Graduate "The 7 Strangest Coincidences in the Laws of Nature" (S. Hossenfelder)

[billtodd]

How could it be! One is trancendental and the other is not.

I have a question to you.
Can a Transcendental number to the power of algebraic number be a Trascendental number?

For example take $e^{\varphi}$, where $\varphi$ is the golden number solution to $x^2+x+1=0$, how would one prove that it's transcendental?

Can $\pi$ be a Transcendental number raise to the power of an algebraic number?

That would be interesting if it's possible, and if it's not then I would welcome a proof/argument why it's not.

 

[Vanadium 50]

Can π be a Transcendental number raise to the power of an algebraic number?

π = π¹.

 

[jedishrfu]

Looks like its that time again. This thread has run its transcendental course back to itself and so its a good time to close it.

Thank you all for contributing here.

Jedi