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Pi is IRRATIONAL: animation of a gorgeous proof

Pi Rational T-shirt

This video is my best shot at animating and explaining my favourite proof that pi is irrational. It is due to the Swiss mathematician Johann Lambert who published it over 250 years ago. The original write-up by Lambert is 58 pages long and definitely not for the faint of heart (http://www.kuttaka.org/~JHL/L1768b.pdf). On the other hand, among all the proofs of the irrationality of pi, Lambert's proof is probably the most "natural" one, the one that's easiest to motivate and explain, and one that's ideally suited for the sort of animations that I do. Anyway it's been an absolute killer to put this video together and overall this is probably the most ambitious topic I've tackled so fa...

Proving Pi Is Irrational - What You Never Learned In School!

Pi Rational T-shirt

Happy Pi Day (3/14)! Everyone knows that pi is an irrational number, but how do you prove it? This video presents one of the shortest proofs that pi is irrational, and the proof requires only high school calculus to understand. Niven's proof http://www.ams.org/journals/bull/1947-53-06/S0002-9904-1947-08821-2/S0002-9904-1947-08821-2.pdf http://mathschallenge.net/full/irrationality_of_pi https://wp.me/p6aMk-8jZ Images https://en.wikipedia.org/wiki/Archimedes#/media/File:Archimedes_Palimpsest.jpg https://en.wikipedia.org/wiki/File:%E4%B9%9D%E7%AB%A0%E7%AE%97%E8%A1%93%E7%B4%B0%E8%8D%89%E5%9C%96%E8%AA%AA.jpg https://en.wikipedia.org/wiki/William_Jones_(mathematician)#/media/File:Synopsis_Pal...

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