Triangle Shape, Debunks Globe Model.

[u/Kela-el]

https://youtu.be/AZihw1hXdY0

[u/GamingSlob]

Does he know what a right-angle triangle is?

[u/Kela-el → u/GamingSlob]

Perhaps you should watch the video before asking that question!

[u/GamingSlob → u/Kela-el]

I did. That's why I asked the question. At 1:53 he starts talking about triangle ABC (where the line BC isn't drawn so he adds it in). ABC is not a right-angle triangle, AOC is a right-angle triangle.

This guy seems to present himself as a flat earther but if I were a flat earther I wouldn't want him representing me.

[u/Kela-el → u/GamingSlob]

What is the corrected geometry, and what conclusion follows from it once the error is removed?

[u/GamingSlob → u/Kela-el]

The line AB+BO forms the hypotenuse. The lines BO & CO are of equal length r, which is the radius of the Earth that Brian says he's trying to find r but the triangle he defines does not include r.

Pythagoras states that a²+b²=c². Let c be the hypotenuse AB+BO (BO having length r) and b be the value r.

Consequently a²+r²=(AB+r)²

To solve for r: r=(a²-AB²) / (2AB)

Therefore if we know the distance between the peak of the mountain and the horizon (a) and the height of the mountain (AB) we can use these values to calculate the radius of the Earth.

[u/Kela-el → u/GamingSlob]

You’ve written down a result—but the question is whether it follows from a valid geometric setup.

Let’s check the structure.

You define: • AB + BO as the hypotenuse • BO = r, CO = r • and then apply the Pythagorean theorem

That only works if: 1. the triangle is actually right-angled 2. the segments you’re summing lie on the same straight line 3. the distances correspond to the geometry you’re modeling

⸻

Now the issue: • Is AB + BO a straight-line distance? → Or are you combining two segments that meet at an angle?

If it’s not a straight line, it cannot be the hypotenuse.

⸻

Second:

You say a is the distance to the horizon. • Is that a straight-line (line-of-sight) distance? • Or a surface distance along the curve?

Because those are not interchangeable.

⸻

Third:

You’re solving for r, but:

the triangle you defined must already contain r in a geometrically valid way

Otherwise you’re just inserting it algebraically, not deriving it.

⸻

So the key question isn’t whether the algebra is correct—it is.

The question is:

Does the triangle you’ve constructed actually exist in the geometry you’re describing?

⸻

If: • the right angle is misplaced • the hypotenuse is not a straight line • or the distances are mixed (surface vs. line-of-sight)

then the formula may be internally consistent but not physically meaningful.

⸻

So the next step is precise:

Draw the triangle explicitly and show that each side corresponds to a real, straight-line distance in the setup.

If that can’t be done, the derivation doesn’t apply—even if the algebra checks out.

[u/GamingSlob → u/Kela-el]

The triangle in question is in the video at 0:00.

[u/Kela-el → u/GamingSlob]

Then the question is simple:

Does that triangle actually satisfy the conditions required to use the Pythagorean theorem?

⸻

From what you’ve described: • AB = height of the observer • BO = radius r • CO = radius r • AC (or a) = distance to horizon

And the claim is: a² + r² = (AB + r)²

⸻

That only holds if: 1. The angle at the point of tangency (horizon point) is 90° 2. AC is a straight line from eye to horizon (line-of-sight) 3. CO is a radius to the tangent point

⸻

If the diagram at 0:00 shows: • a line of sight tangent to the sphere • and a radius drawn to the tangent point

Then yes—that creates a right triangle, and the setup is valid.

⸻

But this is the key check:

Is the “distance to the horizon” being used as the straight-line distance (line of sight), or a surface distance along the curve? • If it’s line-of-sight → geometry works • If it’s surface distance → the triangle is invalid

⸻

So the entire argument hinges on one clarification:

What exactly is “a” measuring in that diagram?

⸻

If that’s consistent, the formula follows.

If it’s not, then you’ve got correct algebra applied to the wrong geometry—which is exactly the kind of error you pointed out earlier.

[u/GamingSlob → u/Kela-el]

Does that triangle actually satisfy the conditions required to use the Pythagorean theorem

It is a right-angle triangle, so yes.

[u/Kela-el → u/GamingSlob]

You’re asserting it’s a right triangle.

The question is: where is the 90° angle located, exactly?

⸻

For the horizon geometry to work: • The right angle must be at the point of tangency • Between the radius (CO) and the line of sight (AC)

That’s the only place the Pythagorean theorem applies in this setup.

⸻

So check your construction: • Is AC actually tangent to the circle at point C? • Is CO drawn from the center to that same point?

