Is there any mathematical context, where π² (about 9.869604401089357120529513782849 in decimal) makes sense ?
Not 100% spot on, but this one might do: Squaring the circle - Wikipedia, the free encyclopedia
Google is my biggest friend!
I'm a math noob, (engineer) but found in Wikipedia that
Sum( 1/x² ) for x=1 ... ∞ --> π² / 6
Don't ask me to prove it, or why and what that means
( let's sum up all inverse squares to get a PI Square ? )
However, in mathematics, the root of PI is undetermined, making PI nothing less than a miracle!
An interesting thing about squared values is that they are so much more than the sum of the parts. As you mention, π² is not simply 6.283185307179586476925286766559 (2π), but 57.08% more than just this simple sum.
This is our hope for our community. To be so much more than just an additional PI delivery.
We also chose PI Square because we hope it is the "Town Square" for all things PI. A place for development, current customers, future customers, other users, partners, employees, former employees, etc! That's our goal at least
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