An example of tiling the plane with regular hexagons. Well, maybe not the whole plane, but you get the idea.
A valid tiling of the plane means that everything fits together perfectly–no gaps.
A nice simple little exercise is trying to figure out which regular polygons can be used to tile the plane like this. The next step is to allow the use of more than one kind of regular pentagon, and so on.
I am very proud to be a 2010 recipient of the Sloan Award for Excellence in Teaching Science and Mathematics.
The awards are given out by the Fund for the City of New York, and are sponsored by the Alfred P. Sloan Foundation.
This award is particularly meaningful as selection is based on testimonials from current and former students, colleagues, and administrators. It is a true honor, and the award ceremony was an uplifting and humbling experience.
As many speakers mentioned–both invited guests and award winners–if more organizations like FCNY and the Sloan Foundation can celebrate teaching, perhaps that will change public discourse on education for the better.
A brief writeup of all the award winners can be found in today’s Cityroom Blog at the New York Times.
http://cityroom.blogs.nytimes.com/2010/11/18/sloan-awards-are-given-to-eight-teachers/
At Math for America events, guests are traditionally invited to find their seats in some math-y way. (This is just one of the many ways MfA uses math creatively at their functions). Here is my seating card from a recent dinner at the MoMA.
The keynote speaker, Dr. Eric Lander, is, among many other things, a mathematician-turned biologist who has been working on the human genome project. Dr. Lander gave a remarkably clear explanation of the inherent mathematics of genetics. And, as a lover of number theory, Dr Lander expressed some appreciation for the seating assignments.
Dr. Lander pointed out that the mathematical fact on display here is that every integer can be expressed as a sum of four squares. This is commonly known as the Lagrange Four Square Theorem.
Here are a few examples of the phenomenon:
Dr. Lander, a former International Mathematics Olympiad competitor, said that it is fairly easy to show that you need at least four squares to express every number as such a sum, but it’s much harder to show that you need at most four squares to get the job done.
Of course, the words “easy” and “hard” probably have unique meaning to someone cracking the human genome for a living!
Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
http://learning.blogs.nytimes.com/2010/11/17/test-yourself-math-nov-17-2010/
This question was based on a new world record in computational speed set by a Chinese supercomputer. We’ve officially fallen behind
There’s an interesting article in the NYT about the economics of baseball’s revenue-sharing system.
The revenue-sharing system is essentially a robin-hood style redistribution of baseball income, taking money from the most profitable teams and dividing it up among the least profitable. The system, in theory, gives smaller-market teams a chance to compete with their big-market brethren by providing them with addtional cash to invest on players. But are the recipients of these baseball bailouts really using the money to improve their teams? Thanks to an anonymous leak last summer, the public was given an unprecedented look at some MLB financial information.
It was quite interesting to see that the Pittsburgh Pirates, who not only have posted a league-record 18 consecutive losing seasons but also rank near the bottom of the MLB in both popularity and team payroll, have actually been quite profitable the past few years. For example, in 2007 and 2008 the Pirates, who routinely traded away their best players, not only made around $30 million in profit but also collected around $70 million in revenue sharing payouts!
Maybe the owners of the Pirates have figured out that spending their yearly $35 million bonus on players doesn’t increase revenue enough to make it worthwhile. Why not just take the safe money? Not a bad year for a business that hasn’t seen success in two decades.