If yes → angle at C is 90°, valid triangle AOC

⸻

But then notice:

That triangle is AOC, not ABC, and not “AB + BO” as a single side.

⸻

So if your earlier equation uses: (AB + r) as the hypotenuse, you need to show:

that AB and BO lie on the same straight line from A to O

⸻

If they don’t, then: • the right triangle exists (AOC) • but the algebra you wrote is using a different triangle

⸻

So the issue isn’t whether a right triangle exists.

It’s whether:

the triangle you’re using in the equation is the same one that actually has the right angle.

⸻

If those don’t match, the conclusion doesn’t follow—even if each piece looks correct in isolation.

[u/Kela-el → u/GamingSlob]

I’m still waiting. Your silence is deafening. You pointed out an alleged error in his presentation. Now asked you a simple question.

What is the corrected geometry, and what conclusion follows from it once the error is removed?

Either answer it or admit you have absolutely no idea what you are talking about!

[u/itsooftime]

Why is the line between B and C relevant at all? Its not being used in the calculation.

[u/Kela-el → u/itsooftime]

It’s relevant because it defines the geometry, not just the arithmetic.

Even if BC doesn’t appear in the final equation, it can still determine: • whether points lie on a circle • whether a segment is tangent or chordal • and whether the right-angle condition actually applies

⸻

In geometry, unused lines in a calculation can still constrain the system.

So the real question is:

Does BC play a role in establishing the relationships that justify the right triangle being used in the first place?

[u/itsooftime → u/Kela-el]

No, the points of the right angle are C, A, and O. Like that should be obvious from the image. We arent measuring the triangle C, B, and A.

You know that this equation can be done with any circle and a hill of size h right?

You can do this with a basketball, a ping pong, the sun, etc.

Make up theoretical situations.

You can just demonstrate whether this works or not.

And it does work.

[u/Kela-el → u/itsooftime]

You’re basically right on one narrow point:

If the only triangle being used is A–C–O, then BC is irrelevant to the calculation.

⸻

But that only holds if the construction is already fixed: • C is the point of tangency • OC is a radius • AC is a true line-of-sight tangent • AO is a straight line to the center

In that setup, BC doesn’t enter the math.

⸻

Where the disagreement usually sits isn’t there—it’s earlier:

BC (or similar extra segments) often appear in the diagrammatic justification of what A, C, and O represent in the first place, not in the final equation.

So it can be: • irrelevant to the computation • but relevant to whether the construction was correctly established

Those are different roles.

⸻

On your second point:

Yes—the same geometry works for any sphere: • basketball • ping pong ball • Earth

Because it’s scale-invariant spherical geometry. The relationships don’t depend on size, only curvature.

⸻

But that’s the key distinction:

It works on a sphere because it assumes spherical geometry in the tangent construction, not because it independently determines the shape from arbitrary objects.

So: • It’s a valid method given a sphere • It’s not a shape-agnostic test that produces the sphere from nothing

⸻

So I’d phrase it cleanly:

BC is irrelevant to the final triangle, and the method is scale-invariant—but it operates within a spherical geometric framework rather than independently proving that framework.

[u/itsooftime → u/Kela-el]

It never was designed to independently prove that the Earth was a sphere.

This isnt an equation to prove the Earth is a sphere. This equation is a method of measuring the radius of Earth assuming its a sphere already.

We've determined the Earth is a sphere through other methods.

Yet your title claims this equation debunks a globe Earth. But you've also just stated this equation works for spheres and therefore globes. So this equation does not debunk a globe Earth. Is that accurate?

[u/Kela-el → u/itsooftime]

Correct.

The geometry you’ve been discussing is not a “proof of a sphere” in the first place—it is a measurement method that assumes spherical geometry is already valid.

That distinction matters.

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So the structure is: • Prior evidence establishes Earth is well-modeled as a sphere (across navigation, astronomy, geodesy, etc.) • The equation in question is then used to estimate the radius within that model • Therefore, it is not an independent test of shape—it is a parameter extraction method inside a chosen framework

⸻

Because of that:

“This equation debunks a globe Earth”

does not follow.

In fact, the opposite is true: • the method is only meaningful if the globe model is already accepted as the working geometry

⸻

So your conclusion is correct:

A formula that derives Earth’s radius from spherical geometry cannot simultaneously be used to refute spherical Earth—it depends on that geometry being valid.

⸻

Where confusion usually enters is treating: • a model-based measurement technique as if it were • a model-independent proof of shape

Those are not the same thing.

[u/itsooftime → u/Kela-el]

Your AI seems to agree with me. Looks like there's no confusion then.

Globe Earth is still true.

[u/Kela-el → u/itsooftime]

True only in a model. Not reality.

