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Geodesic rings

By David Shaw, 20 August 2020

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.

You will need

• Oven
• Oven bake clay (at least two colours)
• Butter knife
• Baking tray
• Oven mitts

What to do

1. Check the packet of clay for instructions on baking. Turn on the oven to the correct temperature. For example, this clay needs to be baked at 110 °C.
2. Take a small piece of clay, about the size of a pen lid. Play with it a bit to make it soft, and then roll it into a fat sausage shape.
3. Take a much smaller piece of clay in another colour. Roll this into a thin strand, the same length as the sausage shape.
4. Lay the thin strand along the sausage.
5. Trim the ends of the clay with the knife so that the ends are neat.
6. Gently roll the combined pieces together. Keep rolling until you get a cylinder longer than your hand is wide.
7. Hold the two ends of the cylinder and twist in opposite directions so the stripe spirals around and around.
8. Wrap the cylinder around your finger and carefully mark the right length to make a ring. Put the cylinder back on the bench and cut it to length. Then join the two ends, making sure the stripe joins up with itself.
9. Put the ring on a baking tray and put it into the oven. Bake according to the instructions on the packet. Once it’s done, use oven mitts to take it out of the oven. Remember that the ring will be hot at first, so give it plenty of time to cool before you try on your new ring!

What’s happening?

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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