Triple Right Triangle

On a flat earth, all triangles would have an interior angle sum of 180°. On a curved Earth, the angles wouldn't add up to 180°, though the amount it differs will depend on the size of the triangle.

While I don't know of anyone who has taken a 10,000-km tape measure to draw straight lines across half the globe, there is a great resource for straight lines across the Earth. Private commercial companies tend to do everything they can to make a profit.

Commercial airlines paths can be used as the shortest distance between cities, and these paths constantly show interior angles of over 180° (the effect is much more pronounced for large triangles).

http://www.theflatearthsociety.org/forum/index.php/topic,59862.0.html#.UjYStJK1Hsk

See that image? Notice the angle we are viewing it from? I'd say the line of latitude we are looking directly at is about 60°N. Notice how curved that particular line of latitude is?

North and South are not the same as East and West when dealing with the earth. North and South are references to a specific magnetic point at each of the poles. East and West are simply a direction parallel to the equator. Sure, a mariner's compass we'll point you in the right direction but it doesn't know the difference either.

Notice how all lines of longitude intersect each other at the poles while lines of latitude are all parallel? The only lines that are straight on the earth are lines that you can imagine cutting the sphere directly in half. That is a straight line. That's precisely what lines of longitude do.

Quote from: Ævan on September 15, 2013, 12:55:52 PM

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 to the north at the last turn.  Only that he turned north. 

Added to that, ninety degrees latitude west/east at 89.85N longitude, about ten miles, 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.

Yeah, my dictionary definition of east should help you over this bit. But you are getting there. You'll be telling everyone how flat the earth is at work on Monday.

Quote from: Pyrolizard on September 15, 2013, 01:12:40 PM

Quote from: Ævan on September 15, 2013, 12:55:52 PM

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 to the north at the last turn.  Only that he turned north. 

Added to that, ninety degrees latitude west/east at 89.85N longitude, about ten miles, 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.

Yeah, my dictionary definition of east should help you over this bit. But you are getting there. You'll be telling everyone how flat the earth is at work on Monday.

That's the definition of east on a compass. I didn't know we were talking about compasses. I thought we were talking about the earth. Get your cherry picking off this thread and stop embarrassing yourself.

east [iːst]
n
1. (Earth Sciences / Physical Geography) the direction along a parallel towards the sunrise, at 90° to north; the direction of the earth's rotation

That's the definition of east on a compass. I didn't know we were talking about compasses. I thought we were talking about the earth.

Do compasses not work on earth?
It's actually the definition of East full stop. Geographic east as well as how a magnetic compass works.

Its not my fault that round earth theory has got itself confused. It's a terrible theory.

Quote from: Pyrolizard on September 15, 2013, 01:12:40 PM

Quote from: Ævan on September 15, 2013, 12:55:52 PM

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 to the north at the last turn.  Only that he turned north. 

Added to that, ninety degrees latitude west/east at 89.85N longitude, about ten miles, 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.

Yeah, my dictionary definition of east should help you over this bit. But you are getting there. You'll be telling everyone how flat the earth is at work on Monday.

I see no reason your definition invalidates anything.  He walked ten miles due south, turned ninety degrees east at 89.85N longitude.  He walked for ten miles due east.  He then turned ninety degrees northward and walked ten miles, completing an angle that isn't ninety degrees.  To clarify, if he started walking south at zero degrees latitude, he'd have turned northward again at sixty degrees east latitude.

Ah, I see where I screwed up, I mixed the final turn and final angle in my head, and it came out a bit jumbled.  I'll fix it, sorry about that.

Ah, I see where I screwed up, I mixed the final turn and final angle in my head, and it came out a bit jumbled.  I'll fix it, sorry about that.

Yeah, its a good puzzle. Flat Earthers aren't as dumb as the media makes us out to be.

Quote from: rottingroom on September 15, 2013, 01:20:03 PM

That's the definition of east on a compass. I didn't know we were talking about compasses. I thought we were talking about the earth.

Do compasses not work on earth?
It's actually the definition of East full stop. Geographic east as well as how a magnetic compass works.

