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The plastic constant

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.

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Reply to
bitrex
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An infinite transmission line:

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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?

Reply to
RichD

sqrt(L/C) ?

Reply to
John S

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.

Reply to
RichD

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
Reply to
bitrex

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

Reply to
bitrex

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

Reply to
bitrex

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