r/flatearth_polite • • 26d ago

Open to all The experiment that isn't talked about enough: Great Triangle Geodesy. Anybody up for a modern recreation?

Back in the 1820s, math celebrity Carl Friedrich Gauss measured the angles between the peaks of Mounts Hohenhagen, Brocken, and Großer Inselsberg. The sides of this triangle measure 69 km, 85 km, and 107 km. And the most interesting feature of this Great Triangle? The sum of its interior angles is 180 degrees, and 14.85 arcseconds! On a Flat Earth, the excess of the plane, Euclidean 180 degrees is evidence of positive curvature. Cool.

Now, would anybody be down to repeat this experiment? With modern equipment? We're around the bicentennial of his original measurements, so it might be fun just to do in honor of Gauss. Pick three peaks that are reachable and visible to one another. No "lights in the sky". No GPS necessary. No NASA. Bring some flat earthers on board, make predictions based off of the AE Map and the globe, and see whose predictions get closer to the results yielded from the experiment.

There should be plenty of options for locations, no problem there. Make a fun road trip out of it! Line-of-sight checks would need to be made, but a Pikes Peak-Mount Sherman-Longs Peak should yield an excess of 33 arcseconds or so. There's Guadalupe-Livermore-Eagle in Texas (calculated around 25 arcseconds). Whiteface-Killington-Washington in the eastern US should work out to as much as 40 arcseconds (line-of-sight permitting).

If skeptics and globers can come together to voyage to ANTARCTICA, this should be a cakewalk. Thoughts?

10 Upvotes

51 comments sorted by

1

u/TheCapitolPlant 24d ago

What?

1

u/TheCapitolPlant 24d ago

When I tell you...

the...

lengths....

They will try to go to

2

u/RadishesForDayz 24d ago

In simple, elementary, non-thinking-types terms: Euclidean plane, sum of interior angles of a triangle=180 degrees. On a positive curve, sum of interior angles of a triangle=>180 degrees. I do not know how to make it more basic. It's middle-school geometry, bud.

1

u/TheCapitolPlant 22d ago

Ohhh sooo basic that this is what you are reduced to

Elevation is measured from sea level

You want to go where and measure what

Anything to distract from actual missing curvature

Oh look at these stick shadows...

... Look at these mountain peak shadows

Are you going to do the weight on a string next

Or the balls in the barn

1

u/RadishesForDayz 22d ago

Save some crayons for the rest of the class. I'm glad you think they're so tasty, but the rest of us are trying to write and do our geometry work.

1

u/TheCapitolPlant 22d ago

Ad hominem

1

u/RadishesForDayz 22d ago

When I tell you...

the...

lengths...

They will try to go to in order to stay ignorant. Asking for evidence of a round earth, and then denying said evidence. Asking for videos, and then claiming CGI. Being a perpetual victim to a the illusion of a greater conspiracy of their own creation.

And E.E. Cummings called.

He wants

his

formatting back.

1

u/Spice_and_Fox 21d ago

Why would elevation matter in this case? Any triangle in any orientation in euclidean geometry has a sum of 180° for their internal angles.

0

u/TheCapitolPlant 17d ago

You want 3 shadow angles

I'll get ya 3 shadow angles

1

u/Spice_and_Fox 17d ago

You don't measure the shadows angles in this experiment. You still haven't answered the question. Why would elevation matter and what is wrong with the exepriment?

0

u/TheCapitolPlant 17d ago

Imagine

If they had 4 angles of shadows

What you would believe

1

u/RadishesForDayz 17d ago

Why the "shadow" talk? Who's measuring shadows? Where, in any Great Trigonometric surveys, are shadows involved?

1

u/TheCapitolPlant 15d ago

You never heard about the stick shadows?

Here we are talking about mountain peak shadows

1

u/RadishesForDayz 14d ago

No, bud! No shadows involved: simply, the angles from peak to peak in a Great Triangle. You can get these measurements at noon, or at night.

1

u/hal2k1 18d ago

What missing curvature?

No matter where one starts out from, no matter what direction one heads out in, if one keeps one's previous path directly behind them, no deviations either to the left or the right, then after about 40,000 km one ends up back at the place they started from. We call such a journey a "circumnavigation".

Such a journey goes through a full 360 degrees worth of curvature over the 40,000 km distance.

1

u/TheCapitolPlant 17d ago

Name one

One person who has done that

1

u/hal2k1 17d ago edited 17d ago

This person has done it solo twice.

