Dancers perform for audiences to watch in awe to the beauty of the movement. The audience does not realize the complex movements and math that the dancers use to produce the movement. To dance a dancer must know the basic math of dancing such as positioning, placement, musicality, and more.
For ballet there are many positions a dancer must know. For example:
Dancers also need to know how high to lift their legs, we refer to that as degrees. Dancers lift their leg at 45 degrees, 90 degrees, and higher. The number is determined by the distance from the supporting leg.
In this picture you can see the 90 degree angle the leg is giving.
Something else that relates to math is a dancers balance. Dancers have to determine where their center is and how much weight they need to distribute through out the body evenly so they can balance with out falling. This idea gets very precise, with the idea of head over shoulders over hips over feet, you even have to distribute the weight through out the feet and toes even so you dont fall!
Dancers create beautiful lines and curves done through balance.
In this ponche the dancer is very focused on balance, not leaning to far back in the hips and making sure her arms and head is aligned to keep her center balanced.
Musicality is a major mathmatical problem for dancers, dancers have to memorize movements and counts and when to perform on what count. Usually a dancer counts in eight counts but that can easily be changed. Sometimes it is 6 counts, 5 counts, etc. Sometimes it is a combination of counts in a variation of counts. Certain movements and strong accents hit on certain beats of counts.
Over all dance is a complex art that requires music mathmatics along with dance mathmatics combined into one art to create the beautuful movements and elegant lines to create the hard-work performance so that the audience can enjoy!