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# Dance, Folk

Both mathematics and dance are languages that use symbols to convey ideas and expressions. Mathematics uses written symbols to represent abstractions so that users can arrive at a greater understanding of a problem without ambiguity . Dancers use abstract symbols to represent thoughts, feelings, emotions, and ideas, and these symbols may be interpreted in multiple ways. Both disciplines rely to a large extent on pattern recognition.

Many forms of dance, such as classical ballet, involve complex patterns and take years of practice to master. Yet other forms of dance use everyday movements with more simplistic patterns. For example, folk dances have evolved from common movements of work and play.

Although folk dances require concentration and focus, their use of everyday movement invites observers to participate. Similarly, mathematics can be studied at the basic level of arithmetic, which is used to make simple transactions and to understand how things work. More advanced mathematics, such as calculus , chaos theory , or abstract algebra require years to master.

## Discreteness in Mathematics and Dance

Many dances are based on a simple method of counting and discrete sequences, which enables participants to recognize and learn a variety of dances. The word "discrete" also has a common, similar usage in mathematics. Discrete mathematics involves counting separate elements, such as the number of arrangements of letters on a license place, or the number of ways that a presidential candidate can visit all fifty states. Solutions in discrete mathematics can be only whole units. Discrete math is therefore one of the most accessible areas of modern mathematics since many of the questions are easy for anyone to understand.

Contradancing. Contradancing is a popular form of folk dance in the United States that illustrates the mathematics of dance. Its origins go back to colonial days, and its roots can be traced to English country dances.

Contradancing, which shares elements of traditional square dancing, is a form of set dancing in which a dancer's position relative to another dancer traces patterns on the dance floor. As in most dancing, timing is crucial, as is the ability to rapidly carry out called instructions.

Music for contradancing is highly structured. Everything occurs in multiples of four. In one common format, the band plays a tune for sixteen beats, repeats the tune, then plays a new tune for sixteen beats and repeats. An eight-beat section is known as a call, during which each block of four dancers executes a called-out instruction.

When contradancers line up in their groups of four to produce a long column "down" the dance floor (extending away from the band), each square block of two couples can be thought of as a mathematical matrix with the dimension 2 × 2. Each dancer, or element of the matrix, is in a specific position within the array. The called instructions correspond to rearrangements of the elements (dancers). After sixty-four beats, for example, the first and second rows of the matrix may be inter-changed. Of course, this could be done in one step, but the fun of dancing comes from performing the various permutations by which groups of four can reach the end result.

There are many called instructions in contradancing, ranging in complexity from simply circling once around to the left or right within each group of four to sequences of moves that involve exchanging partners or stepping one-quarter, one-half, or three-quarters of the way around the ring. With each call, the matrix representing four dancers changes. In the final configuration, the two rows of the original 2 × 2 matrix may be inter-changed, or they may be the same as when the dance started.

## Chaos Theory and Dance

Computer scientists have applied the basics of chaos theory to generate variations on dance movement sequences. Special symbols represent human body postures, and positions for each of the body's main joints are encoded by defining an axis and angle of rotation given in the form of a mathematical expression called a quaternion . A motion sequence is then mapped onto a chaotic attractor . Following a new trajectory around the attractor produces a variation of the original motion sequence. To smooth out abrupt transitions introduced by the chaotic mapping, the researchers have developed schemes that capture and enforce particular dance styles.

Marilyn K. Simon

## Bibliography

Devlin, Keith. The Language of Mathematics: Making the Invisible Visible. Chicago: W. H. Freeman, 2000.

. Using Chaos to Generate Variations on Movement Sequences." Chaos 8, no. 4 (1998).

### Internet Resources

Bradley, Elizabeth. "Chaographer and Motion Mind: Using Mathematics to Generate Choreographic Variations." Chaography Software. <http://www.cs.colorado.edu/~lizb/chaotic-dance.html>.

Country Dance and Song. <http://www.cdss.org/>.

## THE COMMUNICATION OF MATHEMATICS AND DANCE

According to Keith Devlin in The Language of Mathematics, mathematics seeks to communicate a sense of what humans experience. The simplicity, precision, purity, and elegance of mathematical expressions and patterns give mathematics an aesthetic value. The mathematical connections to dance similarly give dancers a creative, aesthetic, and interpretive means of expressing the human experience.

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## folk dance

folk dance, primitive, tribal, or ethnic form of the dance, sometimes the survival of some ancient ceremony or festival. The term is used also to include characteristic national dances, country dances, and figure dances in costume to folk tunes. Many children's games, such as "London Bridge" and "The Farmer in the Dell," are traditional folk dances. More elaborate examples are the Spanish fandango, the Bohemian polka, the Hungarian czardas, the Irish jig, the Scottish Highland fling, the Hawaiian hula, and the English morris dance, sword dance, and Maypole dance. American barn dances, such as the Virginia reel, are largely derived from European sources. Early in the 20th cent. Cecil James Sharp, founder of the English Folk Dance Society, made a notable collection of English folk songs and dances. The American Folk Dance Society has done much to preserve the knowledge of old American country dances, and a similar interest has developed in other countries. A popular form of recreation, folk dancing is often taught in schools.

See M. D. Lidster and D. H. Tamburini, Folk Dance Progressions (1965, repr. 1978); A. S. Duggan et al., Folk Dance Library (5 vol., 1948, repr. 1980).

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## folk dance

folk dance • n. a popular dance, considered as part of the tradition or custom of a particular people: well-known folk dances | ballet steps complicated by borrowings from folk dance. DERIVATIVES: folk danc·er n. folk danc·ing n.