Sum fun things about numbers courtesy my friend Srinivas Shastri a very wise lover of maths
There was this question once asked in JEE
Which is greater? e^π or π^e?
The solution to this problem is simple yet elegant
The trick is to see that the function x^(1/x) is max when x=e. So:
e^(1/e) > π^(1/π)
Raising both sides to eπ, we get: