Lorelei Koss

Professor of Mathematics
Dickinson College
Carlisle, PA 17013

My mother taught me how to knit and crochet, and my daughter taught me how to make friendship bracelets. I enjoy using mathematical ideas in crafts that have traditionally been associated with "women's work." The seeds of this project came from a conversation with my daughter about how to design friendship bracelets that would exhibit certain patterns.

One-color Frieze Patterns in Friendship Bracelets
14 x 26 cm
cotton thread

Friendship bracelets are a type of macrame typically made with embroidery floss, but the history of friendship bracelets is unclear. Many popular press articles speculate that friendship bracelets originated in Guatemala in the 1970s and then spread worldwide. While the designs and coloring of friendship bracelets from that period often mimicked patterns seen in indigenous Mayan cultures, the method of constructing a friendship bracelet does not seem to be related to any traditional crafts. Not all two-color symmetry patterns are possible in a normal friendship bracelet, but it is possible to make all seven of the one-color symmetry patterns. We show an example of each here.