Today we celebrate a Derangement Day! Usually I call a day like today a permutation day because the digits of the day and month can be rearranged to form the year, but there’s something extra special about today’s date:
The numbers of the month and day are a derangement of the year: that is, they are a permutation of the digits of the year in which no digit remains in its original place!
Derangements pop up in some interesting places, and are connected to many rich mathematical ideas. The question “How many derangements of n objects are there?” is a fun and classic application of the principle of inclusion-exclusion. Derangements also figure in to some calculations of e and rook polynomials.
So enjoy Derangement Day! Today, it’s ok to be totally out of order.
My complete interview with Steven Strogatz in the February 2014 issue of Math Horizons is now freely available.
Math Horizons makes one article from each issue freely available online, and I’m thrilled that for the February 2014 issue they chose my piece. Professor Strogatz is an acclaimed mathematician, writer, and teacher, and I think this interview captures a small amount of his enthusiasm, insight, and brilliance in all these fields.
The full interview is available as a PDF here. You can also find our conversation about math education in the Aftermath section of the magazine (posted online here), as well as some bonus material from our conversation here.
Today we celebrate another Permutation Day! I call days like today permutation days because the digits of the day and month can be rearranged to form the year.
Celebrate Permutation Day by mixing things up! Try doing things in a different order today. Just remember, for some operations, order definitely matters!
We’ve been discussing center of mass in class recently. While this powerful idea extends well beyond its physical interpretation, it’s good to frame the conversation around the idea of balancing objects on their centroids.
One student was inspired by the claim that all physical objects have centroids, and that they can be found fairly easily. So he took a small plate of aluminum, drilled a bunch of random holes in it, and tried to find its center of mass.
He claimed he had done it. But how could we test his hypothesis? It seemed like there was only one way!
It took us a while, and a few attempts, but we were able to do it! It created a nice little challenge for us, and a nice physical experience with the center of mass.
Through Math for America, I am part of an ongoing collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here
Test Yourself — Math, April 2, 2014
This question refers to an article about how dynamic ticket pricing has put the musical The Lion King back on top of the Broadway box office. Approximately how many people see the musical each week?