Stick number

In the mathematical theory of knots, the stick number is a knot invariant that intuitively gives the smallest number of straight "sticks" stuck end to end needed to form a knot. Specifically, given any knot ${\displaystyle K}$, the stick number of ${\displaystyle K}$, denoted by ${\displaystyle \operatorname {stick} (K)}$, is the smallest number of edges of a polygonal path equivalent to ${\displaystyle K}$. A related quantity is the equilateral stick number, the smallest number of edges of the same length that are required to form a knot. It is not currently known whether the equilateral stick number is the same as the stick number for every knot.