[seqfan] Re: Algebraic numbers of high degree
Frank Adams-Watters
franktaw at netscape.net
Sun Nov 2 07:23:06 CET 2014
Any number which is an actual physical measurement cannot be assumed to
be algebraic. So, in A248424, if an AU was defined as "the average
distance of the Earth from the Sun", we would not be able to call that
number algebraic. But in fact, that number can be simply calculated; no
observations are required.
Franklin T. Adams-Watters
-----Original Message-----
From: Bob Selcoe <rselcoe at entouchonline.net>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Sun, Nov 2, 2014 1:10 am
Subject: [seqfan] Re: Algebraic numbers of high degree
>There is an irreducible integer polynomial P(x) of degree 86400 such
that
> P(A248424) = 0, and if Q is an integral polynomial of degree less than
> 86400 then Q(A248424) is nonzero.
Thanks, Charles.
> The degree comes from "...arcscond..." and so the connection to the
number
> of seconds in a day is not entirely coincidental -- both have factors
of
> 60
> * 60, for one thing.
Precisely the reason why I suspect other astrophysical movements might
yield
related results - maybe even of higher degree? For example, perhaps
the
(approximate) astronomical unit for Pluto subtending its 1 arcsecond
angle
is a constant with degree equivalent to the number of seconds (in Earth
units) in one Plutonian day (approx. 550,000). That may be a poor
example
(again, I'm not an astrophysicist), but perhaps something along those
lines.
Cheers,
Bob
--------------------------------------------------
From: "Charles Greathouse" <charles.greathouse at case.edu>
Sent: Friday, October 31, 2014 10:22 AM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Algebraic numbers of high degree
>> I'm not sure what Charles' comment "This constant is algebraic of
degree
> 86400" in A248424 means
>
> There is an irreducible integer polynomial P(x) of degree 86400 such
that
> P(A248424) = 0, and if Q is an integral polynomial of degree less than
> 86400 then Q(A248424) is nonzero.
>
>> since the constant in A248424 pertains to the radius of the Earth's
orbit
> around the Sun (1 AU), might there be some kind of astrophysical
> connection?
>
> The degree comes from "...arcscond..." and so the connection to the
number
> of seconds in a day is not entirely coincidental -- both have factors
of
> 60
> * 60, for one thing.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Oct 31, 2014 at 10:47 AM, Bob Selcoe
<rselcoe at entouchonline.net>
> wrote:
>
>> Hello Charles et al.,
>>
>> I'm not sure what Charles' comment "This constant is algebraic of
degree
>> 86400" in A248424 means, or what makes it such high degree - but
86400
>> is,
>> of course, the number of seconds in a 24 hour day.
>>
>> I'm not an astrophysicist; but since the constant in A248424
pertains to
>> the radius of the Earth's orbit around the Sun (1 AU), might there
be
>> some
>> kind of astrophysical connection?? ( I know 24 hours/day is an
>> approximation, but so is 1 AU - albeit very close).
>>
>> Perhaps other constants of this type "in the wild" might be found in
>> relation to other planetary orbits, or other astrological movements?
>>
>> Cheers,
>> Bob Selcoe
>>
>> --------------------------------------------------
>> From: "Charles Greathouse" <charles.greathouse at case.edu>
>> Sent: Friday, October 31, 2014 12:07 AM
>> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
>> Subject: [seqfan] Algebraic numbers of high degree
>>
>> I just approved sequence A248424, an algebraic number of degree
86400.
>> Are
>>> there other algebraic constants of high degree in the OEIS? I don't
want
>>> to
>>> suggest that this is a record, but it seems rare to find such high
>>> degree
>>> 'in the wild' as it were. (This may be an artifact of our limited
>>> nature.)
>>> For example, I've seen Conway's constant A014715 used as an example
of a
>>> high-degree constant, but it's much lower in degree than this one.
>>>
>>> Charles Greathouse
>>> Analyst/Programmer
>>> Case Western Reserve University
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
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