ABSTRACT
The Principle of Equivalence postulates that an acceleration shall be indistinguishable from gravity by any experiment whatsoever. Clearly, some interaction between gravity and electrodynamics must be included in a better statement of the laws of electricity, to make them consistent with the principle of equivalence. This chapter shows how the notion of the curvature of space arose in discussing geometrical measurements. The demonstration that the quantity is a tensor is tedious but straightforward; all that is required is to convert all coordinates to flat space, and to actually compute the derivative, then to check upon the law of transformation. The generalized definition of curvature of a many-dimensional surface will be given in terms of the change in a vector as it is carried about a closed path, keeping it parallel to itself. The fact that the curvature tensor appears as connecting the second co-variant derivatives serves as a clue that enables people to give another useful geometrical picture of curvature.
