Many years later I got a chance to work on a Java Swing knot visualization tool for students. The tool took declarative descriptions of knots and created projections (visualizations.) It supported knot invariants, diffs, Reidemeister moves and various other operations. No other project has caused as many brain sprains, and no other project has created as much satisfaction upon completion. What was your favorite project?
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Dan Starr: Do you remember the name of that knot theory book? I'm intrigued by your mention of prime knots, knot polynomials and transformations applied to knots.I was afraid someone would ask this :-) Its been too long. I don't remember the title, but I'll ask Brent next time we talk. A prime knot, as you might expect, is a knot that cannot be decomposed into two nontrivial knots. Nontrivial just means they aren't simple loops (the unknot.) You can add prime knots by clipping them and joining the ends. This creates a composite knot.
Dan Starr: I like stumbling on to instructive tutorials about math topics which are palatable to students or people with basic math knowledge. Webpages like these were nonexistent when I was young and I think could be really useful for teachers to foster more curiosity in students.We were just having a conversation about this in the office. If someone had shown me basic knot theory in say, junior high, I would have spent a lot more time on math at a young age. I took a look at some high school math books at a friend's house the other day and they seem very much as I remember them - unnecessarily boring. Topology fields that are easy to visualize seem like a great way of getting young minds excited about math while driving home the essential point that math is about more than pushing numbers around. We leave the explanation of its abstractness, power and beauty until far too late in the educational process.
Dan Starr: Somewhat related: I'm a big proponent of open sourcing US educational plans and material - it can only improve things.I agree. I think the availability of free, high quality educational material is a good metric for the sophistication of a society. Everyone benefits in manifold ways.
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