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 Mathematical Ballroom Dancing
Mathematical Ballroom Dancing
Houston Euler
In [1] Yardley Beers refers to work done on a mathematical theory
of ballroom dancing, but those results were never published.
Much progress has occured in this field during the subsequent years,
but again nothing has appeared in print,
the results just circulating as folk dance theorems.
It therefore seems appropriate to give at least a brief survey
of the many approaches that have been pursued.
Integration and Measure Theory
Since every piece of dance music is a composition of several measures,
this approach can be used with great generality.
Typically, a dance will be expressed as function  such that
 equals the place where the dancer steps at time 
In other words, is a step function (or sometimes named after
one of the leading exponents of this method, Astaire step function),
so its integral is easy to compute.
Plane Geometry
Although elementary geometry is more often associated
with square dancing, it has also been successfully applied
to Latin ballroom dances, such as the rhomba.
With another Latin dance, properties of circles
have yielded the famous Lemma on Merengue Pi.
Point-set Topology
Jitterbug dances lend themselves well to topological methods,
expecially those dances whose main step occurs
on the second count of a measure.
These second-countable dances are exemplified by the Lindylof.
Vectors
Techniques from elementary linear algebra and vector calculus
are helping in dealing with a variety of dances.
It suffices to mention the use of tango vectors
and the polka-dot product.
Reference
1. Y. Beers, in "American Institute of Useless Research", A Random Walk in Science, ed. by R. K. Weber and E. Mendoza,
The Institute of Physics, 1973, pp.23-24.  |
Linear Mode
