Higher Dimensional Geometry
The cluster focuses on discussions about visualizing and understanding geometry in higher dimensions like 4D spaces, using analogies such as balloon surfaces and tesseracts, non-Euclidean manifolds, and references to 3Blue1Brown videos.
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We're talking about being toriodal or curved in a 4th spatial dimension I assume?
Why not in a three-dimensional space?
There are different kinds of dimensions. There are simple, Euclidian dimensions where each dimension is perfectly orthogonal to the others, where parallel lines never intersect, etc. But there are other possibilities, non-Euclidean spaces and volumes. This is where the example of the sphere comes in. If you were a 2-dimensional being you could be on a plane or you could be on the surface of a sphere. Similarly, if you are a 3-dimensional being, such as us, you could be within a simple R^3 volume
Probably a mathematical construct, like a 4-dimensional cube.
You're not thinking fourth dimensionally!
Interesting way to explain this through multiple dimensions angle.
What is it that makes 4d the hardest dimension in topology?
Why not try hyperbolic space too?
Could this be related to our 3 dimensions of space?
TIL a two dimensional plane isn't natural.