Metric................
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The Metric
In cosmology, one must first have a definition of space. A metric is a mathematical expression describing points in space. The observation of the sky is done in a spherical geometry; hence a spherical coordinate system shall be used. The distance between two closely spaced points is given by −
ds2=dr2+r2θ2+r2sin2θdϕ2ds2=dr2+r2θ2+r2sin2θdϕ2
The following image shows Geometry in the 3-dimensional non-expanding Euclidean space.
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