Mar 17, 2009

Posted by in Tuesday Physics Tattoos | 13 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.

basel_equation_tattoo

basel_equation_tattoo

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.

Source Doctordani

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.

pi_lip_tattoo

Source: PeppermintStrips’s Deviant Art.

Talk Like a Physicist

  1. very nice blog and all post is very luxury

  2. I agree with you @arun. With Pi Tattoo the young lady look like more beauty, isn’it.

  3. Which one that more fast convergence between the pi obtained by 4 times arctan of 1 than by 6 times square root of 1/k^2 infinite series at above post. I believe we still need great effort to obtain pi approximation using both above formulas.

  4. @Rohedi, I think the last comment from you very educational posting.Thx.

  5. Oh thanks Barbara, you have promoted my website http://rohedi.com

  6. Apologise daddy @Rohedi, why do you ask the calculation way of pi number here. Denaya has seen your simple analytic exact formula for the pi number. Maybe that important to be questioned here the information of appropriate journal or paten institution for publishing your formula. Denaya hopes also as soon as employ your exact pi formula, hence not remember again the pi 3.14159265 like remembering my handphone number 3-1415-9265. Denaya believes scientific world need a simple exact formula for the pi, because when they use the formula pi=4*atan(1) or 4*(1-1/3+1/5-1/7+1/9-…) as recommended by Leonhard Euler…wew, so very tiring when it is calculating by my hand, hehehehe … I still remember to your explanation for me that the infinite series of 1-1/3+1/5-1/7+1/9-…) is too difficult to convergen. Sorry daddy, Denaya also promotes your SMT’s smart solver for ODE by putting eqworld address here the link of your SMT’s post

  7. I am a photo researcher working on locating images for a college level math book. The Authors have requested that I locate images of tattoos of equations. I would appreciate any information that you could give me as to who to request permission to use the tattoo image from your blog.

    Thanks

  8. it s come Pi Day again ;)

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