[e^([pi]i)]+1=0 :I had a friend with a T-shirt displaying this deceptively simple equation. I know it to be true, but I have no real understanding of the relationship between these three apparently unrelated, irrational numbers (e,pi and i) within this equation. While I know how significant this discovery is in that it relates and brings a sort of whimsical unification between e, pi, and i, I fail to understand the true nature of this statement, or how it exists for that matter. Could anyone here explain, in somewhat detailed terms, how to create this proof/equation based on prior knowledge of the numbers it involves, but not based on the knowledge that it is infact true. Plus, what does this equation mean in relation to the greater body of mathematics? How can it (if at all) be applied beyond number theory?