Age 16 to 18 Challenge Level:
In mathematics, projections are often used to help understand the
properties of 3 dimensional objects. Formally if an object is
created from a set of points (x_n, y_n, z_n) then the projection in
the z-direction, for example, will be the same set of points with
the z coordinates squashed to zero (x_n, y_n, 0).
An obvious use of projections is in computer games where the 3D
virtual world is shown on a flat screen.
It would be an interesting activity to attempt to construct real 3D
models of the interpenetrated objects. Drinking straws would enable
the creation of a framework and then the surfaces could be tiled
with coloured paper cut to an appropriate size. It would be very
interesting to receive photos of any such constructions!