Games

GAME 1: Mirroring squares

Take five squares from Game Set A. Place one of the squares on the green table area. Now mirror this square along one of its horizontal sides by placing a second square beside it, checking that the adjacent sides are the same color. When doing so, make sure that

• the sides running vertically are always the same color, and
• the squares you lay form a stair-like shape.

How many squares did you have to lay before the colors on the sides lined up the same as the first square you laid?

Now compare your solution with Solution Set B.

GAME 2: Finding a periodic trajectory

Representing a billiard ball trajectory as a straight line simplifies many mathematical problems, including those concerning periodic trajectories. Have a go – the Unfolding trick makes it easy:

Take the folded Solution Set B. The black lines show the trajectory of a ball on a billiard table. First look at the trajectory from above. This is a periodic trajectory, because the ball keeps on following the same trajectory. Now unfold Solution Set B square by square and watch how the trajectory becomes a straight line.

Now try it for yourself: take the squares from Game Set A and arrange them the same way as in the unfolded Solution Set B. Using a marker pen and a ruler, draw a straight line through all the squares. Use the Template 01 provided so that the start and end points in the first and last squares are in exactly the same place.

Now stack all the squares on top of each other so that each side of the stack is the same color. When you look at the stack from above, you should see the periodic trajectory of a billiard ball.

Discover more games ideashere.

Game 3: Laying tiles

The Unfolding trick does not work with all polygons. This game reveals which ones are possible:

Select all the tiles with the same number of corners – e.g. all squares or all hexagons – and lay them next to each other on the green table area by mirroring the tiles, i.e. the sides that touch should be the same color.

Which polygons allow you to tile a plane (a plane is a flat two-dimensional surface that extends indefinitely)?

The exhibition’s info panels explain how mathematicians get from a 2D plane like this to 3D surfaces and why this is important.