Mathematical craft

I am @VickyMaths1729 on Twitter, and that's a good place to find updates on recent projects. On this page...


Symmetry friendship bracelets and scarves

I've been exploring the different kinds of symmetry that are possible in a friendship bracelet or scarf with an (infinitely!) repeating design. (Technical detail: I'm only exploring 'discrete' options, so for example a plain blue bracelet wouldn't count because any translation would be a symmetry.) It turns out there are seven possible types of symmetry pattern that such a bracelet can have. This relates to the mathematical concept of a frieze group.

I've put a few photos below. On a separate page you'll find full sets of bracelets and of scarves showing all the possible types of symmetry, as well as designs you can use if you'd like to make your own, and a video I made with James Grime for MathsWorldUK about the bracelets.

Curled up bracelet with rainbow diagonal stripes                           Bracelet with rainbow zigzags looking like a folded ribbon
Bracelet with rainbow chevrons                           Unfinished bracelet with rainbow chevrons
Red scarf with textured diamonds
Yellow with two undulating waves along the length, each alternately large wave and shallow wave, out of phase so large wave on one is opposite shallow wave on other
Blue textured diamonds of different sizes, large diamonds down centre, on one side half size diamonds, on other side half size diamonds then subdivided further into quarter size diamonds

Crochet multiplication tables

In 2019, I took part in the Big Internet Math-Off. In my first pitch, I shared my crochet versions of multiplication tables in modular arithmetic. Here are some photos of these multiplication tables.

Multiplication modulo 2                           Multiplication modulo 3
Multiplication modulo 4                           Multiplication modulo 5
Multiplication modulo 6                           Multiplication modulo 7
Multiplication modulo 8                           Multiplication modulo 9
Multiplication modulo 10                           All these tables stacked

Knitted Euclid's algorithm

My second Math-Off pitch was about Euclid's algorithm, and including my knitted visualisation of the algorithm. Here's a picture of it.

Euclid's algorithm

Prime scarves

My third and final Math-Off pitch was about my knitted scarves illustrating the distribution of prime numbers. The prime bracelets below illustrate the same mathematics in a different way.

Here are some pictures of the scarves. (In my head, the scarves are always vertical, but that doesn't fit well on a computer screen so I've rotated them here!)

Primes modulo 6
Primes modulo 7

The scarves are double-sided, I knitted them using a technique called double knitting. There's more about this, and more photos, on the Math-Off page.

Some people asked for the patterns. Here they are (two file formats for each).

I pretty much stopped when I ran out of yarn. If you'd like to make longer scarves, you'll want a list of prime numbers to help!


Prime bracelets

I wrote an article for issue 4 of Chalkdust magazine, on Prime jewellery.  Here are some of the pictures from that piece.

Primes on a bracelet of circumference 6                           Primes on a bracelet of circumference 7
Photos above by Jennifer Balakrishnan

Curved stitching cards

In November 2015, I had a guest post on Alex Bellos's Guardian blog, on how to make mathematical Christmas cards.  Below are some pictures from that blog.  To make your own, you'll want to create a suitable template of dots.  Of course you can make your own in any way you like (I find GeoGebra good for this), but here's a pdf with some templates in case anyone finds them helpful.

Curved stitching Christmas cards                           Photo of Vicky doing mathematical craft
Photos above by Jennifer Balakrishnan
Curved stitching parabolas in triangle                           Curved stitching cardioid                           Curved stitching nephroid

This page last updated 2 June 2021.

Vicky Neale