lokame shiva mayam
Do you know Nataraja idol in Chidambaram praharam has one significance?
It was built by the pallava kingdom, and the significance is that it looks like a man for men, woman for women.
Original name of Nataraja was called Viswesa - Vis (man) + Wes (Woman) + a (authority) = The authority of man and woman.
The symbol has nothing got to do with dance, the symbol represents that lokame shiva mayam.