One bit of good news

I think that I finally figured out how to proceed on a problem Now to get to it this afternoon. Who knew that knots in tori could cause so much trouble?

For the uninitiated: imagine a solid torus (bagel) that is twisted into some knot. Now imagine a more complicated curve inside the knotted torus that goes all the way around, possibly several times. The knot represented by the solid torus is said to be the companion knot of the more complicated knot, and the more complicated knot is said to the be the satellite knot of the knotted torus.

In the second diagram, the crudely drawn red represents a knotted solid torus that contains the more complicated black knot. Note: there are at least two other “obvious” companions: the figure 8 and the trefoil.

Workout notes it was only 76 F with 57 percent humidity ..but the non-shade of the 5.2 mile course got to me; today’s “easy” run (shuffle) wasn’t as easy as I had hoped. I then did 15 minutes on the bicycle to cool down. I really need to practice bending my knees as I run.


June 5, 2018 Posted by | mathematics, running | Leave a comment