The Earth and Moon Squared Circle

The Earth and Moon fit perfectly into a squared circle. How unlikely is this fact? Yet it's true. I believe the Universe uses Ideals in it's makeup. While the numbers aren't exactly 1080, 2160, 5040, 7920 exactly, these are Ideal numbers that the Universe is striving for.

The ancients who built Stonehenge somehow knew this,and even used the same Ideal numbers (79.20 ft, 50.40 ft etc). How could they have known the sises of the Earth and the Moon so exactly? What did they know that we don't? Why are the numbers the same, when different measurement standards are used?

Here's a comparison of Stonehenge to the Earth-Moon Squared Circle system, along with the numbers. These same numbers are everywhere. In geometry, in ancient buildings and henges, in religions around the world. They are even in the Bible, in the measurements of the New Jerulsalem,and in Plato's ideal city. Where did these numbers originate from? Multiples of 27 are prevalent. 54, 108, 216, 432, 864. The moon is 1080 miles in diameter,and the sun is 864,000 miles in diameter. Always these numbers. There are a few other canonical numbers that the Universe uses, like 153, 3186, 81, and 64. These are the numbers that the Universe uses to make everything.Somehow, ancient people knew of these things,and used the numbers in the measurements of their buildings and monuments. 

I believe there is a blueprint of an ideal world lurking behind the reality we see. The material world does it's best to fit into the ideal. Certain individuals are able to intuit these ideals,and then use the numbers and ratios in their buildings and monuments,and religious stories. I don't believe it's a supernatural thing at all, I believe it's perfectly natural, it's just that some people are better able to intuit thatn others. It's just another sense. Maybe even no new sense at all, we are just getting information from the environment subconsciously.