Talk:General Relativity/Curvature

Great work! some suggestions
Hi, I'm not an academic but I'm always fascinated by science. Sadly, there are things I don't understand but your text is very compelling for people like me, helped by practical examples and comparison with "real and mundane" things except in a few cases. Here it is:

"Negatively curved surfaces also exist - they are shaped somewhat like an infinitely extended saddle - and Euclidean geometry does not apply to these surfaces either."

"For example, the angles of a triangle add up to less than 180o."

"If we extend these ideas to three dimensions, (do not be worried if you can't imagine a three-dimensional surface of a sphere..."

"Space (...) it is shaped as a hypersphere(3D spherical surface)"

"Space (...) it is shaped like a so-called hypersaddle"

"This predicts that if a giant triangle was to be constructed around the sun (***) these lines are in fact the straightest lines possible (geodesics) in this warped geometry"

"This local curvature can be described in mathematical terms using tensor calculus, an incredibly elegant tool which provides consistent results, regardless of the chosen frame of reference."

The quotations above could be easier with some examples. Maybe there's no examples for that (and I have no idea about what I'm talking about :) but maybe an illustration or an animated gif could make your writings even more tasteful. Informations or pictures of this "tensor calculus" would be amazing!

For instance, a "hypercube". Shamefully I read a lot about it and didn't get it at all. But an simple animation of a 4 dimensional cube rotation make it possible to read about it again with a better understanding and then the impossible, to assimilate it and make it understandable in the naive mind.

Thank you!