But how did we know that 1.732 identical to SQRT(3) ?Interesting way to do it indeed. Thanks.
Look at the following derivation (like the one for coupled RC sections in post#2):
1.) For three decoupled RC sections in series we have H(jw)=1/(1+jwRC)^3
2.) This can be expanded easily (polynominal of 3rd degree) and becaue we want H(jw)=real we set Im(denominator)=0
3.) This gives 3*w*RC - [w(RC)]^3=0
4.) Hence: w=SQRT(3)/RC
5.) At this frequency, the Re(denominator)=-1/8. Thus, we need a gain stage with a gain "-8".