### 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.

# Concrete Wheel

##### Stage: 3 Challenge Level:

Alan Schoenfeld reports that:

Some people think that the room will go (almost) instantaneously dark as the wheel first passes the window, that it will stay dark for a short while and then go (almost) instantaneously light as the wheel leaves.

Others think that the room will go (almost) instantaneously dark as the wheel first passes the window, that it will stay dark for a relatively long time and then go (almost) instantaneously light as the wheel leaves.

Others think that the room darkens slowly, as though a large curtain is being pulled, more or less horizontally (from left to right), or diagonally (from the top left corner), or vertically downwards, as in the sketches below:

The room then stays dark for a short /long period of time, after which it lightens in a way that is complementary to the way it darkened.

What do you think?

Perhaps this interactivity can help:

You can make the wheel bigger and smaller by pressing the up and down arrow keys and you can make it roll by using the other arrow keys. You can also move the blue square around.

Full screen version

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