Why is the lunar month exactly equal to the human female menstrual cycle?

Well, it's not. Not really. Although the Lunar 'synodic month' from Full Moon to Full Moon is 29.53 days, the female menstrual cycle for humans can be anything from 26 days to 30 days, and some women are quite irregular. Just for comparison, here are the cycle lengths for some other mammals:

Chimpanzees......... 37 days
Humans.............. 26 - 30 days
Opossums............ 28 days
Macaque monkeys..... 24 - 26 days
Cows and mares...... 21 days
Sows................ 20 - 22 days
Sheep............... 16 - 17 days
Guinea Pigs......... 11 days
Rats and mice....... 5 days
There is no real correlation with the size of the mammal, the number of legs, the intelligence or brain size, or with the size of the eye. This means if there is a predictor, it is far more complex than some obvious external agent in the environment.
Copyright 1997 Dr. Sten Odenwald
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