A fellow asked a question about computing the "writhe" of the trefoil, although that comment seems to be missing now. FWIW, the easiest way is probably to project the knot down into a series of crossing, give the knot an orientation ( pick a direction an ant would walk along it, say), and then look to see if the crossings are positive or negative. This is typically defined by rotating the two-dimensional projection of the crossing so that both arrows associated to the crossing are pointed up *after* the crossing. It can be tricky to do this, so it helps to draw a lot of arrow heads and rotate the paper around. Defining which is positive or negative (whether the left or right strand is on top) is a matter of convention. Once you set that convention your results should agree with everyone else's up to an overall minus sign. For the specific case of the trefoil, all the crossing have the same sign, so it has three.
A fellow asked a question about computing the "writhe" of the trefoil, although that comment seems to be missing now. FWIW, the easiest way is probably to project the knot down into a series of crossing, give the knot an orientation ( pick a direction an ant would walk along it, say), and then look to see if the crossings are positive or negative. This is typically defined by rotating the two-dimensional projection of the crossing so that both arrows associated to the crossing are pointed up *after* the crossing. It can be tricky to do this, so it helps to draw a lot of arrow heads and rotate the paper around. Defining which is positive or negative (whether the left or right strand is on top) is a matter of convention. Once you set that convention your results should agree with everyone else's up to an overall minus sign. For the specific case of the trefoil, all the crossing have the same sign, so it has three.
Thank you! This is done very clearly and succinctly!
Request: The Unknot
You are a sparkling star, btw i hope your finger is better