I'm a fence sitter on this one. Yes, the moon cover's the sun very well, and among moons in the solar system it is a rather remarkable one due to its mass ratio rather large, save for the competing examples around Pluto Pointing out the eclipse or occultation phenomenon on another e-mail group discussing possible extraterrestrial life, I submitted this as an unlikelihood of itself. Someone replied that, possibly, as a result during solar eclipses the Earth gets a lot of interplanetary tourists to the watch the spectacle.
But beside the fact that it is remarkable occurrence to observe from a presumed "terrestrial" planet, it is also coincidental that we live at a time when the moon's diameter and the sun's distance make the stage show possible. Earth's distance from the sun probably hasn't budged very much, but the moon has been drifting away from the Earth since its formation. How many million years it has taken to reduce its period a day?
A good question, but worth examining with analysis.
So true enough there are many monthly cycles in biology, but to which lunar period are they attached and how precisely? The earth rotates as well as the moon and the two rotate around the sun. If the earth did not rotate about its axis with respect to the moon, we would not notice lunar tides. Just static levels of water on sides of the earth facing or opposite it. The earth did not always rotate at the same rate (even an ice age can redistribute inertia with constant angular momentum to change angular rate) and the moon did not always have the same distance or period.
So, I would be less inclined to look at "Pythagorean" tie-ins for the significance of the numbers. Some will be biological. Others will be subtle stability points in celestial mechanics. Mysterious - but not on a metaphysical plane.