this post was submitted on 08 Jan 2024
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Physics
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Curvature is well defined for manifolds with any number of dimensions. "Flat" in this context means "zero curvature", not "two dimensional".
Can I get an ELI5, please? I understand all of those words, but not the concepts behind them in this context…
The definition of a right angle depends on the number of dimensions. Perpendicularity and parallelism are different in higher dimensions. Space is hard.
https://en.wikipedia.org/wiki/Curvature#Space
https://en.wikipedia.org/wiki/Manifold
https://en.wikipedia.org/wiki/Dimension
https://en.wikipedia.org/wiki/Curvature#Flat_space