let's say we're trying to convey the locations of all the features in the universe, their locations in 3-D space
kinda like a globe (although its a 2-D surface)
You might have seen such a 3-D map of the stars before:
And I was wondering about a 3-D map if space was non-Euclidean, what would be the best ways to display it.
To keep it simple, if you're considering elliptic space, you can consider the entire "global" map. Just like we have world maps of...
So, we have A, the magnetic vector potential, and its divergence is the Lorenz gauge condition.
I want to solve for the two vector fields of F and G, and I'm wondering how I should begin##\nabla \cdot \mathbf{F}=-\nabla \cdot\frac{\partial}{\partial t}\mathbf{A} =-\frac{\partial}{\partial...
slivers meaning just infinitely thin flat planes remaining in 3D space?
If a straight tube is bent into a torus, the inner (red) region will be compressed, while the outer (blue) region will be stretched.
But if the loop is made in the 4th dimension, neither region will be compressed nor...
To form a 2-torus, a narrow tube can be bent into a loop and joined end to end:
But instead of forming this loop in our three-dimensional space, the loop can also be formed in a direction perpendicular to three-dimensional space, moving it into the fourth dimension of space.
What's the name of...
@Ibix as I'm unclear on how to proceed, I'm looking at another example which has a nice infinite map, that of the torus.
above I've posted the infinite map for Pac-Man on a torus. Its a modified Pac-Man, while the 1979 game Asteroids is originally toroidal.