedictionary.com/east

east  (st)
n.
1.  Abbr. E
a.  The cardinal point on the mariner's compass 90° clockwise from due north and directly opposite west.

Combine my two sources. Digest the information. Conclude earth is flat. Good evening gentleman, its getting late.

The thing about your source, it doesn't say he turned ninety degrees and faced south at his final location.

Added to that, ninety degrees latitude east at 89.85N longitude, about ten miles south of the north pole, is fifteen miles away from zero degrees latitude.  So yes, he made it back to where he started.  He did not make a triple right triangle.