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The Wallis Formula
π/2 is the infinite product of even #'s squared divided by its two adjacent oddspic.twitter.com/4iFKFIzuRm
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It must have been so fun to experience the very first infinite series or products for numbers like pi! For this one, I think it looks prettier to write 2 times 2, 4 times 4 etc on top - to make it look more like the denominator.
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That's the way it's usually presented, and I changed it to what *i* found more aesthetically pleasing.. but hey, this is a case where we can have our π and eat it too
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@3blue1brown Any awe-inspiring visualizations to give intuition for this (a la your Basel problem vid)? -
Actually yes! There was a sequel to that video on just this formula, known as the Wallis product.https://youtu.be/8GPy_UMV-08
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Fun paper from a couple years back deriving the Wallis Formula from the Hamiltonian for a Hydrogen atom. https://arxiv.org/abs/1510.07813
Thanks. Twitter will use this to make your timeline better. UndoUndo
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What about the practical: BBP formula (after: Bailey-Borwein-Plouffe) is a formula for calculating Pi discovered in 1995. This formula is a digit-extraction algorithm for in base 16pic.twitter.com/PSl4w2UfKw
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For e.g. k=0 we obtain: Pi ~ 4-1/2-1/5-1/6 ~3.1333333333.... that is quite accurate for the first step ;-) "Rationalizing" (to approximate) Pi by 22/7 is an old one.
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and what does odd sequence converge to? the value of 2.5464... does not seem familiar
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