It's amazing how once your start delving into the realm of sacred geometry, how much of our natural world starts coming into focus. One of the special numbers that keep popping up over and over throughout sacred geometry is what mathematicians refer to as Phi. The number itself is 1.618033.... on off to infinity. It's different from Pi in that it isn't transcendental, you can compute it directly. The formula for deriving it is (sqrt(5) + 1) / 2 - or "half of the sum of square root of 5 and 1". This number has some interesting properties from a mathematical perspective; one being its square is just itself plus 1, or 2.618033... Its inverse is itself minus 1, or .618033... . It also is very closely related to another mathematical construct called the Fibonacci Series. This series of numbers is generated by starting with 0 and 1, and then adding the previous two numbers in the series to generate the next, so 0+1 = 1, 1+1=2, 2+1=3, 3+2=5, 5+3=8, 8+5=13, and so on. The first 12 numbers of the series are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. (Generally the series is thought to start at 1 and not 0). As the series goes on, the ratio of two consecutive numbers of the series tends to get closer to Phi. (21/13 = 1.61538...., while 144/89 = 1.61797..., and 233/144 = 1.61805...)
In this season of solar eclipses and the celebration of Earth Day, there's some interesting things to note about the geometry of the Earth and its moon and the relation to Phi. NASA gives the radius of the Earth at its equator (Earth is slightly egg shaped instead of a perfect sphere) as about 3963 miles. NASA also gives the radius of the moon as about 1080 miles, again it's not a perfectly smooth sphere.
On their own, there's nothing really remarkable about those numbers, but when you look at them together, something a little surprising happens.
If you look at the earth and the moon together, you can see a remarkable Phi relationship. To do this, we'll need to bring the moon down to touch the earth's surface. We can imagine the center of the earth, the center of the moon, and the surface of the earth as 3 points on a right triangle, the right angle being from the line joining the earth and moon centers to the surface of the earth. This means the legs of the triangle would be 5043 miles (the radius of the earth + the radius of the moon), 3963 miles (the radius of the earth) and another number, the hypotenuse of the right triangle. Shout out to Pythagoras, and we can calculate that (a^2 + b^2 = c^2), which works out to about 6413 miles.
So we have the triangle, but we don't see Phi (1.618) anywhere in there. Well, it's actually encoded in the triangle itself. Remember, one leg is the radius of the earth and moon combined, a leg shooting off 90 degrees from that leg is the radius of the earth, and the third leg is the connection of those two legs at their non-joined endpoints.
If you take the hypotenuse of the triangle (6413) and look at it's ratio to Earth's radius (3963) you may be surprised at what happens: 6413 / 3963 = 1.618... approximately Phi!
That's not the only interesting thing about this triangle, if you look at the sum of the radii of earth and the moon (the first leg of the triangle, 5043 miles) and it's ratio to the radius of the earth by itself (3963), you get another interesting number: 5043 / 3963 = 1.272... We haven't seen that number before. If we look at the square root of phi, however, we find that it equals 1.272...
So we have a triangle where if the radius of earth is our unit measure, the sum of the radius of Earth and the Moon is equal to the square root of Phi, and the hypotenuse of the triangle formed by the radius of the Earth and Moon and the radius of the Earth is Phi.
Something to ponder as we keep looking up!