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Torus maze

By David, 12 August 2014 Activity

You’ve seen mazes on paper, you may even have explored big mazes on foot. But this maze has a geometric twist – it’s on the surface of a donut. This is a torus maze!

You will need

A maze, someone has drawn a line from the start, off the edge of the maze.

Start at the square marked start. When you escape the maze…

What to do

This is a maze. There is a start and a finish labelled inside the maze, and you need to get from one to the other.

There are places on the edge where you can escape the maze. If you come off the bottom of the maze, start again at the top of the maze. If you go off the top, then start at the bottom. If you go off the side, start again on the other side. There are symbols at each exit to show you exactly where to go.

Someone is drawing a line from the edge of the maze back in.

Find the matching symbol and enter the maze again.

What’s happening?

The maze in this activity wraps around. If you go off the left side, you end up on the right. If you go off the top, you end up at the bottom. It can be a bit tricky to remember to loop, but with some practice you should be able to solve the maze.

To work out what shape this map represents, imagine rolling the maze into a cylinder so the bottom and top line up. Now imagine stretching the cylinder so the left side and right side meet. This looped cylinder is a donut shape, also known as a torus.

Maps such as this maze are quite common in old computer games. So next time you play Chrono Trigger or Asteroids, think about the shape of the world you’re exploring. It might be a torus!

Someone has drawn a line to a square marked finish.

See if you can make it to the finish!

A map of our sphere-shaped planet would have different rules. If you have a hot air balloon and fly due west, you’ll go off the side of the map and end up on the other side. However, things are different at the north and south. If you start in New Zealand and head north, eventually you’ll reach the North Pole at the top of the map. But if you keep going, you don’t instantly end up at the bottom of the map like in the maze. Instead, you’ll stay at the top of the map, north of Europe, heading south!

More information

Why are fusion reactors donut shaped?

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