Mathematical Patterns Used to Make Bracelets


In the last Natural Science and Mathematics (NS&M) Colloquium of the spring semester series on the afternoon of Wednesday, April 11 in Schaefer 106, Susan Goldstine, Associate Professor of Mathematics at the College, spoke about her experiences with mathematical beading and the connections between math and art.

Her journey started on November 3, 2008 when she received an unexpected email from Ellie Baker, a computer scientist and artist in Massachusetts, whose daughter was a senior in high school and planning to make beaded crochet bracelets based off mathematical patterns on Goldstine’s website for a science project.  Her high school told her it wasn’t science.

Baker’s daughter, Sophie Sommer, designed a bracelet that replicated a seven-color torus, or the surface of a doughnut.  Goldstine was quite impressed with Sommer’s design and exact replica of the seven-color torus, in which every color on the bracelet touches each of the other six at one point in the pattern.

Sommer had then come up with a new seven-color pattern similar to the torus.  Goldstine and the mother-daughter duo had finally decided to meet at the Joint Math Meeting in Washington D.C. in 2009, where they shared their designs in person for the first time.

It was then when Goldstine had learned to finally actually make the bracelets, which are made “by crocheting a strand of beads into a cylinder and sewing the ends together to form a torus,” according to Goldstine’s webpage. Goldstine also noted that Baker and Sommer favored a mathematical approach because it would lead to more perfect symmetry in the bead design, since trying to visualize a finished product based off a 2-D pattern is rather difficult.

After the initial meeting, Baker contacted Goldstine again with a new way to create these seven-color tori with art: knitting and crocheting. Artists Sarah-Marie Belcastro and Caroyln Yackel, who originally created the designs, had inspired Baker to try even more mathematical designs with bead-crochet bracelets such as a torus knot, which is a knot that can be drawn on a torus and measured based on the amount of times the line passes through the hole and also completely around the torus.

Once Baker completed a torus knot on a bracelet, she turned to Goldstine for even more designs like an Esher tessellation, which is the division of a plane or other surface into one or several identical shapes.  Though Baker was sure there was a mathematical theory on how to perfect the Esher bracelet, she just couldn’t find it.  So finally, after working on the bracelet for a while, she brought a finished product to the 2010 Joint Math Meeting in New Orleans.

Now fully interested, and on sabbatical, Goldstine started to devote more time to the art form, and had her breakthrough in September 2010 when she discovered a perfectly symmetric “hockey stick translation.”  In this design, the pattern is described as “to the right, down-right once,” meaning that there would be five beads in a row and then the sixth bead would be located down one row and to the right one space from the initial line of five.  Once they discovered this pattern, Baker and Goldstine began to design back and forth and came up with 11 designs, which they submitted to the 2012 Joint Math Meeting’s art exhibit in San Diego.  Their collection is called the “Crystallographic Bracelet Series.”

Currently, Baker and Goldstine are working on publishing a book about the various mathematical bead crochet bracelets.  “Our goal is to teach people how to make the bracelets while also designing new ones ourselves,” said Goldstine.

Goldstine also noted that Sommer ended up completing the project in high school in 2009 and won a prize for her work. Currently attending Colgate University in New York, Sophie has even sold some of the more simple patterned bracelets on

First year and math major Laura Andre thought the lecture was interesting.  “I liked how it showed that you can incorporate math into art,” she said. The NS&M Colloquium Series plans to return next semester to the College.