Its not my fault that round earth theory has got itself confused. It's a terrible theory.

You just don't like real life. It doesn't make it a terrible theory.

It's appropriate to have different definitions to depict east on the earth and east on a compass. Otherwise people like you will think they have a brain.

Quote from: Ævan on September 15, 2013, 01:25:31 PM

Quote from: rottingroom on September 15, 2013, 01:20:03 PM

That's the definition of east on a compass. I didn't know we were talking about compasses. I thought we were talking about the earth.

Do compasses not work on earth?
It's actually the definition of East full stop. Geographic east as well as how a magnetic compass works.

Its not my fault that round earth theory has got itself confused. It's a terrible theory.

You just don't like real life. It doesn't make it a terrible theory.

It's appropriate to have different definitions to depict east on the earth and east on a compass. Otherwise people like you will think they have a brain.

Are you suggesting that East on the earth is not 90° clockwise from due north and directly opposite west?

So far I have soaked up your condescending mocking with good grace, but if you continue and add insult to injury by being stupid, I'm going to have to humiliate you in front of all the Round Earth guests that are reading this thread. Right now there are 104 of them. some of them likely read here regulalry. They are likely thinking, "Go on Thork, you haven't really let rip at a noob for ages. Kill this one. No one will miss it."

Quote from: Pyrolizard on September 15, 2013, 01:30:46 PM

Ah, I see where I screwed up, I mixed the final turn and final angle in my head, and it came out a bit jumbled.  I'll fix it, sorry about that.

Yeah, its a good puzzle. Flat Earthers aren't as dumb as the media makes us out to be.

Depends on who you ask.  Also:

I see no reason your definition invalidates anything.  He walked ten miles due south, turned ninety degrees east at 89.85N longitude.  He walked for ten miles due east.  He then turned ninety degrees northward and walked ten miles, completing an angle that isn't ninety degrees.  To clarify, if he started walking south at zero degrees latitude, he'd have turned northward again at sixty degrees east latitude.

Ah, I see where I screwed up, I mixed the final turn and final angle in my head, and it came out a bit jumbled.  I'll fix it, sorry about that.

My point applies.  He still wouldn't have ended at ninety degrees east latitude, only sixty degrees.  And you'll notice that, yes, the angles of the triangle are in fact more than one hundred eighty degrees, so although not a triple right triangle, it does demonstrate the point.  I'm with you that such a huge distance need not be covered, but a fairly large one does for it to be relevant.

You're right in that it's possible at a smaller scale, although not with the exact same results, but a scale of miles is still enough for curvature to be present easily.  If you like, see the infamous ENaG for it's chart of drop distances on a round Earth.

Quote from: rottingroom on September 15, 2013, 01:37:41 PM

Quote from: Ævan on September 15, 2013, 01:25:31 PM

Quote from: rottingroom on September 15, 2013, 01:20:03 PM

That's the definition of east on a compass. I didn't know we were talking about compasses. I thought we were talking about the earth.

Do compasses not work on earth?
It's actually the definition of East full stop. Geographic east as well as how a magnetic compass works.

Its not my fault that round earth theory has got itself confused. It's a terrible theory.

You just don't like real life. It doesn't make it a terrible theory.

It's appropriate to have different definitions to depict east on the earth and east on a compass. Otherwise people like you will think they have a brain.

Are you suggesting that East on the earth is not 90° clockwise from due north and directly opposite west?

So far I have soaked up your condescending mocking with good grace, but if you continue and add insult to injury by being stupid, I'm going to have to humiliate you in front of all the Round Earth guests that are reading this thread. Right now there are 104 of them. some of them likely read here regulalry. They are likely thinking, "Go on Thork, you haven't really let rip at a noob for ages. Kill this one. No one will miss it."

Indeed, I am suggesting it is not a perfect 90°. It is a precise at the equator but not everywhere else.

