It never occurred to me that things in the hyperbolic space get rotated around a hyperbole. Consequently, when we move, we also actually move along a hyperbole! That's what makes the surroundings look trippy as you move.
@@-_Nuke_- sometimes it's hard to recall things you were pondering over 6 month ago XD but if I'm not mistaken, when we move straight in a hyperbolic space we actually follow a hyperbolic trajectory.
@@eldarius237 I see! So in special relativity we see that spacetime is hyperbolic right? so that means that when we have a spaceship that goes forward in 3space, it is actually rotating hyperbolically?
What do you mean by "all the points are the same hyperbolic distance away from each other"? I can sense that this sentence makes sense someway, since for normal rotations all points remain the same distance from each other (it's an isometry), but what is this distance that you are talking about?
Nice animation! Got me thinking: It's clear that for three 2D points X,Y,Z, we can compute the triangle volume v_0=V(X,Y;Z). And if we parametrize the motion of the corner points we get a volume v(t)=V(X(t), Y(t), Z(t)). I wonder to what extent v(t) can be expressed as a function of v_0. That is to say, how severely does v(t) depend on the base positions of the triangle, and not just on the volume. I'm afraid a lot, because I have the feel triangles that are far away from the origin in y-direction have a bigger variations than those close to the origin.
i would absolutely love to watch a more detailed video about this. Apparently is a hard thing to find on youtube
It never occurred to me that things in the hyperbolic space get rotated around a hyperbole.
Consequently, when we move, we also actually move along a hyperbole! That's what makes the surroundings look trippy as you move.
What do you mean by "when we move we actually move around a hyperbola"?
@@-_Nuke_- sometimes it's hard to recall things you were pondering over 6 month ago XD but if I'm not mistaken, when we move straight in a hyperbolic space we actually follow a hyperbolic trajectory.
@@eldarius237 I see!
So in special relativity we see that spacetime is hyperbolic right?
so that means that when we have a spaceship that goes forward in 3space, it is actually rotating hyperbolically?
@@-_Nuke_- well hang on special relativity is a different episode XD depending on what you mean
So cool
What do you mean by "all the points are the same hyperbolic distance away from each other"?
I can sense that this sentence makes sense someway, since for normal rotations all points remain the same distance from each other (it's an isometry), but what is this distance that you are talking about?
Nice animation! Got me thinking: It's clear that for three 2D points X,Y,Z, we can compute the triangle volume v_0=V(X,Y;Z). And if we parametrize the motion of the corner points we get a volume v(t)=V(X(t), Y(t), Z(t)). I wonder to what extent v(t) can be expressed as a function of v_0. That is to say, how severely does v(t) depend on the base positions of the triangle, and not just on the volume. I'm afraid a lot, because I have the feel triangles that are far away from the origin in y-direction have a bigger variations than those close to the origin.
I read a wonderful book on this topic. True, it is in Russian. В.Г.Шерватов Гиперболические функции