What are the characteristic ratios of a number?

Question

The Wikipedia article on the plastic number says that its characteristic ratios are $\frac{3}{4}$ and $\frac{1}{7}$. Can anyone tell me what is meant by characteristic ratio in this context? (Using google, I can only find information about the characteristic ratios of polymers - is that related?)

Answer 1

Incomplete answer

From the source of the wikipedia article it seem that it is rather an approximation than an exact value:

Its basic ratios, approximately 3:4 and 1:7, are determined by the lower and upper limits of our normal ability to perceive differences of size among three-dimensional objects.

I don't know anything about the links between math and architecture but it seems that: $$\frac{1}{\rho} = 0.7548.. \simeq \frac{3}{4}$$ I think that it is the same for $1/7$, some rational function of $\rho$ is close to $0.142...$ and this rationnal function is of importance in architecture.