On Tue, Mar 30, 2010 at 9:51 AM, Rob Beezer <[email protected]> wrote:
> Is, of course, impossible, with the usual example being that 60
> degrees cannot be trisected, since 20 degrees is not constructible,
> since the the cosine of 20 degrees is not constructible, since
> adjoining the cosine of 20 degrees to the rationals creates a field
> extension whose degree is not a power of 2.
>
> A modern approach:
>
> sage: isinstance(log(QQ[cos(pi/9)].degree(),2), Integer)
> False

Since

sage: isinstance(4/2, Integer)
False

but

sage: 4/2 in ZZ
True

I would be more comfortable with:

sage: log(QQ[cos(pi/9)].degree(),2) in ZZ
False

William

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