I thought the fabric pattern polka dot and the polka dance would turn out to have some convoluted history that linked them, but it turns out it's ultra simple. There was a craze for this dance in the nineteenth century and when the dance reached America, manufacturers jumped on the bandwagon, naming all sorts of products after it. It seems that polka gauze, polka hats and polka cakes aren't with us any longer, but the dots are.
Fledermaus suggests that Johann Strauss added the word Popular to the title of his 1842 Anna Polka in a deliberate strategy to launch this form as the new dance sensation. If so, it appears to have worked.
Transparent Lanaguage's Polish Blog says:
The polka was such a hit in the 1840s that the word polka was attached to the names of many products sold. There was no connection to the dance at all, and nothing very different about them, but entrepreneurs saw a good way to make a buck from its popularity by adding the word “polka” to an array of goods. There were polka hats, polka fans, polka cakes, polka hairstyles and polka curtain ties. A new fabric print was introduced that featured symmetrical placement of dots throughout the material. This was dubbed polka dot style and it is the only one of these “polka” products to have maintained its name to the present day, undoubtedly due to the fact that it was a new, unique product. The name polka dot stuck.Everybodyeverywear has an overview of the history of this fabric, and includes interesting information from Martha Stewart and Christian Dior.
I've missed out on being fashionable by only twelve months. This time last year, seemingly, polka dots were featuring on the catwalks. But I'm too old to be fashionable, anyway - old enough to remember when we were all singing about that itsy bitsy yellow bikini.