In order to perform accurate continental reconstructions across closed oceans it is necessary to be able to describe mathematically the operation involved in making the geometric fit. This is accomplished according to a theorem of Euler, which states that the movement of a portion of a sphere across its surface is uniquely defined by a single angular rotation about a pole of rotation (Fig. 3.1). The pole of rotation, and its antipodal point on the opposite diameter of the sphere, are the only two points which remain in a fixed position relative to the moving portion. Consequently, the movement of a continent across the surface of the Earth to its pre-drift position can be described by its pole and angle of rotation.
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