Intuition for the Golden Ratio and the Quadratic Formula in Electronics
Wired and Wound
Posts: 22
In the attachment shows a system of how the Golden Ratio is significant to the natural behavior of Frequency, Ohm's Law, and Magnetism.
The reason I explored this was for the necessity of helping me see the intuitive nature of the how frequency affects electrical circuits.
What I ended up finding out was that it was much more than I expected, and it did certainly help me understand how and why the Golden Ratio
was important to everything that concerned my mathematical intuition.
I hope this will help some people out. It is also important to understand that this document is a philosophical concept, not just a mathematical expression. The point is to observe that there is a pattern which is indicative of nature.
(correction): The (K) variable used in the document for magnetism is no longer (z), which was based off of the classical understanding, but has been found to be the ratio for the refractory time index of the medium of propagation, as in: (kε) = t s/m; or: µ/k = t s/m, and relative permittivity is: (kεc)^2; or ((µ/k)c)^2,
The reason I explored this was for the necessity of helping me see the intuitive nature of the how frequency affects electrical circuits.
What I ended up finding out was that it was much more than I expected, and it did certainly help me understand how and why the Golden Ratio
was important to everything that concerned my mathematical intuition.
I hope this will help some people out. It is also important to understand that this document is a philosophical concept, not just a mathematical expression. The point is to observe that there is a pattern which is indicative of nature.
(correction): The (K) variable used in the document for magnetism is no longer (z), which was based off of the classical understanding, but has been found to be the ratio for the refractory time index of the medium of propagation, as in: (kε) = t s/m; or: µ/k = t s/m, and relative permittivity is: (kεc)^2; or ((µ/k)c)^2,
I consider all of my comments about science and physics to be theoretical and open for debate. My posts are not the views of Ethereal Mechanics, and are not meant to prove or disprove anyone else's theories. Anyone is welcome to correct or dispute them.
Comments
knowing that |jXL - jXC| = jX(L or -C, whichever is greater), it makes sense that the relative permittivity of a medium would be |µ - ε|.
This means that all matter would contain a proportionate quality of both permeability and permittivity, and the difference would account for a medium's absolute characteristic quality. Using relative permittivity to describe a medium's characteristics is adequate enough for the application of electrical currents, but it does not allow for the understanding of the dielectric and magnetic fields.
Using the formula from the document:
free space time constant = 3 1/3e^-9 s/m
free space permeability = 5.393e^-9 L/m
free space permittivity = 2.060e^-9 C/m
free space ƒr = 47.75 MHz (2π m/wavelength)
K constant = 1.618
Notice that the values of permeability and permittivity have changed. This is because the new values are not based on the arbitrary 4π, but what the natural mathematical expression shown in the attachment dictates.
- The magnetic flux unit magnetic mass (or "unit magnet pole") herby became 4π lines of force, and this introduced the factor 4π into many magnetic quantities. An attempt to drop this factor 4π has failed, as the magnetic units were already too well established - (C.P. Steinmetz Electric Discharges, Waves, and Impulses(18)).
In conjunction with the Ethereal Mechanics model of inertialess particles, of the ethons and pretons, we can deduce that propagation in free space is purely reactive, thusly (Q = ∞) and (Bw = 1/∞) at resonance. Resonance being the fulcrum point at which a medium has either a relative permittivity, or a relative permeability.