why isnt sqrt(x^2 + y^2) a polynomial?
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From: mike on 4 Jul 2010 01:07 why isnt sqrt(x^2 + y^2) a polynomial? Thanks in advance! Mike
From: Gerry on 4 Jul 2010 01:33 On Jul 4, 3:07 pm, mike <mike_newsgro...(a)yahoo.com> wrote: > why isnt sqrt(x^2 + y^2) a polynomial? > > Thanks in advance! Which polynomial do you think it should be? -- GM
From: Edson on 3 Jul 2010 21:33 Because, by definition, a polynomial in 2 variables is a function of the form P(x, y) = Sum(i = 0, m) Sum(j = 0, n) c_i_j x^i y^j f(x, y) = sqrt(x^2 + y^2) = (x^2 + y^2)^(1/2) is not of this form. f^2 is, but not f. Edson
From: Axel Vogt on 4 Jul 2010 03:26 mike wrote: > why isnt sqrt(x^2 + y^2) a polynomial? The question is a bit ill-posed: what do you mean by 'sqrt'? About what 'objects' you are talking?
From: Frederick Williams on 4 Jul 2010 05:34 Edson wrote: > > Because, by definition, a polynomial in 2 variables is a function of the form > > P(x, y) = Sum(i = 0, m) Sum(j = 0, n) c_i_j x^i y^j > > f(x, y) = sqrt(x^2 + y^2) = (x^2 + y^2)^(1/2) is not of this form. Maybe the OP wants a proof that (x^2 + y^2)^(1/2) can't be put in the form P(x, y). > f^2 is, but not f. -- I can't go on, I'll go on.
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