Religion
In reply to the discussion: An interesting graphic about Easter (Dial-up warning large) [View all]struggle4progress
(118,379 posts)The mean sidereal year (that is, the average number of days from vernal equinox to vernal equinox) is about 365.242 days; the mean synodic month (that is, the average number of days from full moon to full moon) is about 29.530 days
The continued fraction expansion of 365242/29530 is (12; 2, 1, 2, 2, 31, 1, 23); dropping the 31 and subsequent terms (since 31 is large compared to the prior fractional terms and therefore will not affect the value much] leads to the continued fraction (12;2,1,2,2), which evaluates to 235/19
So 19 sidereal years contain almost exactly 235 synodic months
You can (if you like) check that the difference 365242/29530 - 235/19 is not even one part in ten thousand, so the approximation is really quite good
So we can make a circular table with 19 entries, showing (say) the phase of the moon on the vernal equinox in 19 successive years, and we can (with very good results) re-use the table again and again, year after year, to predict the phase of the moon on the vernal equinox, making only a very small error each time
The "golden number" of a year is just the number from 1 to 19 telling where the year sits in the Metonic cycle and therefore telling us which of our 19 different table entries to use to predict the phase of the moon on the vernal equinox
And these "golden numbers" occur in an entirely predictable sequence: if the "golden number" for the prior year was a number n < 19, the "golden number" for the current year is n + 1; but if the "golden number" for the prior year was 19, the "golden number" for the current year is 1