In general, determining whether or not a tangled loop is a knot or unknot is still an unsolved problem. In 1961, Wolfgang Haken determined one algorithm, but it is considered far too complex to be usable. In 1976, Dr. Haken proved something simpler, the four color theorem. The Wolfram Demonstrations Project has various knot diagrams, and a demonstration for how 7 points are intrinsically knotted. A good place to learn more about knots is the KnotPlot site.