<p> Golden ratio </p>

e20cad4c-7739-4fbc-a411-50dc28ceecc2 25 4 5 decimal

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Circuit Analyser ... adapted from Norm.

a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + :

Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema y1 y2 ≥ max in range ≡ y1 y2 ≤ min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / iter 21 mat 61 line :

1. All modules/functions in "Symbolic" optimiz. 2. Once in target: shrink the range 3. respect the search y1≥y2≡"max in range" y1≤y2≡"min in range"

4 appVersion 0.98.6179.21440 ≡

R 10 Ω * :

C 10 mF * :

f 60 Hz * :

ω 2 π * f * :

r 0.001 Ω * (2 Ω * (0.01 Ω * range :

'r' ... tunning parameter
wrt impedance response ...
'i' imaginary native Smath. r Z 11 r / i ω * C * + / Re R + (2^11 r / i ω * C * + / Im (2^+ sqrt :

Zap units for the suite . P r Ω / r Z Ω / vectorize augment :

isolate/store P P eval :

X P 1 col : Y P 2 col : 12 mat

TOL 1012 -^:

x f X Y x cinterp :

spot check 0 f 1 f 21 mat 10.000 10.069 21 mat

X f 0 0.5 y1 y2 ≥ TOL Extrema 1 el :

kg m 2^* A 2^s 3^* / Ω ≡

X X f 12 mat 0.2688 10.1335 12 mat

user explorer u 1.5 :

P 2 col Max 10.1335

Ω 1 :

track user/plot track 2.5 10.1 1 10.1 u u f 32 mat :

solve 
twins 'r' s x f 10.075 - 0 ≡ x 02 solve : 0.082 0.898 21 mat

r Ω / r Z Ω / vectorize augment X X f 1 2 mat track 3 1 sys

P Ω 0.001 10.001 0.01 10.01 0.019 10.019 0.028 10.028 0.037 10.036 0.046 10.045 0.055 10.053 0.064 10.06 0.073 10.068 0.082 10.075 0.091 10.081 0.1 10.088 0.109 10.093 0.118 10.099 0.127 10.103 0.136 10.108 0.145 10.112 172 mat

u u f 12 mat 1.5 10.05 12 mat

r Ω / r Z Ω / vectorize augment X X f 12 mat track 31 sys