Comment by GuB-42
1 year ago
Not a coincidence. They defined the meter from the second using the pendulum formula, and the pandulum formula has a pi in it, so pi is going to appear somewhere. The reason there is pi is probably because a pendulum is defined by its length and follows a circular motion that has the length as its radius.
We could imagine removing pi from the pendulum equation, but that would mean putting it back elsewhere, which would be inconvenient.
Right, that connection is not a coincidence. The connection the previous commenter drew between the meter, pi, and the circumference of the earth is a coincidence.
> The reason there is pi is probably because a pendulum is defined by its length and follows a circular motion that has the length as its radius.
It’s not quite that easy: For small excursions x the equation of motion boils down to x’’+(g/L)x=0. There is not a π in sight there! But the solution has the form x=cos(√(g/L)t+φ), with a half period T=π√(L/g), thus bringing π back in the picture. So indeed not a coincidence.