This looks like fun: Dance Through Time, although probably the only reference to squares is here:

A Nineteenth Century Romance

A Nineteeth Century Romance presents a world of ritualized flirtation. The elegant dances of the Regency, Romantic and Victorian eras sweep the audience along to witness the birth of the great waltz, stately quadrilles, playful cotillions and the “revolutionary” polka and mazurka.

Notice the reference to the quadrille…