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## Ballroom Dance## J M (Mike) Nelson |

## Box Step MathThe box step is the most iconic, stereotyped, misunderstood, abused, and neglected "step" in partner dance. It is also the most versatile, whether the dance is ballroom, country, or folk. It is also the most ubiquitous, and its simplicity and its versatility often go unrecognized. The simplicity lies in its limited parameters, two sets of steps, three steps per set, with each set tracing a portion of the perimeter of a rectangle. The two sets are often referred to as "first half" and "second half" of the box. In addition, depending on the dance style, the first step is foot-specific, e.g. in American Style, the man begins with his left foot and the woman her right foot. The versatility of the box step lies in its symmetry in time and space. Each partner mirrors the other in space and reflects the other in time. Thus, that which can be done in one direction can be done alternately in the opposite direction. These characteristics give rise to an easily-acquired variety, and, in combinations related to direction, time, and step length, result in an enormity of easily-executed "steps." To wit. Given the limitations of a starting foot, there are exactly three directions for the first step of the first half of the box: forward, backward, side. If one categorizes step length options as short, medium, long, there are exactly three options for the length of the first step. The two, common timing options, "slow" and "quick," provide two timing choices for the first step. Thus, there are exactly 3 x 3 x 2 = 18 ways to take the first step. Given the same options for the remaining two steps, there are then 18 x 18 x 18 = 5,832 ways to complete the first half of the box, and there are 5,832 x 5832 = 3,4012,224 ways to complete the box step. Clearly all these options are not practical, and many perhaps impossible. Even so, if we examine our use of the lowly box step, we likely implement more variety than we realize. If by now your "head is spinning," consider that we have not yet incorporated the option to turn. If we consider only the directions for a turn, right or left, we double the options to 68,024,448 ways to implement a box step with an underarm turn. Perhaps it is no cliché to say that when we dance, we're always learning, but even the beginner likely knows more "steps" than they realize. Thinkaboutit. |

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