The Mathematics of Ballet

And Lastly...Don't Forget to Count!

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Counting is a very important part of ballet. Dancers must constantly be counting their steps in order to keep time with the music. If they miss a beat, they will no longer be synchronized with the other dancers.

Eight corners

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The 4 corners and 4 walls in the studio are referred to as the “eight corners.” How many degrees do you have to rotate to get to each “corner”?

Symmetry

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Symmetry is an important part of ballet. It helps dancers balance. Notice the perfect symmetry of first and second position.

Equality doesn't always look the same.

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In a movement called fondue (“to melt”), the dancer must bend and straighten her legs equally at the same time. Although the legs do not appear the same, the angle at which the two knees are bent should remain equal throughout the movement. This is very challenging!

Clockwise and Counterclockwise

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Make sure you know which direction to turn! Choreographers specify if turns should be en dehors (clockwise) or en dedans (counterclockwise).

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Can you guess what double time would mean?
Here’s a clue…

Half Time

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No, we’re not talking about a break in a football game…

In dance, if a movement is does in half time, the amount of time has been cut in half.

This means a dancer can complete the movement twice in the same length of time as when the movement was at it’s regular speed.

Speed

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Pirouettes are turns of the body. A single pirouette is a full 360 degree rotation. A double pirouette rotates twice.

Similar to the last examples, a double turn should be completed in the same amount of time as a single turn. This means a dancer must double the SPEED of the turn.

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Similarly, if you add an extra beat to a jump, it must still be completed in the same amount of time.

In an entrechat, a dancer moves her legs twice as fast to complete the jump in the same amount of time as a changement.

Constants and variables

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Dance looks beautiful when arm and leg movements are coordinated.

In this example, the movement of the arms remains constant, while the speed of the legs changes.

The arms must move along at the same rate, regardless of whether the leg movements double or triple in speed.

Odd or Even?

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If you are doing an EVEN number of tendus, cross in the front of your other leg first.

If you are doing an ODD number, cross in the back first.

CHALLENGE: Where would you cross first if you were asked to do 6 tendus?

In a Cross

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Barre exercies are often done with the feet working in the following order: front, side, back, side. This order is called “en croix,” which means “in a cross.”
When moving the feet to the side, you must alternate closing in front and back of your other leg. But where do you close first? That depends on on how many tendus you are doing in each direction. Is the number odd or even?

Drawing circles...with your toes!

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In preschool and kindergarten we learn how to identify and draw a circle.
As we have seen, dancers need to have a good understanding of angles of rotation, and that includes 360 degrees.
In an exercise called “rondejamb en lair” dancers draw circles with their toes, while keeping the rest of the body stationary.

Name that Angle!

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Many dance exercises have precise specifications regarding the angle of the legs. Can you name the angles you see?

Pas de Chat "Step of the Cat"

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Here you can see how “half” and “full” movements are applied in a pas de chat and grande pas de chat.

The concept of half

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Ballet dancers must have a good understanding of the physical capabilities of their bodies. This includes their maximum flexibility. During a class, dancers warm up their muscles gradually. They do this by initially doing a smaller movement, followed by a larger movement. The smaller movement is usually the half-way mark of their full capacity. Here are two examples:

A demi-plie (half bend of knees) bends half as much as a grande plie (full bend of knees).

In a cambre, the dancer stops at the half-way mark (90 degrees) before extending fulling to 180 degrees.

Math in ballet? No way...

2008-04-13T08:26:00.000-07:00

Ballet dancers are renowned for their flexibility and grace, but did you know that dancers must also be quick thinking mathematicians? Well, grab your leg warmers and read on, my friend!