Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface of the water make around the cube?
Imagine you have six different colours of paint. You paint a cube
using a different colour for each of the six faces. How many
different cubes can be painted using the same set of six colours?
A rectangular field has two posts with a ring on top of each post.
There are two quarrelsome goats and plenty of ropes which you can
tie to their collars. How can you secure them so they can't fight
each other but can reach every corner of the field?
Several teachers didn't like this trick but is it really a
trick? When the rotation takes place the grid lines up along the
slopping sides but does it exactly fit? When you count the squares
the second time what are you counting? The counting may not be
accurate. Are the 'half' squares all exactly half?
Many of you were puzzled by this. What is really going on here?
We can't 'make' an extra square of area just by chopping a shape up
and putting the pieces together differently so what is happening?
William from Tattingstone describes it like this:
I think he is trying to tell us that the rectangle C doesn't
quite fit in there. The line on the sloping side of the triangle
isn't really a straight line is it? Measuring is never absolutely
accurate is it?