Developing our three-dimensional footing: a first look at the mathematics of socks

Feet are anatomically complex. Many toes. Lots of joints. Bones and curves and odd bits that stick out. It follows only makes sense that socks are also complex. To create these little forms of feet clothing, the crafter must consider the length of the foot, the circumference of the foot at multiple points, and the features of the foot arch. In addition, there are elements of design, such as how high up the leg the socks will go, that must be considered before the cast on is initialized.  

These simple socks use a regular cast-on in the round, as opposed to a toe-up cast-on.

Though we will continue to explore yarnbombing, Angela and I have taken on the challenge of knitting socks - a fitting project for these cold-weather months. We had an idea that the process of making would be tricky, but it was not until we began to leaf through books on sock-making that we began to gain awareness of the depth of design that goes into the creation of socks. 

In the beginning, I was excited by all of the sock patterns (what better way to have cozy toes?), but soon, with some exasperation, I realized that the book I was working with was much too advanced for me. Even the cast on was complicated, let alone the sheer magic that is Judy's Magic Cast-On. Just wait until we write about Judy's Magic Loop! 

I crafted this sock specifically for my body dimensions. Each crafter can personalize the sock pattern for herself. 

We were not trying to find the mathematics of feet and socks, but it was impossible for us to start these knitting projects without seeing the three-dimensional features and possible variations. It was as if the sock maths found us. 

Many socks are made using a toe-up approach, meaning that the cast-on starts at the toe and the knitter knits from toe up to the ankle. To simplify the crafting practice for myself, I chose to start with a pattern that worked opposite in direction, so the cast on was more similar to a hat, a technique I was already familiar with. Angela is currently knitting toe-up socks. 

Both of us are still engaged in the processes of making for our sock projects. 

The heel for this sock pattern is created with a special heel flap, which is knitted with a series of slipped stitches.

The beginning of the socks were fairly simple, except for the series of slipped stitches and yarn-overs that led to the rugged stitch pattern along the ankle. Now, I am at the heel flap, which will eventually reconnect with the body of the heel and remainder of the sock. 

I have had to consider the length of my ankle, the desired length of the sock, and the dimensions of my heel. We have both learned that socks are highly personalizable. 

(Note: In retrospect, I do wish that I had started two socks in the beginning, instead of one, as now I will need to complete a full second sock once the first is finished before I can wear either or both.)