Pretzel Unlinking

Imagine that each of the ropes in the two sets of links in Figure 1 are solid (with thickness) and made of very flexible and stretchy rubber.

Question: is it possible to deform one set of links into the other in a continuous motion (without tearing or cutting)? In other words, can you get the purple pretzel off the red ring?

Surprise answer: Yes!!

Presentation Suggestions:
Students (as well as you) may find this very hard to believe!

The Math Behind the Fact:
The transformation can best be explained by a sequence of pictures that demonstrate the transformation, since it is not easy to describe in words! It is important here that the ropes are solid, with thickness, and very stretchy; it wouldn’t be possible otherwise. See Unbelievable Unlinking for a hint on how it can be done. The reference contains a solution.

A course in topology is the best place to learn about links and knots and continuous deformations.

How to Cite this Page: 
Su, Francis E., et al. “Pretzel Unlinking.” Math Fun Facts. <>.

V.V. Prasalov, Intuitive Topology.

Fun Fact suggested by:
Francis Su

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