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If pi+e=a/b then you can write one as a/b minus the other Which is pretty insane because these two numbers are not supposed to be related
by charlieyu1 2y ago
If pi+e=a/b then you can write one as a/b minus the other
Which is pretty insane because these two numbers are not supposed to be related
- hn_throwaway_99 2y ago> Which is pretty insane because these two numbers are not supposed to be related Not really, there is Euler's identity: https://en.m.wikipedia.org/wiki/Euler%27s_identity https://en.m.wikipedia.org/wiki/Euler%27s_identity
- sunshowers 2y agoThat one's "just" a special case of how complex numbers happen to work. I think the really cool relationship between e and pi is the fact that the Gaussian integral acts as a fixpoint/attractor when sampling and summing data from any distribution (this is the central limit theorem): ∫(−∞ to ∞) e^(-x²) dx = √π I think the attractor property makes it a little more fundamental in some sense, whereas Euler's identity is "just" one special case of e^ix. The Gaussian is kind of the "lowest energy" or "highest entropy" state of randomness, which I think is really cool.
- octachron 2y agoThis is only true for distributions with finite variance (and the edge case of distribution with slowly growing infinite variance). And for a given variance, gaussian distributions are exactly the maximal entropy distribution.
- pishpash 2y agoe and pi are highly related, both pop out of periodic phenomenon.
- Someone 2y ago> because these two numbers are not supposed to be related Says who? They’re not known to be related in that way, but it’s not like nature set out to prevent such a thing, or that large parts of mathematics would break down if it happened to be the case.