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Dance comes in many different forms. Professional dancers can work alone or in a group. Singers and musicians often use dance routines as part of their performances, and people dance to exercise and have fun. Maybe you even take dance lessons at school or in your spare time.

What you may not realise is that all types of dancing, from break-dancing to ballet, use ideas found in maths. Dancers must understand symmetry and geometry, as well as being able to count in time to the music. Choreographers also use these ideas to design new dances.

Symmetry, geometry … dance? In a spin

Think about a dancer spinning around. To stay in control and not get dizzy, dancers use a technique called ‘spotting’. As they turn their body, they keep their head fixed for as long as possible, and then quickly rotate their neck to catch up with their body. They try to keep their head looking in the same direction after each rotation, because this helps them to balance and prevent dizziness.

Why can’t dancers just spin round continually? It is easy to keep a ball spinning because a sphere has an infinite or unlimited number of rotational symmetries. The human body has no rotational symmetry, meaning anyone trying to spin continually will soon lose their balance and fall over!

Symmetry, geometry … dance? The power of symmetry

We may not have rotational symmetry, but we do have another type of symmetry called mirror symmetry. You may have also heard this called line or reflection symmetry. Imagine a line going from the top of your head to the ground between your feet. The left side of your body looks like a mirror image of the right side. You might have a few freckles in the wrong place, but your left arm matches your right arm, your left leg matches your right leg, and so on. We call this imaginary line the line of symmetry.

Symmetry is important, but so is geometry. Dancers form shapes with their bodies, and choreographers think about how to use lines and angles to make their dances more interesting. A choreographer called Rudolf Laban, has even created a system of notation for dance that can be manipulated like a mathematical equation.

Dancers use symmetry and geometry to improve their performances and make them visually appealing. We enjoy looking at symmetrical things because our brains like to hunt for patterns. We like regular geometrical shapes for the same reason, and these often form the basis for dance. So when a dancer lifts their arms together, or traces out a square as they move, they’re making use of maths to create a better dance.

What is symmetry?

If something has symmetry then it can be rotated, shifted, or reflected and still end up looking the same. For example, a square can be turned by 90 degrees, shifted in any direction, or reflected in a mirror, and it still looks like a square. Can you think of a shape that doesn’t behave like this?

What is geometry?

Geometry is the study of shapes and sizes, angles and lines. It has many uses in the real world, and was one of the earliest areas of maths to be studied.