Dance, Transformations and Geometry.

  In Geometry, students are studying reflection, rotation, and translation, so the other day, I had them get up out of their seats to move.  We held our hands in a position so we had an invisible partner. 

We moved four steps to the right while saying "Translation, two, three, four"  Then we turned in place with "Rotation, two, three, four, followed by a half turn, pause, second half turn while saying "Reflection".  We repeated this several time but by the end of it, my students knew those three types of transformations and could explain them in their own words.  

In college, I took modern dance for my P.E. credit because  I was not and still am not the athletic person who plays hours and hours of basketball, volleyball or other sport.  I love to dance, so I was able to get my credit.  As I created the dance on the spot, I realized that most choreographed dances involve transformations to move the dancer around the stage using one of those three transformations or perhaps even dilation.  In addition, the choreographer looks at angles, parallel and perpendicular movement, shapes, patterns, or symmetry. 

Lets look at how each of the above connects between mathematical ideas and dance. 

1. Translations occur when the dancer changes position in a vertical, horizontal, or combination.  This is one way they are able to move around the stage.

2. Rotations are when the dancer does a pirouette in place or across the stage in which case it would be a translation with several rotations.  Usually rotations are 360 degrees but they don't have to be.

3.  Reflections happen with two different groups are dancing the same moves in opposite directions as if there is an line of reflection running between the dancers. 

5. Angles - Dancers use angles in different ways from the arrangement of the whole body so a leg might be at a 45 degree angle to the torso or the dancer might be in a deep plie so the legs for 90 degree angles when bent at the knee.  Angles could appear in the movement of the dance itself.

6. Parallel and perpendicular movement often occurs as the dancers move around the stage in lines or they head towards each other such as when Baby ran to Patrick Swayze in Dirty Dancing so he could lift her over his head.  She ran straight at him so if you had one line through Patrick Swayze and another running from her to Patrick, the lines are perpendicular.

7. As for shapes, many choreographers have the dancers move so at the end of a set of steps, the dancer has moved in the shape of a rectangle, or a circle, or even a spiral. 

8.  Patterns are applied to dance in the form of AABA or ABAB where A represents one set of moves while B represents another set of moves so the patterns are based on the combination ad repetition of the sets.

9.  Symmetry often occurs in the actual.  First you move 4 steps to the right and move the same number back so they are exactly the same but in the opposite direction.  The moves are symmetrical.  Sometimes, symmetry appears when you have an equal number of dancers on the left side of the stage and the right side.  The audience loves symmetry because it looks right. When its not symmetrical, the audience feels the dance is jarring.

So these are some places you find transformations and other geometrical concepts in dance.  To introduce the topic, show a dance video and have students look for certain things that represent transformations, or angles and identify these as they watch the video.

If you have any dancers in your class, you could let them create their own dance using geometric concepts.  Or get your filmmakers to create a short film or animated film to show where these concepts appear in dance.

I hope you found this interesting today.  Let me know what you think, I'd love to hear.  Have a great day. Tomorrow I'll share information on e-books designed to create a more inquiry based classroom using art and sculpture, dance, and other "liberal arts" topics.