That approximation is only used in the USA, Liberia, and Myanmar tho. In the rest of the world, we use the metric maritime approximation,
π * φ km = e nm
historically, maritime navigation has always required much higher precision since a small error compounds into missing an island entirely. land-based measurements could afford to be fuzzier because you can course-correct using visible landmarks. this is also why maritime measurements standardized globally much earlier than land measurements.
That was a super long post to just say “the ratio of mph/knots ≈ π/e … and it’s not very useful, but a cool coincidence.”
It's about the journey, not the destination.
There’s not much of a “journey” though … because both mile and knot are just arbitrary assigned measurements.
——-
mile = 1,000 paces (as defined by Romans)
knot = how many logs would pass by in 30 seconds.
There’s no mathematical reason why their value is what it is.
Unlike π and e that do.
The nautical mile came first. It is one minute of longitude or latitude at equator.
The speed was measured with knots at specific lengths.
Interesting to see xkcd's Randall Munroe's live tour linked!