This is a call for help—or for suggestions, at least. I’m teaching a knot theory class next semester. I’m looking for good props to use in the class to make knots. I would like to be able to make knots such as the following (and have my students do so as well). 
I suppose the criteria are:
- Inexpensive (It would be nice to find something that is cheap enough that I can ask the students to buy it without forking over too much more money on top of what they are paying for the text.)
- Flexible
- Holds its shape if set on the table
- Long enough to make complicated knots
- Short enough that it is possible to see what is going on
- Easy to disconnect, knot/unknot, and reconnect (I’m thinking of velcro ends, snaps, plugs, something like that.)
This is what I have come up with so far. 1. Rope/string—satisfies a lot of the criteria, except #6. If anyone can think of a good way to attach a connector to the ends of a piece of rope, let me know. 2. Extension cord—this is a pretty good solution if I can find one of the right length and flexibility. 3. Tangles—a fun toy made out of many snapped-together pieces of quarter-circle-shaped tubes (see below). It is easy to plug and unplug the links of the toy. Fun to play with, but the knots are very “wiggly” looking and we would need several sets to make a long knot.
4. Rubber tubing—I bought some 1/4″ vinyl rubber tubing and some connectors (shown below). This works pretty well. The tubing plugs and unplugs easily. The downside is that the tubing doesn’t hold its shape well. It has a memory and wants to straighten out on its own.
5. Smart Bungees—I had never seen this product before. They are bungee cords without hooks on the end. Instead it has plugs that you can snap into any number of different adapters (sold separately). I bought a set of two bungees (48″ each) for about $5 and a pack of two connectors (as shown below) for $2. I won’t ask the students to buy this, but I think I may use this for demos in front of the class. 
6. Wire rope—I could use a wire rope with a thimble at each end, then connect the ends with some sort of carabiner. Seems too clumsy and inelegant. 
Ideas?!?! Let me know. Thanks!
David Richeson: Division by Zero 
as i just twittered (as ‘dansmath’) / for your knot theory class / how about insulated 10 or 12 gauge electrical wire or NM-B cable? / lots of colors, holds its shape, super cheap, lots of end connectors; crimp or tube. / remember: “it’s not just theory, it’s knot theory!”
A knot theory class taught last summer at Canada/USA Mathcamp used, I believe, mardi-gras beads. If you can find some that connect and disconnect, they’re pretty good.
We used some thick string with a ball of bluetac on the end to fix the two ends together..
Great suggestions. Thanks! Keep them coming. Maybe I’ll just have a box of assorted knot-making materials to bring to class.
You might want to look at Wikki Stix. They are a kids craft item. Its been a long time since I used them, but I think that they hold their shape pretty well, and you can put the ends together like you would clay. They are also pretty cheap.
Don’t know that this will be helpful as I have not searched for a source for the product, but I recall a childhood magic kit which included “magic” rope. The key to the trick was magnets inserted into the ends of the rope, which could be “cut” and magically reattached ;) The rope had an outer core which was similar to (another childhood memory sparked) Chinese finger torture (a weave which tightened as you try to pull out your finger — or in this case the magnet).
Hmmm… interesting idea! I’ll have to keep my eyes open for this product. Thanks.
I’m a bit late, but maybe you can use pipe cleaners. You can bend them and they hold their shape. They come in nice colors and they are soft for the hands. I think they fulfill all your requirements, although maybe number 4 will be a problem. Most of them are maybe 15-20 cm long, but they have jumbo versions. The ends can be attached by twisting them.
You can buy them in stores selling craft materials (?), at least in The Netherlands, but I found the jumbo version also here: http://www.brainnoodle.net/shop/index.html?page=1.
Wel, thanks for the suggestion. Class starts in two days. I’m looking forward to it.