= Manifold
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We map each point and a small enough <neighbourhood (mathematics)> of it to <\R^n>, so we can talk about the manifold points in terms of coordinates.
Does not require any further structure besides a consistent <topological> map. Notably, does not require <metric (mathematics)> nor an addition operation to make a <vector space>.
Manifolds are <good>[cool]. Especially <differentiable manifolds> which we can do <calculus> on.
A notable example of a <Non-Euclidean geometry> manifold is the space of <generalized coordinates> of a <Lagrangian>. For example, in a problem such as the <double pendulum>, some of those generalized coordinates could be angles, which wrap around and thus are not <euclidean>.