I can think of many interesting dance-related subjects--though it greatly depends on what class the paper would be for (assuming it's for a class and, of course, what sort of dancing we're talking about.
The social aspects are what I find most interesting, especially the whole idea of someone going to a dance... and, well, dancing (dancing? Dancing! :shock with random strangers. Some of the ballroom dances can be rather "intimate"; Tango, for instance, or the Charleston--and there are plenty of other examples. This behavior (close physical touching with strangers) is socially acceptable, but, say, running up to a total stranger and giving them a "PC hug" is not.
And that's just one rather wacky angle to it of many. If the social aspects aren't interesting to you (or would be inappropriate material for Algebra class), then there's the blatantly obvious history schtick. Exactly which drunken Chinese ex-kung-fu instructor came up with the Charleston, and why wasn't he kicked out of town on a rock step? Who is that mystery guy that showed up in every social dance photo taken during the 1920s and what exactly does he have to do with the Hindenburg disaster? Can "dance mathematics" help those less-fortunate souls to learn math in bases 3, 4 or 5?
If that's no good, there are many other topics that can be fruitfully debated... Did/does/will dancing impose some sort of genetic evolutionary pressure on humans that's resulted in most people being given one left foot and one right foot? What does Salsa the dance have to do with Taco Bell's "salsa" condiment, and will this horrible conflict be resolved in our lifetime? Why does all Latin dance music sound the same (except for Tango) and what can you, the reader, do about it? Would juvenile crime be forever erased from our planet if every child learned to dance the Froog?
Finally, there's the personal touch. Tell your own dance story--about how you got really [drunk/wasted/hypnotized by Arthur Murray/beaten up by dance gangs] and how this has led to a life of pining for pine wood fjords (er, sorry, floors) and the incessant monotonic rhythmic chanting of "One...Two...Three...One...Two...Three". About how your entire life was destroyed by that awful night of trying to dance slow waltzes to Vietnamese Waltz dance music.