"The idea of a parallel displacement along some given curve in a two-dimensional surface can be given an intuitive interpretation. Suppose the surface is developable. Then we can unroll it on to a plane and parallel-displace vectors in the plane. The surface is then rolled back and we have the required parallel-transported vector. If a given surface is not developable, we must first select a path for parallel transport, then erect a tangent plane at each point of the path. These tangent planes will envelope a developable surface. This new developable surface can then be unrolled and the operations of parallel transport and rerolling carried out. If the curve along which the parallel displacement is to be carried out happens to be a geodesic, it becomes a straight line when unrolled on to a plane. It is then clear that the angle between a geodesic and a vector remains unchanged in a parallel displacement."
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Original Language: English
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Joseph Weber, (1st edition, 1961)
https://en.wikiquote.org/wiki/Geodesic
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Geodesic
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