Okay, what is
e in the first place? It the one of the few mathematical constant you might ever encounter.
e is an irrational number, and it can't be rerepresented as a fraction. The value of
e is 2.7182 8182 8459 0452 3536 0287 4713 5266 2497 7572…. Where … is a non repeating sequence. Where does this enigmatic number came from?
It turns out that it begins with money. Yes, I'm not kidding. In 17th century,
Jacob Bernoulli was studying an interesting problem about compound interest. What is the problem you may ask. Well, here it is.
Let's say that a bank give you 100% interest per year (no bank will give you that much
) and you put $1.00 in your account. At the end of the year the money in your acount will be $2.00. But what if there is another bank that give 50% interest per half a year? At the end of the year your saving will be $2.25 if you put your money there. What about 33.3…% per 4 months? Your saving will be $2.37 at the end of the year. You obviously want the one that give the highest interest right? If there is another bank that offer higher frequency of interest computation, we will jump over it don't we (assuming the number of computation of interest times percentage of interest is the same)? This leads us to infinite division of interest.
So, what is the formula? It is basically f(n) = (1+1/n)^n. Where n is the number of division (assuming that the the number of computation of interest times percentage of interest is 100%. If it's not, then you need to do some manipulation).
What
e has to do with this? Before I answer the question, try playing with the formula a little bit. You might notice something interesting. As you increase the value of n, the difference between f(n) and f(n-1) become smaller and smaller. It tells you that there is a limit to the value of f(n) as n approaches infinity. And what it is? It's the famous
e!
-Mit freundlichem Gruss und, Heil Schrödingers Katze!
