Posted by Sunny Kalara | 8 Comments
Tuesday Physics Tattoo: Pi Day edition
This is a remarkable tattoo of the Basel equation and Pi.
I wanted to post this tattoo in the Pi edition to show that the magical number Pi appears at the strangest of places. One would not have expected the summation of inverse squares of integers to add up to some combination related to Pi, but here it is.
This little baby is also due to Euler. In 1644 Mengoli asked if anyone could find a closed-form value (and prove it rigorously) for the infinite sum of the reciprocals of the squares. So, what is 1+1/4+1/9+1/16……. and so forth off to infinity. Contrary to intuition this series does not diverge to infinity. Although we are adding infinitely-many positive amounts together we still get a finite number. This is because the positive amounts that we are adding are getting smaller sufficiently fast. It was known that this sum was approximately 1.644. However, when Mengoli asked for a closed-form value he was looking for an EXACT expression, not a decimal approximation. In 1735 Euler found the closed-form solution. If you continue to Tattoo Number 4 part 2 you will see the sum.
More about Basel Function here.
Talking about the strangest places Pi appears, I wasn’t thinking of Pi being on PeppermintStripe’s lips. I bet she can recite 100 digits of Pi, easy! This is really cool.
Source: PeppermintStrips’s Deviant Art.
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