High Quality Content by WIKIPEDIA articles! In the theory of general relativity, and differential geometry more generally, Schild's ladder is a first-order method for approximating parallel transport of a vector along a curve using only geodesics. The method is named for Alfred Schild, who introduced the method during lectures at Princeton University. The idea is to identify a tangent vector x at a point A0 with a geodesic segment of unit length A0X0, and to construct an approximate parallelogram with approximately parallel sides A0X0 and A1X1 as an approximation of the Levi-Civita parallelogramoid; the new segment A1X1 thus corresponds an approximately parallel translated tangent vector at A1.

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