In measuring the crystalline structure of a typical hen's egg with the harmonic lattice, I noticed the following in this order...

2Phi / Pi = 1.03007243

Subtracting the identity 1 from this, we have the factional number 0.030072429601..., which we will affectionately call "Phu."

It may look ordinary and insignificant, but it represents a bridge between the two numbers. For example, for variables A and B:

A = Pi / (Phu -1) = 104.4675371

B = 2Phi / (Phu - 1) = 107.6091297

From this, we find the difference between the two to be Pi,

B - A = Pi


This suggested to me that a more direct relationship could be found between Pi and Phi, leading me to express Phu as:

Phu = 2Phi / Pi -1

This is proven as:

Pi + (Pi * Phu) = 2Phi

2Phi - (Pi * Phu) = Pi
2Phi = Pi + (Pi * Phu)
(2Phi - Pi) / Pi = Phu
2Phi / Pi - 1 = Phu

So, now we have a constant of nature that I am not able to find anywhere else that bridges two irrational infinite numbers, one representing resonance (Pi) and the other representing damping (Phi). Here it is again to the 16th place:

Phu = 2Phi / Pi - 1 = 0.0300724296009658