In spite of their different dimensions, the numerical value of $\pi^2$ and $g$ (in the SI unit system) are surprisingly similar($\frac{\pi^2}{g} \approx 1.00642$).

After some search, I thought that this fact isn't a coincidence, but an inevitable result of the definition of "metre", which is based on a pendulum with a one-second period.

However, the definition of "metre" has changed later(which is reasonable, for $g$ varies from place to place), but $\pi^2 \approx g$ still holds true after this vital change.

This confused me: is $\pi^2 \approx g$ a coincidence?

Clarification: This post has nothing to do about numerology, and I don't think the similarity between the constant $\pi^2$ and $g$ of the planet we live on reflects divine power or anything alike -- I consider it the outcome of the definitions of SI units.

This question is, as @Jay and @NorbertSchuch pointed out in their comments below, about units(closely related) and history(not very related) of physics. So in my humble opinion, it's on-topic on this site.