Many maps show circles of latitude as straight lines, but a circle of latitude is not (except the Equator) the shortest distance between two points on the Earth. In other words, circles of latitude (except for the Equator) are not great circles (see also great-circle distance), but are rhumb lines. So an aircraft flying between a European and North American city that share the same latitude will fly farther north, over Greenland for example.

http://en.wikipedia.org/wiki/Circle_of_latitude

and in case you don't know what a great circle is...



http://en.wikipedia.org/wiki/Great_circle

It is the only true straight line on the earth.

and in case you don't know what a great circle is...

I have an ATPL. 

Quote from: rottingroom on September 15, 2013, 01:56:09 PM

and in case you don't know what a great circle is...

I have an ATPL. 

well then why the hell don't you know that a great circle is the only true straight line? Why are you trying to say the line of latitude at 10°N is a straight line?

Why are you trying to say the line of latitude at 10°N is a straight line?

Feel free to quote where I said that.

Your weasel words do not hide your intent to troll.

Feel free to quote where I said that.

Your weasel words do not hide your intent to troll.

Ok, I will...

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.

Seems you said it there and then there is the implication here that they always bisect at 90°...

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.

and here....

Are you suggesting that East on the earth is not 90° clockwise from due north and directly opposite west?

and then when you say things like this...

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

it is irritating and since it is apparently only you that is full of hot air and bluster.

They do always bisect at 90 degrees. You are making such a fool of yourself.

Meridian—An imaginary arc on the Earth's surface from the North Pole to the South Pole that associates all locations running along it with a given longitude. The position of a point on the meridian is given by its intersecting latitude. Each meridian is perpendicular to all circles of latitude at the intersection points.

I have an ATPL. 

I find that particularly hard to believe, unless you are only pretending to be an imbecile.


Anyway, the point is that to make the triple-right-triangle, the sides must be 1/4 segments of great circles. This means there is no left/right deviation while traveling the line, unlike Ævan's 300yd example, or the 10 mile sided triangle in the riddle.

Spherical excess is present in smaller triangles though, even Rowbotham encountered it, although he dismissed it (incorrectly) as equipment error: ENaG - Spherical Excess

I find that particularly hard to believe, unless you are only pretending to be an imbecile.

Coming from someone who can't spell 'scientific', I'm not going to lose any sleep.

Quote from: Scintific Method on September 15, 2013, 02:53:15 PM

I find that particularly hard to believe, unless you are only pretending to be an imbecile.

Coming from someone who can't spell 'scientific', I'm not going to lose any sleep.

Typo...

What about the rest of my post? Or are you going to ignore it, just like FE's always ignore pertinent points?

They do always bisect at 90 degrees. You are making such a fool of yourself.

Quote from: http://nationalatlas.gov/articles/mapping/a_latlong.html

Meridian—An imaginary arc on the Earth's surface from the North Pole to the South Pole that associates all locations running along it with a given longitude. The position of a point on the meridian is given by its intersecting latitude. Each meridian is perpendicular to all circles of latitude at the intersection points.

If a line of latitude is not a straight line (except for the equator), which I have conclusively shown you, then it stands to reason that while it is exceptionally close to being perfectly perpendicular to a meridian, it's not quite.

This is not much different than the difference between a FE'r and RE'r anyways is it? When we debate about the curvature of the Earth the FE'r says it is perfectly flat because it looks flat but really it's not quite. The curvature is so slight but at earths enormous size that slight curvature forms a sphere. The same goes with lines of latitude. It is almost straight, but not quite and at Earths enormous size that slightly less than straight line will change everything, especially in arguments like this.

Where, if the starting point is the north pole and if you intend to take three 45° turns to form a triangle, you'll need to get your ass down to the equator.

By the way saying stuff like this...

You are making such a fool of yourself.

is not benefiting you, it just makes you look desperate.

Don't be mad though alright, we all good, I just needed to correct you.

If a line of latitude is not a straight line (except for the equator), which I have conclusively shown you, then it stands to reason that while it is exceptionally close to being perfectly perpendicular to a meridian, it's not quite.

well they are perfectly perpendicular, so somewhere your reasoning has gone arry. Whilst re-examining I suggest you start with your assumptions about earth's shape.

