[math-fun] Computing pi (or anything else) to N digits
"Transcendental" means not the root of any finite polynomial with integer coefficients. http://en.wikipedia.org/wiki/Transcendental_number Is there a name for a number which isn't algebraic for a _solvable_ Galois polynomial -- i.e., a number which can't be constructed by rational & root operations?
It is unclear to me exactly what you are asking. But in case you're referring to the (real or complex) root of a polynomial with integer (or more generally, rational) coefficients, those roots are all called "algebraic" numbers. (Regardless of whether there is a formula for them in terms of the coefficients that uses only the four arithmetic operations and integer powers or roots.) --Dan On 2012-10-15, at 7:45 PM, Henry Baker wrote:
"Transcendental" means not the root of any finite polynomial with integer coefficients.
http://en.wikipedia.org/wiki/Transcendental_number
Is there a name for a number which isn't algebraic for a _solvable_ Galois polynomial -- i.e., a number which can't be constructed by rational & root operations?
On Mon, Oct 15, 2012 at 10:45 PM, Henry Baker <hbaker1@pipeline.com> wrote:
"Transcendental" means not the root of any finite polynomial with integer coefficients.
http://en.wikipedia.org/wiki/Transcendental_number
Is there a name for a number which isn't algebraic for a _solvable_ Galois polynomial -- i.e., a number which can't be constructed by rational & root operations?
I think the most common description would be "[not] solvable/expressible by radicals". I don't know of a dedicated term for either state. --Michael -- Forewarned is worth an octopus in the bush.
Radical numbers? -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Michael Kleber Sent: Tuesday, October 16, 2012 6:57 PM To: math-fun Subject: [EXTERNAL] Re: [math-fun] Computing pi (or anything else) to N digits On Mon, Oct 15, 2012 at 10:45 PM, Henry Baker <hbaker1@pipeline.com> wrote:
"Transcendental" means not the root of any finite polynomial with integer coefficients.
http://en.wikipedia.org/wiki/Transcendental_number
Is there a name for a number which isn't algebraic for a _solvable_ Galois polynomial -- i.e., a number which can't be constructed by rational & root operations?
I think the most common description would be "[not] solvable/expressible by radicals". I don't know of a dedicated term for either state. --Michael -- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
-
Dan Asimov -
Henry Baker -
Michael Kleber -
Schroeppel, Richard