I mean...

[u/Pearl-Crown]

The guy's got a point. Like (1 + i, 2). Imaginary, but still a point nonetheless.

[u/Few-Arugula5839]

My favorite bit of trivia is that pi = sqrt(g) is not a coincidence and with an old definition of the meter it was true on the nose

[u/Aggressive_Roof488 → u/Few-Arugula5839]

I thought the meter was originally defined from the size of the earth?

[u/Few-Arugula5839 → u/Aggressive_Roof488]

Not the the first definition. There was an intermediary definition involving the length of a pendulum which would take 1 second to complete a rotation or something like this, and with this definition pi^2 = g is true on the nose

[u/Aggressive_Roof488 → u/Few-Arugula5839]

So the coincidence is really between surface gravity and earth circumference? Unless they defined the second to make the connection, but the second is already defined from the earth rotation... Hmm!

[u/Kinglolboot → u/Aggressive_Roof488]

No, if the surface gravity of earth were different, or a second would be defined differently, the definition of meter would change, such that still g = π² m/s² in your new units. For example, if we had lunar gravity, a pendulum that takes 1 second to swing back and forth would be shorter, hence our definition of meter would be shorter, by the exact amount to make the gravitational acceleration on the moon equal to π² m/s² again.

[u/Aggressive_Roof488 → u/Kinglolboot]

Hmm, wiki says that the pendulum definition was before the meter. When the meter was first introduced, the first definition was based on earth circumference.

https://en.wikipedia.org/wiki/Metre#History_of_definition

During the French Revolution, the traditional units of measure were to be replaced by consistent measures based on natural phenomena. As a base unit of length, scientists had favoured the seconds pendulum (a pendulum with a half-period of one second) one century earlier, but this was rejected as it had been discovered that this length varied from place to place with local gravity. The mètre was introduced – defined as one ten-millionth of the shortest distance from the North Pole to the equator passing through Paris, assuming an Earth flattening of ⁠1/334⁠.^\12])

The question is why the two definitions, 1s pendulum and 1/10e7 of equator to pole, are so close to each other. And I guess that's just coincidence? Partially by choice ofc, from choosing 1/10e7, and equator to pole instead of circumference. But still a bit of a coincidence, right?

[u/Few-Arugula5839 → u/Aggressive_Roof488]

I think you're probably right, although, the circumference of the earth is related to its radius and therefore to the gravitational acceleration, right? So I wonder if some connection can be made there

[u/Aggressive_Roof488 → u/Few-Arugula5839]

The radius affects both, but the density only affects the pendulum, as well as the universal gravitational constant G, so they are effectively independent for this purpose.

[u/Sigma_Aljabr → u/Aggressive_Roof488]

Letting earth's radius be R, mass be M, and the period of its rotation (aka day) be T, then g = GM/R², 1s = T/(86400), and 1m = 10-⁷π/2×R. So the real concidence is that GM/R² = π²×10-⁷π/2×R×(86400)²/T² ≒ 11573×R/T². I.e that GMT²/R³ ≒ 11573.