21 December 2007

Links for 2007-12-21

Mathematicians solve the mystery of traffic jams, which has been making the rounds lately. Basically, sometimes traffic jams come out of nowhere because someone taps their brakes and the traffic propagates backwards. I remember reading this ten or fifteen years ago. It must be a slow news day.

Thanks to Wing Mui, The trouble with five by Craig Kaplan. Why is it that we can tile the plane with triangles, quadrilaterals, or hexagons -- but not pentagons? And what sort of structure do tilings with some sort of fivefold symmetry have?

Also, a few days ago I wrote about Galileo's argument that the thickness of bones should scale like the 3/2 power of an animal's height, which I learned about from Walter Lewin's lectures, but that this turns out not to be true. Having gotten a bit further into Lewin's lectures, I found out that the real thing we're protecting against is buckling, not crushing.

Greg Mankiw a couple months ago provided a link to a paper on optimal mortgage refinancing by Sumit Agarwaland, John Driscoll, and David Laibson. The Lambert W function (the inverse of f(x) = xex) turns out to be good for something! If you use this, I want a cut of your savings for pointing you to it.


Anonymous said...

Do you know if it is possible to continue on as in Figure 3 in ``The trouble with five,'' with more and more complicated figures, if necessary, to give a tiling of R^2 with 5-fold symmetric pieces?

Blake Stacey said...

There was a computer kiosk thingy in the Boston Museum of Science about, oh, five years ago, which demonstrated how traffic jams happen. That part is old news. There are still open questions in traffic modeling, of course, and people are busily at work inventing new schemes for traffic-light synchronization and all that. See, e.g., arXiv:nlin.AO/0411066.

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