= Coordinate system
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A <coordinate system> assigns numerical labels to positions so that the labels determine the point in the region described. A <Cartesian coordinate system> uses components along chosen axes; <polar coordinates> use a radius and an <angle>. For example, $(1,1)$ has <polar coordinates> $(\sqrt2,\pi/4)$ on the usual angular branch. On a <manifold>, a <coordinate chart> gives a <homeomorphism> from an open region to an open subset of <Euclidean space>. Coordinates describe points but do not alone specify a <metric>.
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