### All in the Mind

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?

### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

### Instant Insanity

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.

# Rolling Around

##### Stage: 3 Challenge Level:

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square.
Describe the locus of the centre of the circle and its length.

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If the circle now rolls around an equilateral triangle, can you describe the locus of the centre of the circle and its length?

Can you generalise your findings?

Here are two related problems you might like to take a look at:
Rollin' Rollin' Rollin'
Is There a Theorem?