The stripe on the ring in this activity traces a geodesic line.
Craft yourself a mathematical ring to learn about straight lines on donuts. Don’t laugh, they do exist!
Safety: This activity uses an oven. Ask an adult to help.
First aid: If you burn yourself, run the burn under cool, running water for 20 minutes.
Not all rings will have the same number of twists. How many twists does your ring have?
What’s the shortest distance from one place to another? It’s easy to find on a flat surface such as a sheet of paper – just rule a straight line. On a curved surface such as a ring, it can be much harder.
The stripe on the ring in this activity traces a geodesic line. For two close-together points on your ring, a geodesic is the shortest path – that’s what the word geodesic means. But if you look at two far apart points on your stripe, there may well be a shorter path between them.
Not all geodesics look like the stripe on your ring. A circle around the inside of the hole is also a geodesic. Another geodesic goes down through the centre hole, and up the outside to make a circle around the cylinder of the ring. And some geodesics twist like your stripe does, but they don’t join back up to make a closed loop. Instead, they keep going around and around the ring forever.
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