My personal favorite relation between π and e 
Is there any other mathematician whose work is instantly recognizable?pic.twitter.com/WMliDN17Vs
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Does this imply the the square root of pi times e over 2 is irrational? (I ask because IIRC it’s still unknown whether pi times e is irrational, though “everybody” thinks it is.)
Hmmm I’m not sure.. since the series is in there too.. but an irrational plus an irrational is also irrational, so naively it would at least seem like it
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The square root of two plus its negative is zero, so the sum of two irrational numbers can be rational. Of course that’s a somewhat silly counterexample; if you add two “random” irrational numbers, their sum “should” be irrational. But Ramanujan’s two summands aren’t very random.
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It at least shows that it has an irrational part, no?
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