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### $\pi$ from the unit circle, $\sqrt 2$ from the unit square but what about $e$? [duplicate]

If one wants to introduce $\pi$ to a not mathematically savvy person, the unit circle would be a good choice. The unit square would be the way to go for $\sqrt 2$. But what about $e$? I've reviewed ...
### Two questions about Euler's number $e$
I am on derivatives at the moment and I just bumped into this number $e$, "Euler's number" . I am told that this number is special especially when I take the derivative of $e^x$ , because its slope of ...
If we have to find differential coefficient of $x$ to the power $x$ with respect to $x$ , we take logarithm base $e$ of both sides of $x^x=y$. Why is $e$ selected as base instead of any other number ? ...