Why is ln($\pi^{\pi}$) rational?
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
closed as off topic by darij grinberg, Ryan Budney, Henry Cohn, Yemon Choi, Tom Church Feb 19 '12 at 0:53Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question. 


It is not known if it is rational. It's suspected to be transcendental over $\mathbb Q$. It is known that $e^\pi$ is transcendental, but none of $e^e,\pi^e,\pi^\pi$ is known to be irrational or transcendental. 

