Math Fun Facts!
hosted by the Harvey Mudd College Math Department created, authored and ©1999-2010 by Francis Su
Subscribe to our RSS feed   or follow us on Twitter.
Get a random Fun Fact!
No subject limitations
Search only in selected subjects
    Calculus or Analysis
    Number Theory
    Other subjects
  Select Difficulty  
Enter keywords 

  The Math Fun Facts App!
  List All : List Recent : List Popular
  About Math Fun Facts / How to Use
  Contributors / Fun Facts Home
© 1999-2010 by Francis Edward Su
All rights reserved.

From the Fun Fact files, here is a Random Fun Fact, at the Medium level:

Pretzel Unlinking

Figure 1
Figure 1

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. <>.

The Link for this Fun Fact: is directly accessible here.

Subjects:    topology
Level:    Medium
Fun Fact suggested by:   Francis Su
Suggestions? Use this form.
Click to rate this Fun Fact...
    *   Awesome! I totally dig it!
    *   Fun enough to tell a friend!
    *   Mildly interesting
    *   Not really noteworthy
and see the most popular Facts!
New: get the MathFeed iPhone App!

Brings you news and views on math:
showcasing its power, beauty, and humanity

Want another Math Fun Fact?

For more fun, tour the Mathematics Department at Harvey Mudd College!