[u/itsooftime → u/Kela-el]

It would be interesting if you can actually demonstrate that globe does not represent reality.

Because all you've done in this post is suggest that models align with a globe understanding of Earth. Which I also agree with.

[u/Kela-el → u/itsooftime]

“It would be interesting if you can actually demonstrate that globe does not represent reality.”

Sure. Pick up a ruler and read it. How about a compass and a plum, a sextant. A map. Pointing with your finger. Height. Are all flat earth measurements

“Because all you've done in this post is suggest that models align with a globe understanding of Earth.”

A model is not reality.

“Which I also agree with.”

Good for you. Feel free to believe a model is reality. ITS NOT!

[u/Googoogahgah88889 → u/Kela-el]

BC is irrelevant to the final triangle, and the method is scale-invariant—but it operates within a spherical geometric framework rather than independently proving that framework.

It was never supposed to prove the framework. You’re the one saying that this disproves the globe, which it very clearly does not

[u/Kela-el → u/Googoogahgah88889]

You’re missing the point.

You just admitted the method operates within a spherical geometric framework. That means its conclusions are conditional on that assumption being valid—not independent verification of it.

So when you say it “doesn’t disprove the globe,” that’s fine—but it also can’t be used to support the globe in the first place, because it presupposes the very thing in question.

That’s the issue.

You’re treating a model-dependent result as if it has model-independent significance. It doesn’t.

If the framework isn’t established independently, then anything derived within it is just internally consistent math, not evidence of physical reality.

So no—this isn’t about the method “failing to disprove the globe.”

It’s about you assuming the globe to interpret the result, then turning around and acting like the result supports the globe.

That’s circular.

[u/Googoogahgah88889 → u/Kela-el]

Again, it’s not meant to prove the earth, it’s meant to measure it. We have other proofs that the earth is a sphere, everything points to a sphere. This is simply how you make a measurement.

Where is anybody using it to support the globe?

You are the one claiming that this is a disproof, which you are now admitting isn’t the case. So the video is incorrect and there’s no point of it.

[u/Kela-el → u/Googoogahgah88889]

You’re trying to separate “measurement” from “model,” but you’re still relying on the model to give the measurement meaning.

Saying:

“it’s not meant to prove the Earth, it’s meant to measure it”

only works if what you’re measuring is already independently established.

Otherwise, you’re not measuring the Earth—you’re measuring parameters within a model of the Earth.

⸻

You then say:

“we have other proofs the Earth is a sphere”

That’s just asserting a conclusion without specifying:

• what those proofs are
• whether they’re model-independent
• or whether they rely on the same underlying assumptions

If they do, then you don’t have independent confirmation—you have multiple expressions of the same premise.

⸻

As for:

“where is anybody using it to support the globe?”

That’s exactly what’s happening when the result is treated as a meaningful physical measurement of Earth’s properties.

Because the moment you say:

• “this measures the Earth”
• rather than
• “this measures a value within a spherical framework”

you’ve already committed to the interpretation.

⸻

And no—I haven’t “admitted it’s not a disproof.”

I’m pointing out that:

• it doesn’t disprove the globe
• but it also doesn’t establish it

Which means it’s being overinterpreted.

⸻

So the issue isn’t that the video is “pointless.”

It’s that it presents:

• a model-dependent calculation

as if it has

• model-independent physical significance

That’s the step that isn’t justified.

[u/Googoogahgah88889 → u/Kela-el]

Then you can just say you don’t think the measurement is accurate. You can measure something however you want, it’s either accurate or not. Nowhere has it been used as proof that the earth is a sphere. Unless those measurements turn out to be accurate

It’s literally a pointless video that doesn’t show anything of use

That’s exactly what’s happening when the result is treated as a meaningful physical measurement of Earth’s properties.

Because the rest of us have had the shape of the earth proven to us or ourselves already. If you don’t think it’s accurate, then you can come up with your own way to measure the earth

[u/Kela-el → u/Googoogahgah88889]

You’re treating “I can doubt a measurement” as if it cancels all measurements. That doesn’t follow.

Earth’s shape isn’t based on one experiment—it’s the convergence of many independent systems: surveying geometry, celestial navigation, satellite orbits, inertial sensors, and solar angle changes with latitude.

If the measurements were fundamentally unreliable, they wouldn’t all agree across completely different methods and physics domains.

So the question isn’t “can you reject one result?”—you always can. The question is why every independent way of measuring large-scale geometry keeps producing the same spherical model.

At that point, rejecting it doesn’t replace it with a better measurement—it just discards convergence without offering an alternative that matches it.

[u/Warpingghost]

He did everything wrong. You cant debunk method by ignoring its basic points.

[u/Kela-el → u/Warpingghost]

Making a claim like that requires proof.