The golden constant phi = 1.61803... is the limiting quotient of the
terms of the Fibonacci sequence, is the only positive root of the
polynomial equation x^2 - x - 1 = 0, and is also equal to the infinite
nested square root sqrt(1(sqrt(1(sqrt1(sqrt(1...

and shows up many places in nature.

If you take the limiting quotient of the sequence g_0 = 3, g_1, = 0, g_2
= 2, g_n = g(n-2) + g(n - 3) for n >=3....you get the "plastic constant"
psi = 1.32471... it's the only non-complex root of the polynomial
equation x^3 - x - 1 = 0, and is also equal to the infinite nested cube
root cbrt(1(cbrt(1(cbrt(1(cbrt(1....

and rarely if ever shows up in nature.

<https://en.wikipedia.org/wiki/Plastic_number>

On July 29, 2021, bitrex wrote:
> The golden constant phi = 1.61803... is the limiting quotient of the
> terms of the Fibonacci sequence, is the only positive root of the
> polynomial equation x^2 - x - 1 = 0, and is also equal to the infinite
> nested square root sqrt(1(sqrt(1(sqrt1(sqrt(1...

An infinite transmission line:
https://www.electronicsteacher.com/alternating-current/transmission-lines/02357.png

Each inductor has value L, and each cap has value C.
Ignore the inductors along the bottom line.

What's the equivalent load impedance, seen from the source?

--
Rich

On 7/31/2021 6:50 PM, RichD wrote:
> On July 29, 2021, bitrex wrote:
>> The golden constant phi = 1.61803... is the limiting quotient of the
>> terms of the Fibonacci sequence, is the only positive root of the
>> polynomial equation x^2 - x - 1 = 0, and is also equal to the infinite
>> nested square root sqrt(1(sqrt(1(sqrt1(sqrt(1...
>
> An infinite transmission line:
> https://www.electronicsteacher.com/alternating-current/transmission-lines/02357.png
>
> Each inductor has value L, and each cap has value C.
> Ignore the inductors along the bottom line.
>
> What's the equivalent load impedance, seen from the source?
>
>
> --
> Rich
>

sqrt(L/C) ?

On July 31, John S wrote:
>>> The golden constant phi = 1.61803... is the limiting quotient of the
>>> terms of the Fibonacci sequence, is the only positive root of the
>>> polynomial equation x^2 - x - 1 = 0
>
>> An infinite transmission line:
>> https://www.electronicsteacher.com/alternating-current/transmission-lines/02357.png
>> Each inductor has value L, and each cap has value C.
>> Ignore the inductors along the bottom line.
>> What's the equivalent load impedance, seen from the source?
>
> sqrt(L/C) ?

What's your alma mater?
I plan to write the dean, and demand they revoke your degree.

First, look at the bit I quoted, the golden constant... maybe that's relevant?

Big hint: everybody takes a programming course nowadays, at some point
one is exposed to the technique of recursion... which leads directly to the solution.

--
Rich

On 7/31/2021 7:50 PM, RichD wrote:
> On July 29, 2021, bitrex wrote:
>> The golden constant phi = 1.61803... is the limiting quotient of the
>> terms of the Fibonacci sequence, is the only positive root of the
>> polynomial equation x^2 - x - 1 = 0, and is also equal to the infinite
>> nested square root sqrt(1(sqrt(1(sqrt1(sqrt(1...
>
> An infinite transmission line:
> https://www.electronicsteacher.com/alternating-current/transmission-lines/02357.png
>
> Each inductor has value L, and each cap has value C.
> Ignore the inductors along the bottom line.
>
> What's the equivalent load impedance, seen from the source?
>
>
> --
> Rich
>

Easiest to write it in terms of admittance, the admittance looking in is
Y_net = 1/(Y_L + 1/(Y_net + Y_C)) and rearrange that as a quadratic in
Y_net, if U grunge thru that and set omega = C = L = 1 I believe you get
1.61803... ohms for 1/Y_net

On 8/2/2021 6:53 PM, RichD wrote:
> On July 31, John S wrote:
>>>> The golden constant phi = 1.61803... is the limiting quotient of the
>>>> terms of the Fibonacci sequence, is the only positive root of the
>>>> polynomial equation x^2 - x - 1 = 0
>>
>>> An infinite transmission line:
>>> https://www.electronicsteacher.com/alternating-current/transmission-lines/02357.png
>>> Each inductor has value L, and each cap has value C.
>>> Ignore the inductors along the bottom line.
>>> What's the equivalent load impedance, seen from the source?
>>
>> sqrt(L/C) ?
>
> What's your alma mater?
> I plan to write the dean, and demand they revoke your degree.
>
> First, look at the bit I quoted, the golden constant... maybe that's relevant?
>
> Big hint: everybody takes a programming course nowadays, at some point
> one is exposed to the technique of recursion... which leads directly to the solution.
>
> --
> Rich
>

The analysis that leads to the telegrapher's equation assumes the LCs
are infinitesimals.

On 7/31/2021 10:31 PM, John S wrote:
> On 7/31/2021 6:50 PM, RichD wrote:
>> On July 29, 2021, bitrex wrote:
>>> The golden constant phi = 1.61803... is the limiting quotient of the
>>> terms of the Fibonacci sequence, is the only positive root of the
>>> polynomial equation x^2 - x - 1 = 0, and is also equal to the infinite
>>> nested square root sqrt(1(sqrt(1(sqrt1(sqrt(1...
>>
>> An infinite transmission line:
>> https://www.electronicsteacher.com/alternating-current/transmission-lines/02357.png
>>
>>
>> Each inductor has value L, and each cap has value C.
>> Ignore the inductors along the bottom line.
>>
>> What's the equivalent load impedance, seen from the source?
>> --
>> Rich
>>
>
> sqrt(L/C) ?

You'd get that if you assume the physical length of each LC element is
"dx" and solve in the time domain, but if the LCs are just assumed to be
lumped elements with no physical size or length you can do the recursive
frequency domain _small signal_ analysis and get a load impedance for
_small signals_.

But that cute result is still kinda bullshit anyway even for small
signals because the recursive lumped-element frequency domain analysis
claims there is still non-zero current thru the infinite LC network down
to 0 Hz in the limit, where does the current go "at infinity" in that
case? Either it should damp to 0 at infinity which a network of ideal
LCs can't make happen, or there's a discontinuous boundary condition at
infinity to accommodate it, which means you can't really analyze it
recursively in the first place