What is Euler’s number and Pi ?
In: Mathematics
PI has already been explained by the other comments, it is just the ratio between a circle’s diameter and circumference. So a circle with diameter 1 has a circumference of pi (around 3.141).
Euler’s number e is a little bit harder to explain. In short, Euler’s number is a way of capturing how things grow or shrink when they change at a continuous rate, like populations, investments, or even certain natural processes. I think the easiest explanation is with interest at a bank.
Imagine you have $1 in a bank that offers 100% interest per year. If the bank pays the interest once a year, you’d get $1 of interest after one year, ending up with $2 in total.
If the bank instead pays out 50% interest every 6 months, this is still 100% interest per year, but you end up with slightly more than $2 in the end, because in the last 6 months the interest from the first 6 months is already in your account, helping to generate more interest during the remaining time of the year. The smaller the intervals of the payout are, the stronger this effect and the more money you end up with after one year.
Now, if the bank pays the interest at the smallest possible interval, which is continuous payment (imagine it’s adding a tiny amount of interest an infinite number of times per second, but still only 100% per year in total), the final amount you’d have after one year is exactly the euler number, which is roughly $2.718.
So e is the factor by which an amount grows when it increases continuously at a rate of 100% for one unit of time—starting from 1, it grows to about 2.718 (instead of 2.0 which is for a single non-continous step of growth).
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