Helicoid String Art

A helicoid is a surface that looks like a (double) spiral staircase or a strand of DNA. It is a ruled surface, meaning that it can be generated by sweeping a line through space. Since it is made up of straight lines, it can be modeled as string art.

Materials

• A plastic 1-liter soda bottle.
  
• Craft thread and needle.
  
• Pushpin and nail
  

Steps

1. Cut out the piece from the pattern, wrap it around the soda bottle centered in the cylindrical section of the bottle, and tape it in place. If this pattern doesn't fit snugly around the soda bottle that you are using, make a similar pattern that is the right size for your bottle.
   
2. Using a pushpin, poke holes in the bottle at the crosses. Remove the pattern and enlarge the holes with a nail or a bamboo skewer. I leave the cap on the bottle when I poke the holes because the air pressure helps give the bottle a bit of rigidity. Of course, the effect is diminished as you poke more holes.
   
3. Cut off the top and bottom of the bottle leaving only the straight cylindrical section.
   
4. Thread the craft thread into a bottom hole and bring it out the hole directly across the bottle from it.
   
5. Bring the thread back into the next higher hole and out the hole directly opposite it.
   
6. Repeat step 5 until you have threaded all the holes.
   

Notes

• You can create a helicoid by dipping a wire wound into a helix with a wire running along its axis into a container of bubble solution. A helicoid is a minimal surface.
  

Links

• The Department of Mathematics at the University of Arizona has an amazing collection of mathematical models including these models of ruled surfaces.