ABSTRACT
For a student of knot theory, bead crochet bracelets offer a new avenue of fun exploration because they are, in many ways, the perfect medium for modeling knots. And, of course, they also offer yet another way to adorn yourself with a mathematical model! The primary focus of knot theory is to understand, categorize, and identify different knots. A knot is a strand that is (perhaps) tangled in some way and then connected at the ends. A bead crochet invisible join provides the perfect way of creating such a connection with a smooth seamlessness that helps capture the essence of a mathematical knot. Unlike a piece of tied string, bead crochet bracelets have no obstacle at the join to interfere with manipulating and exploring the knot in its varied forms. Additionally, the slipperiness of glass or metal beads facilitates easy manipulation between the different forms of a knot. A mathematical knot can be rearranged in any way possible and still be considered the same knot, as long as it is never cut. For example, you may find it surprising that the purple knots and the blue knots in Figure 5.1 are all different incarnations of the same knot, the trefoil (which you may recall was introduced in Chapter 4 as a type of torus knot). Careful inspection also reveals that the purple and blue knots are subtly different versions of the trefoil. In each configuration, whenever the strand of each knot crosses itself, the part of the strand that is on the top in the purple knot is on the bottom in the blue knot, creating
a kind of left-and right-handed trait. Color aside, no matter how you manipulate them, you will never be able to make the purple knot look exactly like the blue one! They are fundamentally different creatures. These kinds of fundamental traits are what knot theorists seek to identify.
