#locally euclidean vs euclidean what's the difference?I understa

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I understand locally euclidean is property of an object whereas the observer sees the 2d flat space qbd not the curvature

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Locally Euclidean is a local property - near any point, it looks Euclidian and so it's approximately flat near that point. Euclidean is global - it's actually flat everywhere. Think about a sphere. Any part of it looks Euclidean, but the whole thing is clearly not flat. Curvature has to do with how you put flat pieces together.

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