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 

List of Places where π^2 can be seen-


*

*π is present in some structural engineering formulae, such as the buckling formula derived by Euler, which gives the maximum axial load F that a long, slender column of length L, modulus of elasticity E, and area moment of inertia I can carry without buckling

*The fact that π is approximately equal to 3 plays a role in the relatively long lifetime of orthopositronium. The inverse lifetime to lowest order in the fine-structure constant α has a term of π^2

*Kepler's Third Law of Planetary Motion

*Volume and Bounding Area of 4-D and 5-D Sphere

*Basel Problem (As mentioned in another answer)
And many more as well
Sources-
https://en.m.wikipedia.org/wiki/Pi
https://en.m.wikipedia.org/wiki/Basel_problem
https://en.m.wikipedia.org/wiki/Buckling
https://en.m.wikipedia.org/wiki/Fine-structure_constant
https://en.m.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion
https://en.m.wikipedia.org/wiki/N-sphere
