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.

  • zaknenou@lemmy.dbzer0.comOPEnglish
    1·
    6 hours ago

    It sounds like you’re just beginning you journey in higher maths

    I’m actually old and lurked in university stuff for a long time and dropped out of engineering in university and started with math all anew, yet at the same time I’m still a beginner.

    Hmm. Where did the question in OP come from?

    I don’t exactly remember How I started thinking about the “distance between plane and a point formula”, I think I stumbled upon it while organizing my old bookmarks. Tried to make a proof, and in the process that question came, and when I couldn’t solve it on the fly I though like “it’s so over for me”. Then ChatGPT also got it wrong and was like “It’s so over for mankind”. And I ended up making this post to share my despair. Actually many answers were eye opening.