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!!
Students (as well as you) may find this very hard
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.