Michael Heleus- comment
7/5 Relates Closely to PHI
Seven fifths raised to its own power,
(7/5)^(7/5)= 1.6016928982=PHI x (1+98.0162794848^-1)^-1, so this relation is good to about a part in 98, and is much closer to the fibonacci number ratio 8/5 at one part in 945(.124757059). Working the other way by solving x^x=PHI for x we get 1.40757981446, which is 7/5 times (1+184.701090983^-1). This means that by stretching 7/5 just about a part in 185 and raising it to its own power, we get exactly PHI. We could also start with the relation of the diagonal of a square to its side, which is the square root of two to one or
1.41421356237:1-- taking the square root of two and raising it to its own power giving 1.63252691944 which overshoots PHI by 1/111.642981226, good for gematria students.
The square root of 2 has to be reduced by 1/212.184700511 to get the number which raised to itself equals PHI, so let's give this nearly 7/5 phi-number a descriptive name, phi first order equi-exponential decomposition. (Not one to say while brushing your teeth! And it sounds too much like a mouse-squeak to make a good mantram.)
This mouthful means that this number is the first time (first order) you split PHI looking for a number that when raised to itself (equi-exponential) equals PHI. Let's call these eexd1's for equi-exponential decompositions of first order(1). Note that there are higher orders as you fractally, self-referringly, keep splitting the result number. The result raised to itself, and that result raised to itself, etc, until the order number is reached giving PHI gives a series of numbers made from nothing but PHI in a different operational way than phi powers that can be very interesting. You can do this with any number with some amazing results. The matter of harmonizing 6 with 5 is a major focus in sacred geometry studies, so take 6, decompose it this way once, and you get 6eexd1=2.23182862441 which is less than the square root of 5 that PHI is based on to by only 1/526.454998334! CAN ANYONE SHOW ME A CONSTRUCTION FOR THIS? (You won't ordinarily see an error of this size in a geometric model at hand-craft scale or a drafted blueprint.) Or show me any exponential operation whose exponent is not=3?