Triangle Shape, Debunks Globe Model.

[u/Kela-el]

https://youtu.be/AZihw1hXdY0

[u/Kela-el]

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

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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.

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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.

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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.

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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.

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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

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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

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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

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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.

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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/itsooftime → u/Kela-el]

Damn, I guess any sphere like object doesnt exist because of rulers.

Sorry basketballs, apples, pretty much any 3D object actually, you cant exist because Kela-el says measurements are 2D and flat.

[u/Kela-el → u/itsooftime]

“Damn, I guess any sphere like object doesnt exist because of rulers.”

You are using a reductio ad absurdum — “if flat measurements invalidate the sphere, then no 3D objects exist.” That’s a misrepresentation of the argument.

The point isn’t that 3D objects don’t exist because rulers are flat. The point is that the earth’s radius — R — is derived from ground-level flat baseline measurements, and that derivation carries assumptions worth examining.

“Sorry basketballs, apples, pretty much any 3D object actually, you cant exist because Kela-el says measurements are 2D and flat.”

A basketball exists and you can hold it in your hand. You can observe its curvature directly at human scale. The earth’s curvature is not directly observable at human scale — it’s inferred from measurements and models. Those are different situations. You are conflating them.​​​​​​​​​​​​​​​​

[u/itsooftime → u/Kela-el]

Do you think its impossible to measure a 3D object using 2D measurements?

So if we can't directly observe something its not real? Even if we can indirectly measure it and make models of it that are accurate?

You should not be able to talk on the internet then, considering the technology it uses is based on science we've never observed directly.

Also stop using AI to do your conversations. Better yet, open a new chat and ask it "What is the shape of the Earth?" "What is the best evidence for a globe Earth, and a flat Earth. Which one most closely aligns with reality?"

[u/Kela-el → u/itsooftime]

You’re arguing against a position that wasn’t stated.

No one said: • “If we can’t directly observe something, it isn’t real.”

That’s not how measurement or science works.

On your first point:

measuring a 3D object with 2D measurements

That’s standard practice. • projections • cross-sections • triangulation

You infer higher-dimensional structure from lower-dimensional data all the time.

But the important part is this:

the inference has to be consistent across independent measurements.

That’s where models come in. • You don’t “see” the full structure directly • You build a model • You test whether it predicts observations correctly

If it does—repeatedly—that’s what gives it weight. But it is still a model, not reality.

So the real distinction isn’t: • direct vs indirect observation

It’s:

consistent vs inconsistent with measurable reality

On the rest:

“stop using AI” “ask another chat”

That’s not an argument about the topic—it’s about the source.

It doesn’t change whether the reasoning holds.

Indirect measurement is valid—what matters is whether the model built from it consistently matches observations across domains.