Waltz
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The waltz, meaning "to roll or revolve") is a ballroom and folk dance, normally in triple, performed primarily in closed position.
Detail from frontispiece to Thomas Wilson Correct Method of German and French Waltzing (1816), showing nine positions of the waltz, clockwise from the left (the musicians are at far left). At that time, the waltz was a relatively new dance in England, and the fact that it was a couples dance (as opposed to the traditional group dances), and that the gentleman clasped his arm around the lady's waist, gave it a dubious moral status.
The Waltz, by Camille Claudel (cast in 1905)
Polka
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Polka is a dance and genre of dance music originating in nineteenth-century Bohemia, now part of the Czech Republic. Though associated with Czech culture, polka is popular throughout Europe and the Americas.
Street musicians in Prague playing a polka
Polka, c. 1840
People dancing polka in Tampere, Finland in 2006