# [seqfan] Re: Algebraic numbers of high degree

Charles Greathouse charles.greathouse at case.edu
Fri Oct 31 16:22:13 CET 2014

```> 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
>>
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>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
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