The Ladies Chained

Viewpoints Conference Math and Folk Dance Presentation

About two weeks ago I gave a talk titled Patterns and Mathematics in Traditional Folk Dances at the Viewpoints Grand Reunion Conference. The presentation is the final result of a combination of a workshop on math and contradancing that I taught with my colleague Amy Cann, lots of late night conversations and thinking while preparing to teach that class and some communication with a mailing list full of dance callers. In the presentation I spent most of my time talking about contradancing, though there are some stuff in the end about maypole dances, sword dances and waltzes. Since I promised at least several people a copy of my slides I’ve decided to just put them up here.

Slides for Math and Traditional Dance talk at Viewpoints 2008 (12MB PDF file)

There are several important caveats regarding these slides.

1. The file is a 12 MB PDF file because of a good number of pictures and diagrams.
2. There are spelling mistakes and typos. I can’t fix them because the original Keynote file is 100 miles away on another computer.
3. This is the 60+ slide version along with many slides that I did not actually present. So it should be more understandable without my endless ranting. The last bits are, however, still quite incomprehensible with the slides alone.
4. The bibliography is not actually done yet. I’ll post it here once I have it done.

Currently I’m trying to turn the presentation into a paper. If you have any suggestions or ideas or whatever, send me a note!

Bending a Line of Four

So let’s talk about that post with the diagram that I said had something to do with a contradance.

In the last week, caller and fiddler Amy Cann and I co-taught a seven-day-ish course called Patterns and Mathematics in Traditional Folk Dancing. It was basically a short, intensive workshop on analyzing contra and English country dances as mathematicians, dancers and choreographers. The goal was to use mathematics to help us become better dancers and choreographers. As part of the course, Amy solicited from a dance caller’s mailing list various caller’s lists of favorite and least favorite transitions. The diagram I had in the previous post is a still from an animation that illustrates a geometry problem that came from one of these transitions.

First, let’s look at the problem mathematically.

In the diagram above, we have segment a formed by points A and B and segment b formed by points C and D. The goal is to rotate segment a as one rigid object on to segment b so that point A rotates to point C and point B rotates to point D. In order to do that, we need the center of rotation. This is not a hard geometric problem; it takes some thinking, especially if your geometry is rusty, but it’s perfectly solvable using straightedge and compass in a few steps.(Side note: I proclaimed when giving this problem that I did not expect any of my students educated in the United States to be able to solve this problem. I was half right; two of our students solved this problem: one learned geometry in Germany and the other in a Waldorf school in the United States. Double side note: I’m considering sending my kids to Waldorf schools. Triple side note: I don’t have any kids yet and don’t really plan to have any.)

The fun part is where this problem came from!

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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.

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.

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Math and Contradancing Link Dump

This entry has three purposes. First, I want to get all these links in one place and, somehow, I don’t use bookmarks. Second, in case you are ever looking for a list of relevant links to the relationship between contradancing and mathematics, you found it. Third, apparently I am on the first page of Google if you search for some combination of the words “mathematics” and “contradance” in their various forms. Whoever clicks on that link would be left completely unsatisfied because it leads to a dead-end page (my online CV with the title of two talks I’ve given on the subject). So let me pick up the slack and actually write something useful on the subject; by that I mean I will try to compile on the relevant links on the subject. Why write my own blog post when others can write it for me?

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