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?
Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Faisal from Arnold House School offered
a strategy for working on this problem:
We had several more good solutions for the
first part of this problem from pupils at Highcliffe Primary
School. Whitney and Joe said:
Sam and John explained that the length
of the locus ...