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A Review of Basic Geometry—Activity 2

More Topological Abnormalities

Remember that topologically, a single-handled mug is equivalent to a torus (doughnut). Now take a piece of string or yarn and tie it in the fashion indicated below left to the handle of a mug. Have someone hold the string and another person take the cup off the string through the knot (i.e. while the first person hold both ends of the string). Is the string really tied to the cup. Now reverse the process. Interesting!

[single-handled mug with loop knot around handle] [small wooden board with three holes, string loop tied in center hole, tied each end, and pair of large washers on strong]
Pictured above right is only one example of readily encountered puzzles loosely based on this same principle. The goal is to move the nut from one loop to the other without untying the knot at either end. If you make your own wooden puzzle like the one above, be sure the nut or washer is too large to fit through the hole and please use two nuts/washers. The goal then is to split them, which is much easier to verify then moving it from one side to the other.

Here is yet another puzzle application for this problem.

Three Post puzzle--Start Three Post puzzle--End

Having solved the above puzzles can we apply what we have learned to another situation? This interesting topological problem makes for an interesting party game. Select a pair from each table group and see if you can help them find the solution for becoming untangled. (See figure below.)

[boy and girl each with strings joining own wrists, looped]

Here are yet some more puzzles loosely based on these same principles.

Sneaky Pete Chinese Rings or Torture Horseshoe Puzzle

I had forgotten how to solve Sneaky Pete and lost the instructions. However, this web site was recently e-mailed to me. Please note it does not ever need to be forced and actually we have had to have the rings welded shut because students abused it. Please do not force it. However, if you solve it, please let me know.

The Chinese Rings are one of my favorite puzzles. I discovered this one when I was 15 years old. It was made out of coat hanger wire. I was instantly hooked! There seems to be a binary pattern to it. Can you describe it? Here is another view.

The "original" horseshoe puzzle is also a fun one.

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