Google's Material Design guidelines such as Typography - Style - Google design guidelines or Metrics & keylines - Layout - Google design guidelines contains many ad hoc metrics for font sizing, spacing, margins etc.
I wonder if there are any mathematical patterns behind?
For instance, analysis of the proposed font sizes gives the following sequence of ratios (next font size divided by previous):
1.166, 1.143, 1.25, 1.2, 1.417, 1.323, 1.244, 2
The ratios here fall (roughly) in the range of
1.14 - 1.42 (with the exception of the last one). This suggests there might be some fundamental value behind, such as the square root of golden ratio
Replacing all those ad hoc ratios by single consistent value would certainly simplify the whole system and make design calculations as well as any implementation much easier.
The same question goes for the layout sizes, the model here being clearly more complicated but not hopelessly impossible.
Are there reasons why the more verbose ad hoc system was preferred and whether using more consistent mathematical model would have had any downside?