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):
Famous quotes containing the words stick and/or number:
“It is commonly said ... that ridicule is the best test of truth; for that it will not stick where it is not just. I deny it. A truth learned in a certain light, and attacked in certain words, by men of wit and humour, may, and often doth, become ridiculous, at least so far, that the truth is only remembered and repeated for the sake of the ridicule.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“I will not adopt that ungenerous and impolitic custom so common with novel writers, of degrading by their contemptuous censure the very performances, to the number of which they are themselves adding—joining with their greatest enemies in bestowing the harshest epithets on such works, and scarcely ever permitting them to be read by their own heroine, who, if she accidentally take up a novel, is sure to turn over its insipid leaves with disgust.”
—Jane Austen (1775–1817)