Astronomical ratio, convention for continued fractions

[Gerald McGarvey]

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-
>>