After last week’s column on mathematical quilts, I thought I should continue in the fiber arts category with mathematical objects that can be made by crochet. Matthew Wright at the University of Chicago has crocheted some beautiful Seifert surfaces, shown below. These are (approximately) the form that a soap film would take if you made a knot out of wire and dipped it in soap solution. The first is based on a trefoil knot, made from a continuous path of blue yarn, with a red Seifert surface spanning it.
The example below is based on the Borromean rings — three separate loops which are locked together. The black surface shows the intricate shape of the soap film that would form between them.
If you would like to crochet your own Seifert surfaces, you can explore an infinite variety to choose from with the SeifertView program.
You can see all of the “Math Monday” columns here.