Perhaps more than any other art form, dance is subject to the constantly changing tastes of the public, and a choreographer celebrated as a forward-thinking genius in one decade can see his work become dated and clichèd only a few years later. So the fact that the works of George Balanchine can still inspire the same visceral reactions today as they did nearly a century ago is a remarkable thing. Balanchine’s centennial is coming up this month, and New York’s dance community will be showcasing his work all year.