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 *K*, the stick number of *K*, denoted by stick(*K*), is the smallest number of edges of a polygonal path equivalent to *K*.

Six is the lowest stick number for any nontrivial knot. There are few knots whose stick number can be determined exactly. Gyo Taek Jin determined the stick number of a (*p*, *q*)-torus knot *T*(*p*, *q*) in case the parameters *p* and *q* are not too far from each other (Jin 1997):

The same result was found independently around the same time by a research group around Colin Adams, but for a smaller range of parameters (Adams et al. 1997). They also found the following upper bound for the behavior of stick number under knot sum (Adams et al. 1997, Jin 1997):

The stick number of a knot K is related to its crossing number c(K) by the following inequalities (Negami 1991, Calvo 2001, Huh & Oh 2011):

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