"Steve Gray" <stevebg@adelphia.net> asks:

Questions related to the one I posted earlier today: Pick 6 random points A,B,...F uniformly distributed inside the unit sphere and in general position ( no 4 lying in a plane). (So we agree on the meaning, just pick -1 < x,y,z < 1 uniformly and independently and throw out points outside the sphere.) What is the probability that the closed polygon ABCDEFA forms a "stick knot"? Is there an easy way to show that 6 is the minimum? It's easy enough to convince oneself that it is, but that's not much of a "proof.") Find 6 points having the greatest number of sequences (permutations of the string) which form knots. Also the least number. Something I asked a year or so ago: Characterize knottedness with inequalities among the coordinates of the 6 points and polynomials in them, or whatever algebraic or other techniques it takes. In general how would one write a reasonably simple program (if possible to determine knotted/unknotted? Generalize to N>6 points. How many stick-knot topologies are there for N points? What is the probability for each? Where does this computation lie in the P,NP, etc. spectrum? Do any of these questions fall into the category of "officially unsolved problems" or ones of long standing? Steve Gray