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 formula_1, the stick number of formula_1, denoted by formula_3, is the smallest number of edges of a polygonal path equivalent Known values. 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 formula_4-torus knot formula_5 in case the parameters formula_6 and formula_7  are not too far from each other: The same result was found independently around the same time by a research group around Colin Adams, but for a smaller range of parameters. Bounds. The stick number of a knot sum can be upper bounded by the stick numbers of the summands: formula_8 Related invariants. The stick number of a knot formula_1 is related to its crossing number formula_10 by the following inequalities: formula_11 These inequalities are both tight for the trefoil knot, which has a crossing number of 3 and a stick number of 6.