Predicting Partitions

This recent news from the American Institute of Mathematics:

January 20, 2011.   Researchers from Emory, the University of Wisconsin at Madison, Yale, and Germany’s Technical University of Darmstadt discovered that partition numbers behave like fractals, possessing an infinitely-repeating structure.

In a collaborative effort sponsored by the American Institute of Mathematics and the National Science Foundation, a team of mathematicians led by Ken Ono developed new techniques to explore the nature of the partition numbers. “We prove that partition numbers are ‘fractal’ for every prime. Our ‘zooming’ procedure resolves several open conjectures,” says Ono.

Accompanying this result was another achievement developing an explicit finite formula for the partition function. Previous expressions involved an infinite sum, where each term could only be expressed as an infinite non-repeating decimal number.

Counting the number of ways that a number can be ‘partitioned’ has captured the imagination of mathematicians for centuries. Euler, in the 1700s, was the first to make tangible progress in understanding the partition function by writing down the generating series for the function. These new results involve techniques which could have applications to other problems in number theory.

[original article]

Wired.com also just reported on it, and you can find their coverage here.

Vi Hart’s Blog

It’s high time I gave a bit of press to Vi Hart’s Blog. If you haven’t checked it out, do so right away. It’s brilliant.  A number of people have pointed me to her blog, including one of my Calc students. Her little math videos are fresh, funny, and insightful. Denise, at Let’s Play Math, gave her some press too, which is what reminded me to finally make this post. Here’s the video Denise highlighted (the most recent of Vi’s creations):

This is particularly appropriate because there were a couple of us in our math department discussing this very question: In total, how many gifts are given during the 12 Days of Christmas song? It’s a nice problem, perfect for a Precalculus student. Or any student. Here’s a super nice explanation of how to calculate this total, posted at squareCircleZ. But before you go clicking that link, take out a piece of scrap paper and a pencil and figure it out yourself!

Here’s another nice video from Vi Hart:

You could spend a lot of time on her site. Here’s another awesome video. I’ll have to have my Precalculus class watch this one when we do our unit on sequences and series.

And you’ve got to love the regular polyhedra made with Smarties ,  right?

Plus, Vi Hart plays StarCraft, which is awesome too.  Back in the day, I really loved playing. I haven’t played in a while, and I certainly haven’t tried SC 2 yet, because then I’d never grade my students’ papers.

Bottom line is, you need to check out all the playful stuff Vi Hart is doing at her blog. Happy Wednesday everyone!

 

Benoit Mandelbrot

I know this is old news, but I wanted to make sure and acknowledge that mathematical great, Benoit Mandelbrot passed away twelve days ago on October 14. There’s a nice set of videos on the TED blog if you care to check them out, including this TED talk that Benoit just gave in February of this past year:

At some point I’ll have to post more about fractals, for my own sake. I’d like to research them a bit more and make some of my own. For some beautiful fractals that appear in nature, you can see this post.