The headline that Occupy Math first noticed told him that a new shape had been discovered — and as often happens, the journalists had focused on a simple and relatively minor point in the story. The new shape is called a scutoid, two adjacent scutoids are shown above, and the big story is that a mathematical model was used to explain a very clever solution to making your skin and the lining of your blood vessels stable and strong. These parts of your body are made of epithelial cells and they are packed to achieve high stability.
This is a second image from the 252-Mandebrot set Occupy Math is currently exploring. It looks like a map of somewhere — a fairly unusual feature for a Mandelbrot set.
Occupy Math has posted about fractals and, in particular, about the Mandelbrot set before. This week Occupy Math is announcing a new discovery inside a strange variation of the Mandelbrot set, the 232-Mandelbrot. The full set is shown above. Unlike the Mandelbrot set the 232-Mandelbrot set is not connected and it is also pretty lumpy. The normal Mandelbrot is generated by squaring over and over. The 232-Mandelbrot is similar, but you go square, cube, square, repeat, so the arithmetic is a bit more complicated. Occupy Math found something really odd inside it.
This is the first image of the week from Occupy Math’s exploration of the 252 Mandelbrot set. These irregular autumn plant like growths are not present in the normal Mandelbrot set.
This week on Occupy Math we are looking at the Ultimatum Game. This is a two-player mathematical game with two roles. The game has $100 at stake. The first player, the proposer, suggests a division of the money. The second player, the responder can accept or reject the proposal. If he accepts, the money is paid out according to the proposed split; otherwise, no money is paid out. This game is used by economists to understand economic behavior. In this post we discuss some of the issues with using this game and propose an activity based on the ultimatum game.
A very deep zoom into the Mandelbrot-232 fractal.
Occupy Math’s editor spent a year in Americorp running a “safe to be smart” program at a library in Rochester NY. Smart kids needed a place to study where people would accept them for being smart — people thought being smart was a way out of the community and viewed it as a form of betrayal. This dysfunctional viewpoint is helped along by institutional racism. Most of the white people left Rochester for its suburbs during the school bussing controversy. At present Rochester is a poor city surrounded by relatively affluent suburbs. One effect of this situation is that the schools in Rochester are in terrible shape — which leads me to the man pictured above, Robert P. Moses and his Algebra Project
This is a Mandelbrot fractal using the standard Mandelbrot iterator followed by the third power one, then the standard one again. This is a field of fractal flowers!
One of the big issues that interests Occupy Math is the teaching of mathematics. In earlier blogs we have looked at teachers being blamed for things that are not under their control, problems with teachers being chained to high stakes standardized tests, math teaching strategies that implement fads without understanding them, teaching topics in silos, and the problem of thinking of math as a form of ritual magic. Parts of this last topic are examined in finer detail in today’s post, where we look at the difference between formal math and understanding math.
Occupy Math’s image this week is one of the hybrid (2nd/3rd power) Mandelbrot sets. This one looks like the coast of somewhere.