Re: e in the time of phi and square root of pi tuplet hijinks

[Alexander Kobel]

On 2016-11-08 08:45, mclaren wrote:
> Technically speaking, we're also dealing with transcendental tuplets rather
> than irrationals here, since the square root of pi is a transcendental
> number (I think. Pi is known to be transcendental, but is the square of pi
> proven to be transcendental?).

Algebraic numbers form a field. So yes - if sqrt(pi) were algebraic, so 
would be pi. Obviously, they are also closed under root extraction (more 
precisely, powers to rational exponents); hence pi^2 is transcendental, too.


Cheers,
Alexander