As far as I can tell, the following assertion (which is the basis for the rest of the math) is something we are to take on faith. How was it determined that this is the optimal ratio? That seems to me the most important question here, yet it is mentioned almost as an aside.
"""In the equation above, the optimal line height is produced when h equals the golden ratio (φ). """
There’s no empirical basis for the mystical claims about the golden ratio, and most of the examples from ancient buildings, famous artworks, attractive people’s faces, and so on are a result of selecting examples which match the pattern while ignoring those which don’t – yay numerology!
It just happens to be a fairly reasonable ratio for a lot of purposes (and happens to be the ratio ϕ = a/b such that ϕ = a/b = (a + b)/a), and sometimes therefore an easy rule-of-thumb. Use it or don’t use it. You won’t be missing some secret of the universe.
Not for the ones typically cited, such as Leonardo’s work, or the Parthenon, they didn’t. Some artists certainly did. Le Corbusier (architect) based a lot of his designs on it, for example, as did Jan Tschichold (typographer).
Anyway, they weren’t working from anything empirical, but from their own mystical preferences.
We don't know what's universally optimal, but we can test different ratios/mathematical bases and see what the results look like.
To my eye, Golden Ratio Typography seems to hit the sweet spot.
In a future article, I'm going to talk about the notions of a "sweet spot" and a "good eye for design" and show how these concepts point to the existence of universal subjective preferences.
"""In the equation above, the optimal line height is produced when h equals the golden ratio (φ). """