# [seqfan] Re: Algebraic numbers of high degree

Bob Selcoe rselcoe at entouchonline.net
Fri Oct 31 16:54:26 CET 2014

``` >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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