Why are they called "polka" dots? I can sort of dance the polka, but don't see any relationship between the two.

polka dot:

1. One of a number of dots or round spots forming a pattern, as on cloth.
2. A pattern or fabric with such dots.
3. A round spot repeated to form a pattern on a textile fabric.
4. design consisting of a pattern of regularly spaced circular spots.

Polka dot is a pattern consisting of dots. Polka dot patterns are quite variable: they range from a series of dots that are equally spaced and sized to a random arrangement of multicoloured dots of different sizes. Polka dots are most commonly seen on children's clothing, toys, and furniture, but they appear in a wide array of contexts. The pattern rarely appears in formal contexts, however, and is generally confined to more playful attire such as bathing suits. Occasionally white on black regularly spaced polka dots appear on more formal clothing.

While polka dots are ancient, they first became common on clothing in the late nineteenth century in Britain. At the same time polka music was extremely popular and the name was also applied to the pattern, despite no real connection between them. Some believed that during the First World War the British used polka dots as a place to hide Morse code and other secrets without being noticed.

http://en.wikipedia.org/wiki/Polka_dot

Back in the mid-19th century, the U.S. was awash in polka dots, that pattern of dots of uniform size and arrangement, because we had all gone polka-crazy. The polka, of course, is a simple, lively dance step that took Europe and America by storm soon after its introduction in 1835. The name "polka" is a minor mystery. Although "polka" is Polish for "Polish woman," the polka dance is actually of Bohemian origin, and "polka" may be a corruption of the Czech word "pulka" (half) referring to the short half steps involved in the dance.

None of which, I realize, explains polka dots, but I'm getting to that. At the peak of the polka craze, from about 1840 to 1890 (this was a very long craze), a variety of manufacturers cashed in on the public's polka-mania by naming a dizzying range of products after the dance. Polka hats, polka gauze, polka curtain ties, and, of course, polka-dotted fabrics, had little or nothing to do with the dance, but sold like hotcakes, for a few years anyway. The polka dot pattern, however, had staying power, and remains popular today, especially in neckties.

http://www.word-detective.com/110598.html#polkadot