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Everyone talks about the 4th dimension, BUT why is 3D geometry so hard for the average person compared to 2D ? (lemmy.ml)

submitted 1 day ago* (last edited 1 day ago) by zaknenou@lemmy.dbzer0.com to c/asklemmy@lemmy.ml

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I think 3D geometry has a lot of quirks and has so many results that un_intuitively don't hold up. In the link I share a discussion with ChatGPT where I asked the following:

assume a plane defined by a point A=(x_0,y_0,z_0), and normal vector n=(a,b,c) which doesn't matter here, suppose a point P=(x,y,z) also sitting on the space R^3. Question is:
If H is a point on the plane such that (AH) is perpendicular to (PH), does it follow immediately that H is the projection of P on the plane ?

I suspected the answer is no before asking, but GPT gives the wrong answer "yes", then corrects it afterwards.

So Don't we need more education about the 3D space in highschools really? It shouldn't be that hard to recall such simple properties on the fly, even for the best knowledge retrieving tool at the moment.

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[–] ProfessorOwl_PhD@hexbear.net 1 points 10 hours ago (1 children)

We use plenty of simple geometry everyday, sure, but you don't need to be able to even understand what OP's example says to engage with the world. Like you don't need to provide a mathematical proof to put a shelf up properly.

[–] CanadaPlus@lemmy.sdf.org 1 points 8 hours ago (1 children)

Besides understanding what a projection is, I'm actually going to say that's all pretty important stuff to know. A point, forming a line between points, how to describe a plane and what perpendicular means.

If you want to do graphics projections suddenly become very important, but sure, you can explain carpentry without it. Although if you want to draft the solution first the concept will be at least relevant.

Like you don’t need to provide a mathematical proof to put a shelf up properly.

Kind of a separate issue yet. Even with OP's example, you can explain the solution in natural language pretty easily, but the obvious way to formally prove it would be with linear algebra.

[–] ProfessorOwl_PhD@hexbear.net 1 points 7 hours ago (1 children)

How many people do you think are working in computer graphics? It's specialised knowledge, exactly the kind of thing that should be taught at university to the people it's relevent to.

you can explain the solution in natural language pretty easily

It's not about how you phrase the solution, it's about needing the solution at all.

[–] CanadaPlus@lemmy.sdf.org 1 points 1 hour ago

Yeah, agreed, but like I said most of this is not advanced or specialised.