Some months ago a professor of mine showed us a 'proof' of why $g\approx 9.8 ~\text{m}/\text{s}^2$ (the gravitational acceleration at the surface of the Earth) is 'equal' to $\pi^2\approx9.86\dots$ Using a differential equation that I think is used to model the movement of a pendulum of something like that.
Does anyone know the DE I'm talking about? Or, has anyone heard such story?
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$\begingroup$Maybe this helps: linkLooks like some time ago the second was defined by $1/2$ of the oscillation time of a $1$ meter long pendulum. The oscillation time of a pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$. With $T = 2$ and $L = 1$ this gives $g = \pi^2$
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