Wednesday, June 15, 2016

Knot theory socks finished!

I finished the knot theory socks in time to give them to my advisor on the day of my Ph.D. hooding.

As I said in my first post about these socks, the left sock (on the right in the pictures; it has four crossings) is a braid representation of the figure eight knot.  The right sock (on the left in these photos, and with six crossings) is a braid representation of a link: the Borromean Rings.

The Borromean rings are a 3-component link, meaning that it consists of three pieces of mathematical string, arranged in 3-dimensional space, with the two ends of each string glued together.  If we ignore how they are arranged in space, what we have is a collection of three circles.  The special thing about the Borromean rings is that they are the simplest Brunnian link.  A Brunnian link is a non-trivial link (with any number of components) with the property that if you remove any one component, the rest form an unlink.  (An unlink is a link in which each component is an unknot, and the components don't interact with each other at all.)

I think these socks turned out wonderfully.  I want to make a pair for myself!

Pattern: The cables are my own design. I referenced the book More Sensational Knitted Socks for numbers of stitches in the heel and toe.
Size: 64 stitches
Yarn: Knitpicks Stroll Fingering in Blue Violet Tonal
Needles: US0 (2mm) DPNs
Started/Completed: April 2016/May 2016
Modifications: No pattern to modify!

1 comment:

  1. Beautiful! I made molecular Borromean rings for part of my Chemistry PhD Thesis. I'm not used to seeing them in a braid form. In the ring form, the nodes are always alternating. This appears not to be true for the braid?