TASK

As with many other Maths Medicine geometry tasks, this task addresses the idea that a transformation (in this case an enlargement) operates not just on a specific set of points or on an object, but on the whole plane. The task has some resemblance to GEOi.

The task plays with the idea of an expanding universe, albeit a universe in only 2 dimensions. We assume that the expansion is uniform, ie that in a given period of time, the distance between two points is stretched by the same scale factor, whatever points we choose. This means the expansion is an enlargement. Intriguingly, this also means that the enlargement appears to be centred on whatever location we happen to choose for our viewpoint. In turn this means that we can not determine the actual position of the centre of enlargement (or the centre of the Big Bang) from the limited information that we've been given.

On these pages we provide two sets of movies - one showing the enlargement from the viewpoint of bug D, the other from the viewpoint of bug E. Each set of movies consists of three versions:
-one which simply shows the six points (or bugs) A to E;
-another which includes a grid (which is fixed to the chosen viewing point and which doesn't expand);
-and one where the points are joined by line segments that emphasise the P-shape.
We also provide JAVA worksheets (one without and one with the emphasised P-shape) that allow the user to vary the viewpoint.

The movies on the next three pages show how the bugs' positions change from D's viewpoint.

FREE:
a high-res pdf file of this new GEOaa-zz task