For Discussion.....

How would you describe Escher's art in mathematical terms?

In the mathematical description of knots, two knots are the same if one can be turned into the shape of the other without having to cut the string anywhere. This is similar to the equivalence of the doughnut and the cup with saucer. Another strange topological result says that a man wearing a suit with a vest really has the vest on the outside of the jacket since the vest can be taken off without removing the jacket! (I've seen it done!!) Can you figure out how to do it?

Take another look at the Escher's art ? ==>

Take another look at knots ? ==>

One practical use of a Mobius strip is with fan belts. Normally, fan belts are placed around the shafts so that only one side of the belt touches. But if you have a Mobius strip for a fan belt, all parts of the belt touch the shafts and so the belt wears longer! Can you think of any other uses a Mobius strip might have?