Is choreography composed according to any set ideals or proportions like the golden ratio?

There are many different kinds of dance, such as ballet, Modern, Jazz, ballroom, square, contra, and various branches of modern. Square dances and contra dances must be very balanced, and to a lesser extend, ballroom dance is balanced because these are couples dances. In square, you have four couples that must all come out in the same place. In contra, you have a line of couples, with couples moving in opposite directions up and down the line.

So these social dances show you a basic kind of balance—a mirroring—that often appears in the dance. In addition, there are other natural formations that appear in many dances: flocking, triangles, lines, following, landscapes (imagine a grid on the dance floor and dancers can only move along the grid—in straight lines or turning in right angles).

You have your solo dances, your couple dances, your group dances, your formation dances, line dances, and more chaotic-seeming dances.

Choreographers work from many different theories and ideals. Buttoh dance is based on the theory that you move so slowly and audience cannot see you move. Other choreographers may work from physical or emotional feelings. Others let the music move them. Still others focus on certain kinds of motions or a certain part of the body.

I’ll leave you with one hint about this. When you see a bunch of dancers who are all doing their own dance on the floor suddenly merge into doing a unison dance, it is almost always an incredibly powerful moment. I’ll leave it to you to think about it and figure out why that is.

Visual art is based on observed relationships that can be described by various math formulas. Music is almost entirely based on such relationships. Dance is not. Dance is a social construct. In English culture the dance is a symbolic trip or hunt, with partners waving at each other or pretending to hide or otherwise acting out some adventure. Scottish country dancing is a foot race set to music, maybe because Scotland tends to be cold. In German countries they either saw a log or pretend to fight over a girl. Yes, they carry an actual log onto the dance floor. The staged fights are called schuhplattler.