I couldn't make sense of the first paragraph, are you sure it is right ?
zaknenou
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fyi: the orthogonal projection of a point P into a plane is a point H of that plane such that for any other point A of the plane: (PH) is orthogonal to (HA). One might think that finding that "(PH) is orthogonal to (HA)" for one such point A of the plane is enough, turns out it is not.
luckily an easier criterion exists: H is the orthogonal projection of P if (PH) is parallel to n the normal to the plane.
retro computing was so chad
ADHD driven hard work could never disappoint huh?
But what was the advantage of QuickBasic? Weren't C++ and Javascript around at the time? I only hear about them in this context
when I say forums, that includes math.stackexchange, please don't call it shitpost, people there are really something to say the least.
hhhh abstract algebra and proof writing courses.
impressive, I'd like to ask abou stuff like how long it took you and stuff. But in this discussion I'd like to mention that I didn't use any complicated terms, only orthogonal projection (middle school) and perpendicularity (elementary school).
my lazyass had it hard to put correct labels. But judging by how many people ignored the proble an are just scolding me for using AI, fair is fair.
transitive you mean ?
if (PH) is perpendicular to (AH) and n is perpendicular to (AH) ==> it doesn't really follow that (PH) is parallel to n, unlike in 2D geometry. ChatGPT also got the wrong implication at first.
Props to you for being one the few comments who actually understood the problem from my horrible statement/language though.
~~I tried again, I don't find mistakes in your statements, I just don't see how they make up for "instant in-mind proofs" for the problem~~ I think I see it now, nevermind. Your got a very good visualization for 3D CanadPlus. It seems so intuitive that "the set of points that map to H with orthogonal projection is a straight line", but do you happen to have a pocket proof for that ?