Chapter 2

Euler’s Theorem


Euler’s Theorem describes the geometry of movement on a sphere. All points in one rigid block move relative to another block along small circles about the pole of rotation; any movement can be achieved by a sequence of such rotations. Bullard Everett and Smith used this geometry in their 1965 reconstruction of the continents, without addressing its implications. In plate tectonics, the ridges move apart along small circles about the pole of rotation; they are offset by transform faults that track small circles about that pole. The fault slip vectors from earthquakes track the instantaneous movements, also along small circles. This velocity vector approach is the simple yet powerful key to understanding plate movements.

Modern photocopy of Euler’s Theorem, taken from ‘Mechanica sive motus scietntia analtice exposita auctore Leonhardo Eulero’ (1736).