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June 2nd, 2016, 08:40 AM  #1 
Banned Camp Joined: Apr 2016 From: Australia Posts: 244 Thanks: 29 Math Focus: horses,cash me outside how bow dah, trash doves  4 times pi squared
is this number transcendental?

June 2nd, 2016, 08:51 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Yes, of course. If it were not it would satisfy a polynomial equation, say nth degree, with integer coefficients. But since any integer power of 4 is an integer that would then give a polynomial equation, of degree 2n, with integer coefficients, satisfied by $\displaystyle \pi$,which is impossible because $\displaystyle \pi$ is transcendental.

June 2nd, 2016, 09:00 AM  #3 
Banned Camp Joined: Apr 2016 From: Australia Posts: 244 Thanks: 29 Math Focus: horses,cash me outside how bow dah, trash doves 
ok sweet so if I then divide it by three, still transcendental?

June 2nd, 2016, 04:12 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Seriously? Since you simply asked whether a specific number was "transcendental", I assumed you knew what "transcendental number" meant! Are you now saying that you do not? A number, a, is "transcendental" if and only there exist a polynomial equation with integer coefficients (equivalently "rational coefficients") having a as a root. If a3 were NOT transcendental, then there would exist a Polynomial, of degree n, having a/3 as a root. Then that same polynomial, multiplied by 3 to the nth power, would have x as a root showing that a is not transcendental. 
June 4th, 2016, 10:56 AM  #5  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Quote:
Quote:
 
July 31st, 2016, 04:13 AM  #6 
Banned Camp Joined: Apr 2016 From: Australia Posts: 244 Thanks: 29 Math Focus: horses,cash me outside how bow dah, trash doves 
yea its ok don't stress I was taking the piss over the gamma(2/3) thing.


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