What is e (2.718…) and why does it literally appear everywhere?
In: 756
Pi is the “constant of circles.” If you’re working with circles, pi isn’t far away. It appears everywhere that circles can be found. Every ellipse has a constant that will appear whenever you use that particular ellipse. For a circle (an ellipse whose foci are in the same spot) we call that constant pi, because it’s useful.
e is the “constant of self growth.” If any system’s rate of change depends on its current size, then e isn’t far away. It appears everywhere “natural growth” occurs: accruing interest, population growth, probability distributions, etc
It’s just one of the mysteries of the universe why the value is what it is, but the concept behind the value is much easier to explain.
And for any pendants reading, yes it’s true that if e were 3 or 1 then it wouldn’t give the same behavior, but that’s tautological. What I’m saying is *why* that particular value gives that particular behavior is unknown to us, just like why pi is 3.14… and not 2.5.
E: phrasing
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