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spacetime itself of such effects as geodesic deviation and tidal effects (described above in the Introduction).

Curvature versus coordinates

In relativistic calculations, one often chooses coordinate systems that simplify the computations. The expression for the Pythagorean theorem, and hence the spacetime interval, depends both on the geometry of spacetime and on the coordinate system used to describe it. For example, in Fig. 3, we see for the following coordinate systems:

In cases (a), (b), and (c), the surfaces

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