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.
Let me guess, you’re the kind of person who thinks we need to understand gravity to make use of it.
I really wish people like you could just have their mouths taped shut and their fingers glued together.
That’s pretty mean, bro/brah/other.
Even in the days of catapults, rough formulas for the effects of gravity made them work a lot better. Knowing “it goes down” can do a bit, but not everything. If you somehow didn’t even know that it would be useless.
Your misunderstanding comes from the type and amount of people that needed to have that knowledge.
For example, we don’t need to know about ballistics to use a gun.
Do you have a source for this? I’m genuinely curious, considering Newton didn’t show up until the 17th century.