Monday, October 31, 2005

Tumbling Rings

Tumbling Rings

chainI recently made myself a set of tumbling rings based on one of Martin Gardner's old Mathematical Games columns in Scientific American. It's a toy or magic trick with an effect that's similar to Jacob's ladder. It looks like a bunch of rings interlocked into a chain, but when you hold one end of the chain and release one of the links, the link appears to tumble down the chain and hang off the bottom. You can repeatedly tumble links down the chain, one at a time. The visual effect and the clicking sound is almost hypnotic. Whenever I pick up my set, I have to tumble several rings like a set of worry beads.
To get your own set of tumbling rings, you can either buy a set or make them yourself. Puzzle Mike's seems to be selling them, but I have no idea if this site is reliable or not. Making your own set is very easy, you just need to buy a bunch of key rings. Any place that cuts keys will probably also sell plain key rings. I bought some from Home Hardware for 40 cents each. A set of 30 adds up to $12 plus tax.
You can find the instructions in Martin Gardner's Mathematical Games column, "Chicago Magic Convention". All of his Mathematical Games columns are now collected on a CD (ISBN 0883855453). The column also appeared in an earlier collection (ISBN 0671200739) that is now out of print.
If you can't find the column, here are some basic instructions and photos. If the photos aren't clear enough, click on them to see higher resolution versions on
  1. To start, create a set of 6 rings with a double link in the middle like this: 1-2-1-1-1.
  2. Move the last ring up and join it to one of the rings in the double link. Only join it to one of the rings, not both.
  3. first8links
  4. Add two more rings to the bottom of the chain. You should now have a chain with two double links like this: 1-2-2-1-1-1.
  5. Move the last ring up and join it to one of the rings in the double link. Only join it to one of the rings, not both.
  6. Continue this pattern: add two rings and move the bottom one up to link with one of the rings in the previous double link. The linked rings should form two interlinked chains that spiral around each other. It's important that they continue to spiral in the same direction all the way down the chain.

To make the rings tumble, hold them as shown in the first photo and let go with your left hand. The released ring should tumble down. Now grab the front half of the left hand ring in the top double link and let go with your right hand. After the released ring tumbles down, you're back to where you started. Continue until you enter a zen-like state.
If your rings don't tumble, there are two possiblities: you built them wrong or you're holding them wrong. Check the link structure against the high resolution photos and make sure you didn't build them wrong. When you hold them correctly and lift your right hand, you should see one chain slide inside the other chain until they are even. You should have two chains that can slide against each other for the height of one ring.
UPDATE: I found a description of these with a couple of decent diagrams. Donald E. Simanek has posted a set of kinetic illusion toys. If you're having trouble seeing where the rings go in my photos, check out his diagrams.


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