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Differentiable Geometry, diff structure for manifold.

Differentiable Geometry. Diff structure for manifold.
Let S^1 a subset of R^2 be the unit-circle; that is, S^1 = { (x,y) element of R^2 : x^2 + y^2 = 1}.

(a) Explicitly find a differentiable structure for S^1 ( and indicate what the dimension of the manifold S^1 is with your differentiable structure).

(b) Specifically describe how you will go about making your structure above maximal.

Solution Summary

This solution is comprised of a detailed explanation to explicitly find a differentiable structure for S^1.