Formerly u/CanadaPlus101 on Reddit.

  • 7 Posts
  • 1.61K Comments
Joined 2 years ago
cake
Cake day: June 12th, 2023

help-circle

  • No for an orthogonal projection, because literally every point in the plane centered at H and normal to (AH) (so dihedrally perpendicular to the plane given in the problem) could potentially be P. In other words, it could project to H, or a point off of P perpendicularly to (AH)

    You don’t really need math for that one, it’s just spacial reasoning, which you can’t really directly teach. I suppose just the concept of solid angle vs. dihedral angle vs. face angle would be good for everyone to know. To formally prove it, it seems like you’d need linear algebra, which they don’t usually teach in high school anyway.

    Now, if you can use oblique projections as well, it’s pretty trivial to find one that’s “tilted” such that any point not already in the plane maps to a given H - the projection can proceed along any set of parallel lines through the space, and there’s always a line between any point X and H. Mathematically, you use the fact that X-H must be in the kernel space of the projection, and the standard formula for constructing a projection operator from a basis complementary to the kernel space and one in the plane it projects to.



















  • Dealing with the way the world is is tough. I wish I could tell you how to feel better, but I can’t. Certainly not without knowing you, anyway.

    Very few could actually totally isolate themselves, and there’s all kinds of people out there in the world that you’ll have to meet. On the other hand, maybe you’ll spend a more manageable amount of time being angry if you stay off of the internet.

    It’s also important just to recognise why you’re angry. You’re probably thinking it’s obvious, but as therapists like to say, you’re feelings don’t come from other people’s actions, but what you think about them. So they’re bigots, what about it? People being bigots makes me sad, personally. And then, if there’s another way to look at things will depends on your values, and what you want out of life exactly.

    Best of luck figuring it out.