Asklemmy

Pretty sure, yes. I'm probably just explaining badly.

There's a full 360 degrees of rays perpendicular to (AH) starting at H. That would be true of line to a point in 3D. In 2D there would be exactly 2 possibilities (left and right), while in 4D they would correspond to an ordinary sphere, and hyperspheres in higher dimensions yet.

Together, they take up a plane. Only points on a certain (infinite) line going through this new plane and H will actually orthogonally map to H, and it's the same one that's normal to to original plane. Let's call the line L.

If point P wasn't in this plane, (PH) couldn't be perpendicular to (AH). It is in the new plane, but we still don't know for sure it's on line L, so it's not true that that implies it projects to H.

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.

Math students in university need to verify basically everything, that's a lot of what the career is about. I remember being humbled when asked to prove something as familiar to everybody as -1 * -1 = 1

Ah, I can see OP's line of thought now:

• you have a point A' on a plane and a random point A
• you find a midpoint B and draw a sphere around it. A and A' are now a diameter of the sphere
• pick two random points D and C at the intersection of the plane and the sphere
• by the "triangle inscribed in a circle/sphere where one side is a diameter" rule, such a triangle must be a right triangle
• therefore both angles ACA' and ADA' are right angles
• thus C and D both satisfy the conditions of the initial question (with all points renamed: A=P, (C or D)=H, A'=A)
• OP never defined what a projection is, it being "4th grade math", but one of the requirements is being unique
• C and D cannot both be the projection, therefore the initial question must be answered "false": just because AH is perpendicular to PH doesn't make H a projection.

I like treating posts as puzzles, figuring out thread by thread WTF they are talking about. But dear OP, let me let you know, your picture and explanation of it are completely incomprehensible to everyone else xD. The picture is not an illustration to the question but a sketch of your search for a counterexample, with all points renamed of course, but also a sphere appearing out of nowhere (for you to invoke the inscribed-triangle-rule, also mentioned nowhere). Your headline question is a non-sequitur, jumping from talking about 4D (never to be mentioned again) into a ChatGPT experiment, into demanding more education in schools. You complain about geometry being hard but also simple. The math problem itself was not even your question, yet it distracted everyone else from whatever it is you were trying to ask. If you ever want to get useful answers from people other than crazed puzzleseekers like me, you'll need to use better communication!

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.

I started from the ground up in December 1998 with a bare wireframe engine, largely inspired from a demo wireframe engine from another developer. I was 17 years old then so it was basically my after school project, not a school assignment, but my teachers were impressed.

I didn't quite just copy/paste his code though, I carefully read over his code and comments to the point that I understood how it all worked, and rewrote a much cleaner wireframe engine of my own that supported colored lines and even loading from files, which the original demo didn't support.

Later on I came across another demo, from the same developer I think, that demonstrated rendering solid triangle shaded 3D models. Again, I read over everything and rewrote everything from the ground up, largely looking to optimize the rendering technique for the highest number of polygons per second, and of course to be able to load different models from file.

Then I just started having a bit of fun with the polygon rendering, starting with an optimized integer based greyscale gouraud shading algorithm, which ran way faster than any similar demos I could find at the time. Note that this was all CPU driven, no fancy GPU at the time, the 3Dfx Voodoo was still a pretty new thing I couldn't afford..

Then I got the idea of trying to bring color to the project via error diffusion, since I was basically limited to 320x200x256 color display mode, unless I wanted to run a high end video mode at a snail's pace LOL! Error diffusion is slow though, so how did I speed that up?

Well, I did away with the gouraud shading and went back to treating each polygon as a single solid RGB color, shaded using the Lambert's Law technique. To speed up the error diffusion process, I'd only process 8 pixels into the diffusion algorithm, then as the polygon rendered, it would just pick randomly from that 8 pixel buffer.

Since I was programming in QuickBasic, arrays were limited to 64KB each, meaning that memory was very tight, and I actually had to allocate two arrays for the Z Buffer, one for the top half of the screen and another for the bottom half.

The inspiration for the camera tracking came from a rather unexpected source, a simple mouse string toy demo of all things LOL! I realized that if I used just one segment of that string algorithm, I could link the viewing angle to follow a point in the model, or with some creative adjustments, basically follow any arbitrary point.

I also made a side project crude CAD scripting thing of sorts, mainly meant to render a torus or sections of a torus with whatever dimensions I wanted. With the right inputs, that also allowed me to easily generate spheres, cylinders, cones and tubes.

I think I finished the original wireframe engine within just a couple or few days, but the other versions that had filled in polygons probably took me a week to start with, and the more advanced techniques probably took me around 2 months each, all in my spare time of course.

I didn't really have any final product in mind, I was just experimenting and learning ya know. When 3D GPUs started becoming a big and common thing, I didn't see much future for my little project, but I sure did learn a lot!

I'm trained on pirated books and I do alright.

Believing forum shitposts would definitely poison the well though.

OH! I see now. Perpendicular-ness is not commutative in 3d. Gotcha, thank you!