You might want to Google “Romain du Roi” if you’re interested in the geometry of typefaces, this is the most famous historical example. I don’t think you’re going to find any secret formula for designing a typeface, though.

AFAIK it’s all addition and subtraction.
Some people have been known to incorporate ratios into things like kerning, so that they scale proportionately in low res rendering.
Luc de Groot developed a formula for the relationship between weights, so that it is not linear, but that’s not really essential.

Whatever numerical rule you discover, you’ll immediately find numerous exceptions. Whatever “rational” or logic-based theories you collect or devise for type design need to be tested against the real-life application of visual assessment; in other words, type is made to be looked at, so the final arbiter of function, beauty, or whatever, will be the human eye. Since there is so much about type design that requires compromise, deception, trickery and illusion, I think you should focus on those aspects. There are examples of alphabets overlaid with intricate geometric schemes, but many of those turn out to be applied for teaching purposes after the fact; they don’t assist in the production of useful or beautiful letters. The Latin alphabet is derived from shapes written by hand.