Where does $\pi^2$ appear spontaneously within Physical Phenomenon and Mathematics Equations? The term $\pi$ is found to appear in many equations and natural phenomenon; however my question is related to $\pi^2$. 
While trying to figure out the reason for some $\pi^2$ terms appearing in certain equalities that I came across, I have a question. And the question is this: 

In which all mathematics/physics equation or contexts does $\pi^2$ appear inherently? 

-- and (now this second part is merely a follow up question that did not form part of the original query but added later)  where that $\pi^2$ term can lend some interpretation of the underlying phenomenon, just like does $\pi$ whereby we can interpret (in most cases i.e.) that some type of circular ambulation in 1 dimension is involved?? 
As you can understand, the $\pi^2$ term is more complex and does not directly lend itself to an interpretation -- as opposed to $\pi$ which is very intuitive. 
Thanks 

Usually $(2 \pi)^{-n}$ appears in the $n$ dimensional Fourier transform: If the Fourier transform of a $L^1(\mathbb{R}^n)$ is defined as
$$\hat{f}(k)=\int_{\mathbb{R}^n} e^{-i k \cdot x} f(x) \,\mathrm{d}^n x$$
Then the inverse transform will be (if the integral is convergent)
$$f(x)= \frac{1}{(2 \pi)^n}\int_{\mathbb{R}^n} e^{i k \cdot x} \hat{f}(k) \,\mathrm{d}^n k$$
But you can also "spread" it to be more symmetric: if
$$\hat{f}(k)= \frac{1}{(2 \pi)^{n/2}}\int_{\mathbb{R}^n} e^{-i k \cdot x} f(x) \,\mathrm{d}^n x$$
then
$$f(x)= \frac{1}{(2 \pi)^{n/2}}\int_{\mathbb{R}^n} e^{i k \cdot x} \hat{f}(k) \,\mathrm{d}^n k$$
