Some Special Numbers?

Question

Some constants 0, 1, i, e, and Pi have many important and unique properties. What are these numbers? How are the related to eachother? How did they develop in the history of mathematics?

Answer 1

0 is need for the additave identity, that is wahat number added to x gives back x - it makes the reals under addition into a group.

1 produces all other numbers, ie 4=1+1+1+1

i is need to make equations like
x^2+1=0 have a solution

Pi is that number which determinies the area of a circle ( it crops up in others things also) - also one of the first transendentals

e is a little harder it comes up in numerous places but im not sure how it was frist found naturaly

Answer 2

Don't forget the Euler-Mascheroni constant which is the limit between the difference of log(n) and the numerical integration approximation to log(n). So limit n -> 00 of sum(1/k,k=1..n)-log(n). Where log=natural log! It is something like .57......