What about the rest of my post? Or are you going to ignore it, just like FE's always ignore pertinent points?

Pertinent? pffft! I ignored it because you haven't bothered to read the thread you just jumped into.

well they are perfectly perpendicular, so somewhere your reasoning has gone arry. Whilst re-examining I suggest you start with your assumptions about earth's shape.

Whatever helps you sleep better. In the meantime I suggest you get started on some reading material that might help you the next time you try to sound like you know what you are talking about.

http://math.about.com/od/geometry/Geometry_Tutorials_Lessons_and_Tips.htm

Quote from: Ævan on September 15, 2013, 03:17:38 PM

well they are perfectly perpendicular, so somewhere your reasoning has gone arry. Whilst re-examining I suggest you start with your assumptions about earth's shape.

Whatever helps you sleep better. In the meantime I suggest you get started on some reading material that might help you the next time you try to sound like you know what you are talking about.

http://math.about.com/od/geometry/Geometry_Tutorials_Lessons_and_Tips.htm

I'm satisfied that you are an idiot. I'll leave this thread to you.

Lines of longitude, called meridians, run perpendicular to lines of latitude

What Is Longitude?
Lines of longitude, called meridians, run perpendicular to lines of latitude

a network of meridians stretching from pole to pole and of lines of latitude perpendicular to them

Latitudes are the lines that run parallel to the equator and measure the north-south direction, whereas longitudes or meridians, the vertical lines running perpendicular to the latitudes measure the east-west direction.

Quote from: Scintific Method on September 15, 2013, 02:59:26 PM

What about the rest of my post? Or are you going to ignore it, just like FE's always ignore pertinent points?

Pertinent? pffft! I ignored it because you haven't bothered to read the thread you just jumped into.

Read it (all 3 pages), saw that certain points hadn't been addressed, and decided to contribute, more or less as follows:

A triple right triangle requires its sides to be 1/4 segments of great circles, no more, no less. (a point you seem ignorant of)
Spherical excess can be (and has been) detected at smaller scales. (a point worth making)

Quote from: rottingroom on September 15, 2013, 03:22:02 PM

Quote from: Ævan on September 15, 2013, 03:17:38 PM

well they are perfectly perpendicular, so somewhere your reasoning has gone arry. Whilst re-examining I suggest you start with your assumptions about earth's shape.

Whatever helps you sleep better. In the meantime I suggest you get started on some reading material that might help you the next time you try to sound like you know what you are talking about.

http://math.about.com/od/geometry/Geometry_Tutorials_Lessons_and_Tips.htm

I'm satisfied that you are an idiot. I'll leave this thread to you.

Quote from: http://www.ecology.com/2012/05/18/latitude-longitude/

Lines of longitude, called meridians, run perpendicular to lines of latitude

Quote from: http://www.neighborhoodlink.com/article/Community/What_Is_Longitude

What Is Longitude?
Lines of longitude, called meridians, run perpendicular to lines of latitude

Quote from: http://parachuteshop.com/Latitude%20and%20Longitude%20History.htm

a network of meridians stretching from pole to pole and of lines of latitude perpendicular to them

Quote from: http://www.mapsofworld.com/lat_long/

Latitudes are the lines that run parallel to the equator and measure the north-south direction, whereas longitudes or meridians, the vertical lines running perpendicular to the latitudes measure the east-west direction.

Sigh. You still don't understand what a great circle is and why that is a true straight line. Some pilot.

I don't think he's a pilot either.

While I'm here..

Quote from: Pyrolizard on Today at 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 Today at 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.

I think you took that a little out of context and didn't read his whole post. At 300 yards on Earth it still would never be a large enough distance to create a triple right triangle... just an abnormal triangle with a >180 degree interior angle sum. This is about a triple right triangle or something at least closer to it.

I have found this definition of perpendicular:

per·pen·dic·u·lar   (pûrpn-dky-lr)
adv.
4. A vertical or nearly vertical line or plane.

It could explain why in this case it can still be appropriate to use that word when describing the intersection of latitude and longitude because clearly they are not perfectly perpendicular.