[seqfan] Re: A sequence from Johannes Kepler's "Harmonices Mundi"

[Neil Sloane]

> Maybe we need an index entry for these fraction trees?

Antti, that would be a great idea. Can you get it started?
It would go under,

fractions, trees of,

in this part of the Index:

 https://oeis.org/wiki/Index_to_OEIS:_Section_Fo

but there should be cross-references to it from other parts of the Index
where the individual trees (Stern-Brocot, etc) are mentioned.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sun, Feb 12, 2017 at 8:36 AM, Antti Karttunen <antti.karttunen at gmail.com>
wrote:

> On Sun, Feb 12, 2017 at 11:32 AM, <seqfan-request at list.seqfan.eu> wrote:
>
> >
> >
> > Message: 15
> > Date: Sat, 11 Feb 2017 12:34:58 +0100
> > From: Peter Luschny <peter.luschny at gmail.com>
> > To: "seqfan at list.seqfan.eu" <seqfan at list.seqfan.eu>
> > Subject: [seqfan] A sequence from Johannes Kepler's "Harmonices Mundi"
> > Message-ID:
> >         <CAMMbGZYKfrtSwZvvgjpzU7eL8cMnAG1PTxvUCDgFTqfZ6g0uAg at mail.
> > gmail.com>
> > Content-Type: text/plain; charset=UTF-8
> >
> > We all know Stern-Brocot, Dijkstra, and the Calkin and Wilf tree.
> > David Eppstein posted today on G+ this picture [0].
> >
> > And Eppstein added to Wikipedia: "Even earlier, a similar tree appears in
> > Johannes Kepler's "Harmonices Mundi" (1619, volume=III, page=27)." [1]
> >
> > Hope you like it as much as I do.
> >
> > Peter
> >
> > [0] http://www.ics.uci.edu/~eppstein/0xDE/CalkinWilfKepler.png
> > [1] https://archive.org/stream/ioanniskepplerih00kepl#page/27/mode/1up
> > [2] https://oeis.org/A002487
> >
> >
> > ------------------------------
> >
> >
> Please see also
> http://oeis.org/search?q=kepler+tree&language=english&go=Search
> Especially http://oeis.org/A086592 (and the links & references there).
>
> The name adopted in OEIS for the Kepler's variant seems to be settled as
> "Kepler's tree of harmonic fractions".
>
> Mapping the unique fractions between such systems induces several
> permutations of natural numbers, e.g.:
> http://oeis.org/search?q=id%3AA258746%7Cid%3AA258996&sort=
> &language=&go=Search
> but probably not all combinations are yet in OEIS, or then appear under
> another guise.
>
> Maybe we need an index entry for these fraction trees?
>
>
>
> Best regards,
>
> Antti
>
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>