[pollyturples]

Apart from the geometrical explanation linked in the other comment, there's an Anthropic Principle angle here too -- the fact that eclipses seemed so "perfect and meaningful" to our ancestors was probably a big factor in the development of mathematics and engineering as they tried to predict the eclipses. another similarly intelligent species on a planet without such "perfect" eclipses wouldnt be intrigued by them enough to try to explain their timing. The fact that planets with such perfect sun/moon relationships are "rare" could be one of the missing factors in the Drake Equation. [something similar was a plot point in the scifi book Dragon's Egg]