The most renowned chorus line in the world, the Rockettes engendered the American form of precision dancing and have remained the paramount practitioners of synchronized tap-dance routines ever since. A quintessential New York tourist attraction, seen by millions of spectators since their debut at Radio City Music Hall in 1932, the Rockettes spawned multitudinous imitations and made precision kick-lines an established element of American entertainment culture—from amateur theatricals and school productions to Broadway musicals, Las Vegas extravaganzas, ice spectaculars, and half-time shows. The Rockettes are often recognized as epitomizing the "all-American girl," perhaps from a bygone era. They are beautiful, but not overtly sexy, they move in unison, but with a natural athleticism, not as automatons.

The Rockettes on stage.

The Rockettes were the brainchild of Broadway dance director Russell Markert, who was inspired by the Tiller Girls, a precision dance troupe from England that he...