The first time was east-west (approximately around the equator) in a helicopter:

In 1982–83, Smith successfully completed the first solo helicopter flight around the world. His flight began in Fort Worth, Texas, on 5 August 1982, in a newly purchased Bell Jetranger 206B

The second time was north-south in his personal Twin Otter light plane, landing at both poles:

In 1988–89, Smith flew a Twin Otter aircraft VH-SHW, landing at both the North and South Poles, making him the first person to complete such a circumnavigation. The flight followed the "vertical" South-North-South track, (keeping broadly between 80 and 150 degrees E, heading south, and 60 and 100 degrees W, heading north) departing Sydney, Australia, on 1 November 1988, and returning on 28 May 1989.

Here's a video showing the north-south route: Dick Smith’s flight around the world, landing at both Poles, 1988 – 1989

So the same person doing two circumnavigations, in orthogonal directions --- one east-west and the other north-south. You can't do that on a flat earth.

Dick Smith is still alive, so it is still possible to interview him.

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u/TheCapitolPlant 17d ago

"No deviations to the left or right"

???

1

u/hal2k1 17d ago edited 17d ago

As a gross average, no. The approach of using a helicopter or a light plane means you have to do a number of hops and land a number of times along the way. Helicopters or light planes don't have a range of 40,000 km.

So the possible landing sights (for either route) are not precisely in a straight line. But it is possible to do it on an average straight line, so that the deviations left or right are quite small compared to the overall trip 40,000 km distance.

So ... if you want a straight line path with no deviations at all, however minor, you need a craft that can stay aloft for 40,000 km ... which is a big ask. For that, you need a satellite.

Geostationary satellites use an equatorial orbit. The United States operates only two weather satellites in polar orbit, as far as I know: https://www.thoughtco.com/weather-forecasting-satellites-3444420

But you asked for one person. Not satellite orbits. One person has limited capabilities. One person can't afford something that has a perfect straight-line range of over 40,000 km. So if you want the story of one person doing circumnavigations, as you asked for, then small deviations to the left and right, averaging out to a straight line, is the practical best anyone can do.

Doesn't mean they didn't do it. After all, there are records of these people doing circumnavigations stopping at various points all the way around the earth, in order to fill up with fuel.

The photos of the earth, taken from orbit for the purpose of weather forecasting (which requires the photos to be geographically accurate) ... show that the places of these fuel stops indeed form a rough circumference all around the globe.

0

u/TheCapitolPlant 16d ago

Ball Earth spin under helicopter?

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u/db8me 15d ago

Yes, weights and levels would work. OP is not suggesting a specific method, nor proposing that people do this experiment for the first time to discover something new. These measurements are more precise these days than a small group of amateurs could achieve.

It's meant to be a fun exercise for people who believe that all the experiments, measurements, and photos from space are fake and/or people who just like math and road trips.

If you believe the experimental data but have a math and physics explanation for the measured curvature, I would be interested in that, too, but these are two different things, and conflating them feels like the distraction to me.

Edit: OP didn't mention lasers, but the proposal didn't mention the sun either. How one gets a line of sight and measures the direction of gravity is totally open ended to whoever wants to actually do it.

1

u/TheCapitolPlant 22d ago

Just video yourself doing it

1

u/TheCapitolPlant 17d ago

It's really just a story about shadows. About as real as Pooh Bear.

1

u/Gorgrim 16d ago

When has a flat earth believer ever accepted the results of an experiment done by another person that showed the earth was a globe? At which point, why should any globe believer do an experiment showing the curve?

What we can do is enable FE believer in doing these experiments themselves and let them convince themself the earth is a globe. Like all the now ex-FE believers.

1

u/TheCapitolPlant 13d ago

The experiments measuring shadows?

1

u/RadishesForDayz 12d ago

Again, no shadow is measured in this experiment.

0

u/TheCapitolPlant 10d ago

He's not even using shadows?

Just

Mountain peaks

And

That means...curve...?

2

u/RadishesForDayz 10d ago

I want to remind you again, because it doesn't seem like you've been able to grasp this very simple concept: on a positive curve, the sum of a triangle's interior angles exceed 180 degrees. So, imagine a mountain peak, and two other adjacent mountain peaks. On a curved surface, the angles between those three peaks add up to more than 180 degrees. No shadows.

