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I am a high school math teacher with some basic physic/lay person knowledge.
Each year after the AP test, I show the movies Flatland and Sphereland to my calculus classes and talk about the dimensions of our universe.
I know that there have been discussions of our universe having multiple dimensions other than the basic 3 with string theory and other theories. I believe that I also read that general consensus is that our universe tends more towards a Euclidean shape rather than an elliptical or hyperbolic type universe.
I also show a short Youtube video that is a hands-on exploration of gravity and how massive objects "warp" space-time to create gravity wells of some sort.
My question is this: If massive object really do warp space to create a gravity well model, is the universe warped in some 4th dimension that we don't notice similar to how the earth is essentially a 2d surface warped in the 3 dimension that we don't notice?
I don't treat what I tell them as the gospel truth, I just try to share what I've read and encourage them to study the ideas more if they are intrigued by the concepts.
Anything that could be shared so I can enlighten my students further would be great.