>> So, what's a common use of the geometric mean? It's the resonant
>> frequency of a tuned circuit when you are given the upper and
>> lower 3dB frequencies (FL and Fh). Fc=sqrt(FL*Fh) .
>
>Are you sure about this?  It implies the shape of a resonant circuit
>is different on either side of resonance and I see no reason why this
>should be so.

Do not forget that the shape of the bandwidth of  a resonant circuit is
symmetrical to the eye, only if plotted with frequency as a log function. It
gets quite spread out if plotted with frequency as a linear function.

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