Riemann Surface Neck Warmer

Dear Reader: Some of you know that I am a knitter. This craft is something that I learned at a young age, and continue when there is time. The best thing about this craft is that it can be used as a model to explain reinforcement, discrete and continuous behavior, shaping, chaining and fading.

Recently, I developed my first design. This was inspired by a question asked on the Ravelry geekcraft discussion group, where a member needed to develop a scarf for her brother, who asked her to base it on the Riemann Surface. Obviously, the Riemann Surface could not easily be worn, but hopefully you will get the idea from this pattern.

Note that this is a new pattern, and has not been tested extensively. Your feedback on it would be appreciated!

Riemann Surface-Inspired Neck Warmer

This pattern was inspired by a quest for a scarf that approximates the Reimann Surface, which you can read about here. The first thing that I did was to make a quick paper model of this form to understand how it might be constructed. If you would like to do this first, here are the instructions for the paper model:

Cut a thin, long piece of paper (approx 1 inch wide, by 11 inches (clearly influenced by the only paper I had available). Next, cut a vertical slit about 1 inch from the one end that is large enough for the other end to slip through.

Once the other end slips through, then staple that end to the end with the slit. Voila!

When you look at the model, you should notice that if you knit it, then it would provide an automatic double layer all the way around, with a cross-through. Here is the pattern:

Materials:

Worsted weight yarn (at least 440 yards)
One set of 4.5 mm (US/British size 7)
Tension: 20 sts to 10 cm (4 inches)

Provisionally cast on 20 stitches, and using stockinette stitch (k 1 row, purl one row), complete 3 inches of fabric, ending with having completed a wrong-side row. Measure how wide your knitting is at this point. Note that if you are knitting to gauge, then it should 4 inches wide; however, if it is not that exact measurement, it does not matter much as long as you are consistent in your knitting.

Next row: Knit 10, and then start another skein of yarn to knit the remaining 10 stitches. You will now work on both sides of the slit, using separate balls of yarn. Knit the separation part until the length of the separation is equal to the width of your scarf, or approximately 4 inches (it can be slightly shorter, but I’ll leave the ratio up to you - the smaller the slit in relation to the width of the scarf, the more it will bunch up when you pass it through). End with having completed a wrong-side row.

When you have knit to the appropriate length, cut the yarn from the second ball, and continue to knit using just one ball at a time (i.e., close the slit now by knitting straight across).

Now, knit until the length is long enough to have the knitting pass through the slit, wrap around as per the diagram found here, and be ready to graft the stitches to the provisional cast on. The shorter the scarf, the closer it will fit around your neck, so the choice about length it up to you. As per the diagram, if you make it too short, you won’t be able to get your head through. (However, it would make a beautiful model for your collection of geek knitting).

Variations: Using different weights of yarn, experimenting with knitting stitches, length, width, and so forth. Enjoy!

© January 25, 2011, Darlene Crone-Todd