Euler’s number and its significance in real life.
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Eulers number was originally derived by a mathematician named Jacob Bernoulli, in essence he was trying to see what happens when your compund interest compounds infinite times. Euler himself defined it later as an infinite series. Some use cases for e include approximation of really large factorials, probability distribution, waves, and calculus. A little explanation on all examples provided, a useful equation called stirlings approximation is used to estimate the value of incredibly large factorials as calculators cant go past certain values due to restrictions in data type sizes. Normal distributions, or standard bell curves are derived using exponentials with base e as well. Waves is probably its second most important use, being particularly useful in calculating AC power as sine and cosine can be rewritten as exponential functions with base e. Lastly, at the time of eulers definition, the big reason we wanted to define e as a value was so we could integrate and derive exponentials and logarithms. When either of these do not have a base of e, you end up with a factor of the natural log of the base leftover. By defining e, we could now do integrals of logarithmic and exponential functions. e has a lot of other uses in stuff like exponential decay, but im not nearly smart enough to talk about radioactive decay. Hope this helped, also sorry im on phone so hopefully this isnt too bad to read.
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