A lineup of the greatest dance numbers from America’s classic musicals is also a history of the American musical itself. Is the number expressed in popular dance, chorus lines, a flashdance? Is it a mini narrative, a dream ballet, an abstraction? These gems of choreography often contain the heart and soul of a musical, and they’re the raison d’être of American Dance Machine, the company behind Gotta’ Dance, which presents them as a show in itself. The choreographers represented here include Michael Bennett, Bob Fosse, Gene Kelly, Jerome Robbins, Lynne Taylor-Corbette, and Christopher Wheeldon, among others. And the dances comes from such musicals as Singin’ in the Rain, Irving Berlin’s White Christmas, West Side Story, Gypsy, A Chorus Line, An American in Paris, and more. Nikki Feirt Atkins and Randy Skinner co-direct. —Laura Jacobs