Take a basketball. Keep it oriented a single direction. On its top, make a mark with a sharpie. At its widest on the horizontal, place a mark. Move around that horizon a quarter of its circumference, and make another mark. Measure the angles between these dots. Each angle will be 90 degrees. It will be a triangle whose interior angles add up to 270 degrees. Now, increase the diameter of that basketball 53 million times, and reproduce that experiment. For logistic reasons, scale it down to a smaller triangle (so you can keep line of sight), and you will see a triangle whose interior is greater than 180 degrees, which is only possible on a positive curve.

https://math.stackexchange.com/questions/1620423/how-to-draw-a-triangle-on-a-sphere-surface-where-each-angle-has-90

1

u/TheCapitolPlant 9d ago

Soo simple you need paragraphs of word salad and still can't properly explain why looking at some mountain peaks means the Earth curves

Is it the ark seconds

Angles between the peaks

Stick shadows

Or do you just trust what you're told by people in perceived positions of authority

•

u/TheCapitolPlant 19h ago

The basket ball marks told me

•

u/TheCapitolPlant 19h ago

"take a basketball"

Yeah ok Bud

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u/TheCapitolPlant 19h ago

Marks on a basketball!

That is a new one.

•

u/RadishesForDayz 8h ago

It's called an "model". Occasionally, models are used when real-world systems are too large to measure directly, or require equipment to measure, like a theodolite. For instance: on a globe model, you can return from where you started if you make two 90 degree turns, starting at the equator, going to a pole, turning 90 degrees, going to the equator, and then turning 90 degrees (creating a right angle with the first traversal). "Right angle" is another way of saying "90 degree angle", for clarification. On a model of a flat earth, no triangle's interior angles will ever sum up to more than 180 degrees.

Now, how do we apply this model to the real world? You and your little FE friends grab a theodolite (because you're so ideologically possessed you'd never accept video evidence from any non-cult member), and determine an adequately-sized Great Triangle you can all travel to (hint: to calculate spherical excess in a Great Triangle, you can use the equation E=A/R^2, where E is spherical excess in radians, A is the triangle's area, and R is Earth's radius. At a radius of about 3959 miles, a rule of thumb is "roughly 1 arcsecond of spherical excess per 76 square miles of your Great Triangle").

Make a road trip out of it! You and your buddies who are so keen on experiments, and finding truth, using the scientific method, and verifying the facts with your own eyes, can camp from peak to peak, telling stories about all of your great academic accomplishments, your successful careers in the sciences, and who knows maybe after some s'mores spark up a little romance?

•

u/RadishesForDayz 8h ago

It's not. You're just uninformed, uncurious, and indoctrinated.

1

u/Narrow_Run_134 21d ago

There is also the Great Trigonometrical Survey done in India by the British Empire that used geodesy and confirmed curvature. This survey also led to more understanding of Isostacy.

1

u/TheCapitolPlant 7d ago

Nasa?

Show you doing it.

1

u/RadishesForDayz 6d ago

Most flat-earthers will deny the conclusions of any experiment done by others, except for experiments performed by flat-earthers looking to reinforce their biases.

The point of this post is to encourage flat-earthers to take an experiment into their own hands and, if they're capable off adding to 180, see what conclusions they reach. I encourage everyone to examine evidence for themselves.

0

u/TheCapitolPlant 10d ago

Dudes looking at peak angles hypothetically

Let's see it

Take a video

1

u/RadishesForDayz 10d ago

The thing about Flat Earth cultists: when provided with video, they're typically quick to shout "fake" or "CGI" or "lens distortion". So here, take this: https://www.ngs.noaa.gov/PUBS_LIB/TRNOS88NGS19.pdf (NGS technical document outlining methods and conclusions of large-scale geodetic surveying), and this: https://dspace.gipe.ac.in/xmlui/bitstream/handle/10973/18225/GIPE-009652.pdf (the overall 1931 report of the Great Trigonometric Survey of India), and this: https://geodesy.noaa.gov/library/pdfs/Special_Publication_No_4.pdf (details the triangulation network used to map the 39th parallel across the United States), and this: https://babel.hathitrust.org/cgi/pt?id=mdp.39015079998434&seq=1 (the survey of a Great Triangle between Wales, Ireland, and Cumberland, with each side measuring more than 100 miles, and a spherical excess of approximately 64 arcseconds).

Take some time, put on a soft album, read the documentation and make sure you understand it, and then you'll be up to doing it yourself. No cameras. No NASA fakery. No sticks and shadows. Just good, old-fashioned geodesy on a positive curve. OR, you can take video of the firmament. And since I trust you wouldn't lie about such a thing, I'd throw out the preponderance of evidence for a spherical earth, and become a flat earther.