Indeed, the trefoil knot bears a resemblance to a 3-leaf clover.
The trefoil knot can be formed in two ways. The two versions of the knot differ only in the over/under placement of the strands.
It seems like you should be able to flip or re-twist one trefoil knot and turn it into the other. If you give it a try, you will find that it is very difficult.
In fact, it's impossible. It was a long time before this was actually proved, however, and that proof -- the only one that is known -- is far more complicated than a pair of trefoil knots appears to be. It involves looking, not at the knots themselves, but the 3-dimensional space that remains after the knots have been removed. (See also, Seifert Surfaces and topology.)
Often, after a complicated proof has appeared, a simpler proof is discovered. Get some rope, make a pair of trefoil knots, play around with them and try to describe what you see. Maybe you will be the one to say "aha!" and find a simpler proof that the two trefoil knots are not the same.
