Astronomical ratio, convention for continued fractions

[Richard Guy]

Right!  I realized this after I'd sent the
earlier message without thinking.     R.

On Sat, 10 Jun 2006, Gerald McGarvey wrote:

>
> Here is a possible explanation ...
>
> http://www.mlahanas.de/Greeks/Kythera.htm
>
> "...19 years almost exactly matches 235 synodic months,
> which correspond to 235+19=254 revolutions of the moon
> with respect to the stars. It picks up an extra one each
> year from its trip with us around the sun. ..."
>
> Gerry
>
> At 02:53 PM 6/7/2006, Richard Guy wrote:
>> Compare The Book of Numbers, p.177.
>> 
>> Should it be 13 or 12 ????    R.
>> 
>> On Wed, 7 Jun 2006, Andrew Plewe wrote:
>> 
>>> I was reading about the Antikythera Mechanism at The Register:
>>> 
>>> http://www.theregister.co.uk/2006/06/07/antikythera_mechanism/
>>> 
>>> and while doing further Googling came across this AMS article detailing a
>>> continued fraction for computing the Astronomical ratio:
>>> 
>>> http://www.ams.org/featurecolumn/archive/kyth3.html
>>> 
>>> 
>>> 13.368267..  = [13, 2, 1, 2, 1, 1, 17, ...]
>>>
>>>                   1
>>>           = 13 + ------------------------
>>>                      1
>>>                  2+ ---------------------
>>>                         1
>>>                     1+ ------------------
>>>                            1
>>>                        2+ ---------------
>>>                               1
>>>                           1+ ------------
>>>                                   1
>>>                               1+ --------
>>>                                       1
>>>                                  17+ ----
>>>                                       etc
>>> 
>>> Anyway, I thought this might be of general interest to the list and worth
>>> adding to the OEIS if it isn't already in there. Would it be best to 
>>> submit
>>> this as a decimal expansion, with the continued fraction listed in the
>>> comments or formula section? I see that the decimal expansion and 
>>> continued
>>> fractions are listed as seperate sequences for the constant Pi but I'm not
>>> sure if people generally hold to this convention. Thanks!
>>>
>>>         -Andrew Plewe-
>>> 
>