In mathematics, a knot is a closed circle in a three-dimensional space that crosses itself multiple times. Since it is closed, it has no ends to tie, meaning you can't actually create such a knot. However, if you tie the ends together after you create a knot in the standard way, you will have something that is close to the mathematical description. In this post, we will explore the creation of mathematical knot sculputures using copper tubing and solid solder wire. This post is inspired by Adam Withrow over at PVC Inovations World, who has been posting up pictures of twisted pvc pipe sculptures and furniture, such as this amazing triple helix table. The curving closures of pipe got me thinking about making mathematical knots as sculpture. I then read a paper by Nathaniel Friedman that had pictures of knots made with copper tubing. The copper tubing works great, but it's a little expensive and even though it is a very ductile metal, I wanted something even easier to work with. Solid core solder wire is very easy to work with and you can easily connect up the ends by using a small soldering iron. Here's a picture of some of the knots I've made over the last few days. The solder ones are closed by soldering the ends together, while the copper ones have a brass part that joins the ends. I used 1/8 inch copper tubing and the largest solder wire I could find, which was also about 1/8 inch diameter.

Materials and Tools Solid core solder wire (get "Lead Free" so you don't worry about lead poisoning)

Small soldering iron (you don't want the iron to get too hot or it will melt your knot)

Copper tubing (smaller diameters are easier to bend and less likely to "krink")

Shears to cut the copper tubing (a hacksaw would probably work well, also)

Small round objects to help you bend smoothly (pens of various sizes work great)

Pliers

Knot diagrams to use as inspiration or at least classification after you make a knot Step 1 Pick a Material and a Knot I would recommend trying these with solder wire first since it is so easy to bend. Use these diagrams to choose a knot. I recommend starting with the simplest knot, the trefoil. Step 2 Cut a Length of Wire or Tubing Use a utility knife to cut the soldering wire, or shears to cut the copper tubing. The shears will bend the ends of the tubing, but you should be able to use pliers to deform it back. Make sure you have more material than you think you need. You can't easily add more after this step. Step 3 Tie the Knot I can't really help you with this step. Follow the diagram or just tie your own original knot. Make sure the ends meet at the end. You might want to trim the ends as well, if you had a lot of excess material. Step 4 Shape the Knot Once you have formed the knot, you can move the metal around until it has a more pleasing shape. I usually try to make the curves as smooth as possible, but perhaps you prefer a kinkier knot. (Pun unfortunately intended) Step 5 Attach the Ends Together For the solid solder knots, you can just use a small soldering iron to solder the ends together by touching the tip to the joined ends. Make sure the iron isn't too hot—and don't leave the iron touching the ends for very long or the entire knot may melt. For the copper tubing knots there are lots of ways to attach the ends. You could solder the ends together by using a torch and some solder. I bought some brass sleeves to join the ends together and used some pliers to crimp the sleeves around the copper. Here are a few close-ups of the knots I made:

Show Off Your Knots If you build one or all of these, let us know by posting a picture or video up on the corkboard. If you have any ideas of how to make these better or faster, be sure to comment. I think they could become pretty fabulous earrings. Perhaps you could make a stand for your knot or suspend it from a frame. You could try making knots from different materials. I'd love to see whether or not Adam could do these in PVC. Yeah, that's a challenge Adam. On Thursday, we'll look at creating some of the most symmetrical types of knots. The torus knots have a very star-like appearance and you can see a couple of the simpler examples of them in the pictures above.