What is e (2.718…) and why does it literally appear everywhere?
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E is a transcendental number (so its 2.7182818…) it goes on and on and never repeats. Now if you think of exponents and logarithms (10^x, 11^x, log_12(x) log_13(x), etc), you quickly see you could just pick any number, and they all work (remember there are formulas to change from one base/log to another). So how do you pick which number to use? Well different fields do it in different ways (computer scientists like to use 2 because of binary, sometime scientists use 10 cause like decibels are in base 10 for example).
Now the reason why math people use e boils down to the fact that it has some really nice calculus properties.
* The main property is that (d/dx) e^x = e^x or more generally (d/dx) e^f(x) = f'(x) e^f(x). So this let’s you start solving problems like y”- y’ + 5y=0 called ordinary differential equations.
* another really nice properties happens to be that e^i*t = cos(t) + i sin(t), which you might notice that the real and imaginary part of that track the x,y coordinates of the unit circle being traced out from t = 0.. 2*pi. So now we have a cool way to relate circles and angles to exponents. This is called De Moivre’s formula and this formula is how you’d figure out those tables of trig identities you saw in geometry class
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