Some Contradance Thing
The reason for the radio silence is because I’m working on something. This something is a class, a workshop, a talk, a bunch of lunchtime conversations and not getting enough sleep. Here’s a pretty picture. I’ll tell you that it’s related to math and it’s also related to contradancing. I won’t tell you how or why, because I want to ask my students that question and I don’t know the exact ramifications of this yet. I will tell you that the top of the picture is the top of the dance.
The problem was posted by my colleague Amy Cann, solved by fellow math teacher Abihah Reed on a napkin, and I just made this drawing of the solution on GeoGebra.
Subscribe to the comments for this postTablets, Revisited
A week ago I finally caved in and got myself a Lenovo X60 Tablet PC. ($989 new on eBay.) One week-long retreat later I got it in my mailbox upon my return last night; I’ve been playing with it since then. Did I say play? I meant to say “exploring it with an intent to create innovative pedagogy for use in the mathematics classroom”.
Note: I’m actually typing this on my MacBook because it’s hard to write long things using a tablet; I am also too lazy to revert it to laptop mode from tablet mode. Also, I really like OS X much better than Windows XP (which is still better than Windows Vista, I suppose) for things that I don’t need a tablet for. Read on for some initial impressions and reasons why I bought one of these things.
Why Doesn’t Circling Right Feel Right
During my brief stop at the NEFFA festival last night, I was in two contradances that included circle rights. Most people around me neither expected nor remembered the circle rights; it just didn’t feel right during the first few times. The entire hall just fell into a little lull. In fact, my shadow for one of the dances had trouble with it about half the time; she seems to be a very experienced dancer, and was fabulous with everything else.
So why does circling right feel weird? In the twenty minutes that I had to think about this in the shower, this is the best answer I can come up with from a dancer/mathematician’s point of view: circling right is the contradance figure that contains the clockwise motion with the largest radius.
If you’re one of my four students who will be studing contradancing and math with me next month, you don’t get to read the rest. Instead, you get to think about it on your own.
Nature Where There was None
This fractal food web site has been floating around for a while. Other food and plant-related fractal pictures aren’t hard to find either. But more recently, there are some “fractal food” web sites that reverse-engineer fractal structures into food. There’s the “fractal pizza”, which seems to be a recursive layering of pizza upon pizza. And then there’s Sierpinski cookies, which is a bunch of cookies that form estimations of the Sierpinski carpet.
Is it just me or does it feel very unnatural to put fractal structures and patterns into foods that didn’t contain them to begin with? Bonus question: would this be a good excuse to bake cookies instead of having class one of these days?
Tablets
Recently I’ve been thinking whether I want to teach with a tablet PC. Two of my colleagues in the department teach math from tablets and they are having moderate/great success with it. Currently I’m using whiteboard and marker and maybe a projection of a diagram or animation once in a blue moon, which works but probably isn’t optimal.
Here’s a list of reasons for or against tablets:
Good: It’s an excuse to buy a tablet PC.
Bad: It requires buying a tablet PC.
Bad: It requires using Windows unless I want to shell out for a Modbook.
Good: Class notes are automatically created and students don’t have to copy anything.
Bad: Class notes fall to me, which means more work.
Good: Not facing the board means that the class is more seminar-like.
Bad: The board is twice as big area-wise as the projector screen.
Bad: The projector screen has a resolution of 1280 by 800, which is very small when you deal with handwriting and diagrams instead of typesetted text.
Bad: I need to be 100% sure that the projector will work, which I am not sure of.
Good: I will never have to buy a whiteboard marker again!
Bad: A tablet PC costs as much as 2000 markers.
So I think, for now, I’ll stick with whiteboards. Maybe when we have a nice, affordable wall-mounted touch-screen, then I’ll think about this again.
Graduation Requirements
A few hours ago a student whose senior project I’m supervising (read: I yell at her whenever she unintentionally makes things explode or destroys the county’s power grid) saw a bunch of large, long, empty boxes in the back of the auditorium. She started talking about how they would lead themselves to great organizational systems for gels for stage lights and started dreaming about how she would make dividers and other wonderful knick-knacks for this marvelous system. Then she dropped down to earth and started talking about her lack or time and motivation and started doubting her crazy idea.
So I told her that turning these boxes into a storage system is now part of her project and thus part of her graduation requirement.
Like I saw her, she grabbed one of the huge boxes and ran away towards the light board in the back.
God Hates The World
A friend recently sent me a link to a YouTube video of God Hates The World, a song about how God hates the world and everything in it. This is not a joke. This is not satire. It is in fact a song about how God hates us all and everything will burn as written and performed by members of the Westboro Baptist Church.
My thoughts about this:
- That soloist is rather bad.
- The flag they are insulting is… Canadian?
- I’m pretty sure they can do better with the arranging.
- Wait a second. There’s already a much, much, much better song about God burning sinners.
- They’re not even using a real piano!!!
Hot Girl Graph Theory
Via Reddit, here is a video segment of some Japanese people testing an algorithm for finding the most attractive female in Italy. They first find a random woman on the street and ask her to introduce them to her most attractive female friend. Then they ask said friend to introduce them to her most attractive female friend. And so on. I’m not clear when this algorithm terminates because I don’t know Japanese.
Even if women can be put into an objective total order this is a horrible algorithm. It’s very easy to see that it doesn’t always reach the maximal element in an arbitrary set of women. (Quick counterexample: start with the third most attractive woman, who know the second and fourth most attractive women; the second most attractive woman does not, however, know the most attractive one. Quicker counterexample: a disconnected set where the most attractive woman has no friends.) And you’re not guareenteed to “go up the ladder” at every step, since the most attractive woman than a woman knows may be herself! In fact, because of this, this algorithm never terminates and goes into an infinite loop even if it finds the most attractive woman in a set.
And besides, even if you find her, hot girl probability theory dictates that she’s already taken.
Concerning SquarO
Through a link on Reddit I found a game called SquarO. The game gives you a square grid with numbers in each square. The number tells you how many black vertices the square has. The goal of the game is to color in the vertices/lattice-points of the grid so that each square has the correct number of black vertices. It’s like a reverse Minesweeper. The “official rules” are here.
The rules page says that each of the grids in the game has a unique solution. This is obviously not true for any randomly generated grid with arbituary numbers placed in the squares. For a grid with multiple solutions, just place a 1 in all the squares. For a grid with no solutions, put a 1 in every square except for one, and put a 0 in that square. Since the game has hundreds of different puzzles I’d assume that they have a way of checking whether a grid has a unique solution. It could just be a brute force algorithm; the game doesn’t seem to generate these grids on-the-fly as they are numbered, so whoever designed the grids don’t have to check for a unique solution very quickly.
Calculus Based Web Host
I came back home from the Western Mass Sacred Harp Convention (possibly more on that later) to discover that this blog was completely down. Turns out my web host got its power shut off intentionally and unexpectedly; as you can probably see they just brought everything back up running.
Before they died, though, I actually wanted to post about their new pricing scheme. Before, they charged $1 for every GB of bandwidth used. Now, the more bandwidth is used the less they charge per GB. More precisely, the price per GB is based on a logarithmic scale. Even more precisely,
