Fun with hyperbolics

I always assumed the peak of tanh'', taken positive, was at log(phi^(3/2)), I never checked. Then one day I did tanh'''=0, low and behold, what is the hyperbolic condition at that point? 3-2=1, I kid you not. Tanh = sqrt(2/3), a familiar ratio.  This is just set combinatorics, and hyperbolics do sets really nicely.