Between the Folds

Happy New Year everyone! Almost time to get back to class, but it should be pretty fun. In the first week back I plan on showing my students the film Between the Folds, a very interesting look at origami, some of its eccentric artists, and the way it relates to math and mathematical thinking. I recommend this film to anyone interested in the arts, creativity, and/or math, from a couple very simple rules (one page, no cutting or pasting) you can produce an infinite array of figures, and in fact it is these limitations that feed the creative force behind the artform.

Classic case of Girls v. Boys

Verdict: case thrown out. Ive never really given too much trust to these types of studies of one gender performing better or worse than the other. Unless the figures consistently come out overwhelmingly lopsided either way, we dont have anything to worry about with this issue.

Sometimes it seems that people assume that these types of results have to be exactly 50/50, but that not true. In reality, one side is almost always going to come out a little bit better than the other, just like coin flips - sure each side is equally as likely on average to come up, but flip a coin 100 times and I'll be surprised if you get a perfect 50/50.

I count myself lucky to get to witness an age in which all sorts of glass ceilings are being shattered, and understand how these types of studies could have interesting facets and social implications, but it seems like they are conducted just to have a headline either way and its always implied that "something must be done because the losing gender is falling behind." I think it would be more constructive to focus on better teaching to both genders in general rather than worrying too much about one or the other.

Today I learned...

That the reason pizza becomes strengthened and doesnt drop all the cheese and toppings onto your lap when you fold a slice down the middle is due to the mathematician Gauss's Theorema Egregium. Something you always know intuitively but dont know why.

From Wikipedia:
"An application of the Theorema Egregium is seen in a common pizza-eating strategy: A slice of pizza can be seen as a surface with constant Gaussian curvature 0. Gently bending a slice must then roughly maintain this curvature (assuming the bend is roughly a local isometry). If one bends a slice horizontally along a radius, non-zero principal curvatures are created along the bend, dictating that the other principal curvature at these points must be zero. This creates rigidity in the direction perpendicular to the fold, an attribute desirable when eating pizza, as it holds its shape long enough to be consumed without a mess. This same principle is used for strengthening in corrugated materials, most familiarly corrugated fiberboard and corrugated galvanised iron."