Euler's theorem states that any movement of an area on the surface of a sphere may be defined by a rotation pole and an angle of rotation about that pole. The animation shows the area (plate) of South America moving with respect to Africa. We need to understand three diffrent types of Euler rotation pole over time.

(1) Interval or stage poles. To move a plate from its position at time t1 to its position at time t2 we need to define the pole that makes that movement happen. The animation shows (in blue) a series of Euler interval poles that reproduce the path followed by South America away from Africa quite closely. Note how the fracture zones in the South Atlantic Ocean align with the parallels of latitude in the Euler segments drawn for each of the eight intervals.

(2) Finite poles define the total movement from the Gondwana 'fit' to the present day of a given plate. The red Euler grid in the animation is the finite pole needed to reconstruct South America to its Gondwana 'fit' position alongside Africa. Note how the ocean fracture zones depart from this red Euler grid over the period of 150 million years shown.

Of course, in reality, Africa itself is not fixed. We will see later how the real movement of Africa with respect to a global reference frame has been worked out. But we can still use the movements of South America with respect to Africa in the first part of the animation to a moving Africa. We need only to define the pole positions with respect to a set of African coordinates - the same as present-day geographical coordinates but fixed to a moving Africa. The third and fourth parts of the animation show the result for eight interval poles and the single finite pole respectively. The principle may, of course, be extended to longer chains of fragments.

(3) The third type of Euler pole is the instantaneous pole which is the pole active between a plate pair at any given instant in time. We would expect this to change with time but, in fact, the times at which instantaneous poles change substantially appear to be quite limited. It follows that interval poles can approximate quite closely to instantaneous poles over long periods - many millions of years. In the animation, for example, we use only eight interval poles to describe quite well the actual path by which South America left Africa over 140 My.

Instantaneous poles - and hence interval poles - relate to the geometry of tectonics at mid-ocean ridges. By studying the times at which spreading directions change (i.e. new interval poles take over) across a whole newtork of plates we would hope to determine instants at which patterns of continental drift change regionally or even at global scale. Such times could be of stratigraphic importance in the geological record.

Unfortunately for tectonic understanding, it has become common practice in the published literature to quote a series of finite poles (t0-t1, t0-t2, t0-t3...) rather than interval poles (t0-t1, t1-t2, t2-t3...) to describe the relative motions of plate pairs. The user then has to calculate the relevant interval poles to predict the active geometry at the mid-ocean ridge at any time.

Gondwana is made up of five large plates and scores of smaller fragments. Determining a sequence interval rotation poles for each plate and its conjugate without offending common sense (e.g. overlapping fragments, gaps that open then close again, etc) or the tectonic record in the ocean floor topography involves a considerable amount of work.

Note, finally in the animation, that the ocean fracture zones off Northwest Africa relate to the movements of North America away from Africa - a different plate pair requiring its own set of Euler poles.