Reflections

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees before being reflected across to the opposite wall and so on until it hits the screen.

Make a footprint pattern using only reflections.

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that was impossible, could you explain why ?

A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.

I am standing behind five pupils who are signalling a five-digit number to someone on the opposite side of the playground. What number is actually being signalled?

Can you find the time between 3 o'clock and 10 o'clock when my digital clock looks the same from both the front and back?

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only one centre of rotation ? Or if you thought that was impossible, could you say why ?