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?
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
A cylindrical helix is just a spiral on a cylinder, like an
ordinary spring or the thread on a bolt. There are two kinds, a
right-handed helix and a left-handed helix and in the case of a
bolt one has to be turned clockwise to screw it down and the other
anti-clockwise. If I turn a left-handed helix over (top to bottom)
does it become a right handed helix? Give as simple an explanation
as you can.