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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 18 hours ago* (last edited 18 hours 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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[–] psychadlligoat@piefed.social 5 points 8 hours ago (1 children)

so you asked an LLM a question and then asked if we should adjust our schooling based on that?

you're the one who might need schooling again, bruh

[–] zaknenou@lemmy.dbzer0.com 1 points 7 hours ago* (last edited 7 hours ago)

yeah, I'm starting all over again with university, so hopefully this will be eventually fixed. About the rest of the population though ...