1) “Cut that out!”
Having trouble tying a trefoil knot? Let the Moebius strip do it for you!
Take a long, thin strip of paper. Make three half twists in one end. Tape the ends together. You now have a special form of the Moebius strip (draw a line down the middle if you want to verify this – it only has one side!)
Next, cut the strip down the middle lengthwise (don’t cut across the narrow dimension).
You will be left with a trefoil knot twice the length of the original Moebius strip! Cool! Try this with five half twists, then seven. See what fun you can create!
(Side note – A molecular process similar to this activity has actually been used by chemists in attempts to create trefoil and other knotted molecules for specific material purposes. Check out the DNA & KT Today page for similar information on knots and our genetic structure.)
2) The Dancing Knot
Can you handle the challenge? Can you make the knot?
Take a piece of string and tie or tape a small weight (an eraser, a coin, etc.) to the end.
Hold the opposite end of the string between your thumb and index finger. Let the weighted end hang down.
Now, try to make a knot just by jerking the string up and down. Don’t let go of the end of the string, and you can only use one hand.
This one might take a little bit of practice, a little bit of thought, and a whole lot of patience! Good luck!
3) Tangled Hands
Here’s another challenge for you to try:
Take an unknotted piece of string by the ends – hold each end between the thumb and index finger of each hand.
Now, without letting go of either end, can you make a knot in the middle of the string?
This exercise is possible – it just takes some clever hand/arm positioning. Hint: Try going at it backwards, starting with a knot in the middle and untying it without letting go of the ends.
Good luck, and enjoy!
4) Human Knots
This can be a fun activity to try with a group of friends – you may have even done it before at camp.
With a large group of people (5 to 10), stand shoulder-to-shoulder in a circle facing inward. On the count of three, everyone puts their hands in the circle and grabs someone else’s hands at random.
Once all the hands are taken, the group has formed a human knot or link.
The challenge is this: Can you untangle this formation into either a circle or into rings without anyone letting go.
Besides being a good “get-acquainted” game, this activity can really build your Knot Theory skills. You may run into questions like these:
1) Have we formed a nontrivial knot or link (one we can never untangle)?
2) What is the likelihood that we will form an unknot?
3) How often do we form links rather than knots?
4) How complex a knot could a certain number of people form?
5) Knot-Knot Jokes [^back to top]
Three strings walk into a bar. The first string goes up to the bartender and asks for three whiskeys. The bartender looks down at the string and says, “Sorry, buddy – we’re not allowed to serve drinks to strings in here.”
The second string steps up to see what’s the matter. “We’re paying customers, and we demand three whiskeys!” he grumbles.
The bartender says, “Listen, fella – I’m just following the rules. No strings allowed in here.”
The two strings sulk back to the table and tell the third string, who really gets angry. “I know how to handle this!” he growls as he begins to double over and tie himself into a messy tangle. Swaggering up to the bar with strands flailing in every direction, he shouts, “Bartender! I want three whiskeys, and I want them NOW!”
The bartender casts a suspicious look and asks, “Hey… Aren’t you one of those strings that came in here earlier?”
The tangled-up little guy shrugs and states confidently, “Nope, I’m a frayed knot!”
6) “Links” to Other Great Knot Sites
There are many great Knot Theory sites on the Internet. This short list contains some of the most interesting, informative, graphically amazing, and just plain fun sites around. If you have a knot site you’d like to add, please feel free to email firstname.lastname@example.org with your site name, and please feel free to link to our site and activities.
Knot Plot Site*** – Dr. Rob Scharein’s main web site for visually exploring knots. Here you’ll find everything from stereoscopic 3D knots to virtual reality knots, in superb color and style. Plus, you can learn a lot while you’re being awed by the graphics! You can jump directly to the Knot Theory page for tons of information on the subject.
Mathmania Knot Theory – Puzzles, tutorials, activities, applications, exercises, research, and a knot glossary combine to make this an entertaining and informative place to learn more about Knot Theory.
New Ideas about Knots – Personal tips and discoveries by an enthusiastic knot theorist take you from making knots with orange extension cord (plugged into itself) to coloring and counting with knots.
More Knot Theory on the Web – A site with hyperlinks to several knot sites online, part of Mouse’s Knot Theory site.
Knots on the Web***- The most complete and exhaustive collection of links to every site you can imagine on knot tying, knot theory, knot art, knot software, knot books, and even a knot gallery for reference and enjoyment.
7) A Few of Mr. Payne’s Knot Photographs
These are a few of my favorite knotty pictures from this project. Be sure to check out the animated knots on the the Wanted and Hunt pages. Special thanks to Bill Ingram for his assistance in making some of the knots in this collection:
The 51 knot
The 61 knot
The 62 knot
The 71 knot