Tight knot video by Henry Segerman — very cool!
I was thrilled yesterday to see this very cool video posted by Henry Segerman, showing some of the tight prime knot models that I did with Eric Rawdon, Michael Piatek, and Ted Ashton. Thank you, Henry! (I don’t actually have printouts of the models as nice as the ones in the video, since the shapes are actually quite tricky to print without extensive support material!) But this is a really great explanation of what that project was all about.
It’s worth saying that the problem of finding an explicit parametrization for the trefoil knot (or any other) is still open, though Pieranski and Przybyl have amazing data now which gives some great clues to what the structure has to look like.