- Michi’s blog » archive for 'Knot theory'
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Applied knot theory
- March 16th, 2009
Tech note: All figures herewithin are produced in SVG. If you cannot see them, I recommend you figure out how to view SVGs in your browser.
A few weeks ago, my friend radii was puzzling in his server hall. He asked if it was possible to prove that what he wanted to do was impossible, or if he had to remain with his gut feeling. I asked him, and got the following explanation:
He had two strands of something ropelike, both fixed at large furnishings at one end, and fixed in a fixed sized loop at the other. He wanted to take these, and link them fast to each other in this fashion:
I started thinking about the problem, and am now convinced I can prove the impossibility he asked for by basic techniques of knot theory. The argument is what I’ll fill this blog post about.
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Restarting high school topology
- May 21st, 2008
My two high-school kids came by today. We’ve been trying to get a new teaching session together since early February, but they had a hell of a time all through February, and all our appointments ended up canceled with little or no notice; and then I spent March and April on tour.
We pressed on with knot theory. Today, we discussed knot sums, prime knots, knot tabulation, behavior of the one invariant (n-colorability) we know so far under knot sums, Dowker codes, and we got started on Conway codes for knots. Next week, I plan for us to finish up talking about the Conway knot notation, get the connection between rational knots and continued fractions down pat, and start looking into new invariants.
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Michi is a recent PhD working in homological algebra and applied algebraic topology. This blog is his outlet for texts with some manner of thought put into them. Over at his LiveJournal intimate details and streams of consciousness might be found.
Not all here is mathematics. All here, though, are my personal thoughts and opinions. Please read the about page (linked above) for more details.
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