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Contra Dancing and Mathematics

Last week I met Larry Copes at the American Mathematical Society and Mathematical Association of America joint meetings in Baltimore, MD, USA. He gave an presentation on the mathematics of contra dancing. He tried to find what I call an omnicontra dance, a dance that omninates through all of the possible dance positions. After some searching and discarding of dance steps that would be rather unnatural, he found 4 good dances.

I too have done some work with the mathematics of contra dancing. I relate it to group theory and compare it to changing a mattress. My article states that the contra dancing foursomes group is the group of symmetries of a square, also called D4. In addition, the overall procedure of passing down the line in contra dancing is also a group, Dn, where n is the number of foursomes in the dance. Today I tried to find the overall group of all of these actions, for eight contra dancers. I used some software to find a group with 384 elements in it; this contains some steps that would never occur in a contra dance, such as the next set of foursomes circling around before the previous set has finished its moves and switched the two partners. I think it may have 64 elements, but am not certain.

Then I actually went out contra dancing and danced in 6 of the dances. It is quite different actually dancing it then analyzing it. I met quite a few people tonight, mostly women. What struck me the most is that people from ordinary walks of life, with little or no knowledge of mathematics, are able to execute all these moves in the required order and move about in a group with maybe hundreds of elements in it. The band was good - a group named Orion. It is also a good way to introduce people to group theory. If I ever teach a course in college abstract algebra, when I get to the group theory part, I will invite my class to the local contra dance. The best way to learn mathematics may be to become a part of mathematics, and contra dancing certainly does that.