# What is a golden number?

scientist with test tubes

There are two very different meanings for a golden number, depending on the context in which the phrase is used. A golden number in mathematics is generally used to refer to the golden ratio, a way in which two quantities interact. A golden number can also refer to a number given to a year to indicate where it falls in an astrological sequence, the Metonic cycle.

The Metonic cycle dates back to antiquity, when Meton of Athens, a famous astronomer, discovered that 19 years corresponded almost exactly to 235 lunar months. The Metonic cycle served as the basis for Western calendar systems until the advent of the Julian calendar in the 1st century and continues to be used in many different situations. Several surviving calendar systems, most notably the Hebrew calendar, continue to be based on a 19-year cycle. Because twelve lunar months are substantially less than a true tropical year, the Metonic cycle included additional months in the third year, 5th year, 8th year, 11th year, 13th year, 16th year, and 19th year of the cycle.

In modern times, the Metonic cycle is used infrequently, but it still gets some use. It was, for example, used to calculate launch windows for lunar missions. It is also most notably used to calculate the date of Easter for the Christian calendar, in both the Eastern Orthodox and Roman Catholic faiths. This calculation, using the golden number and relying on the Metonic cycle, is officially known as the computus.

The golden number is a key part of determining the date of Easter, as it determines which year of the Metonic cycle we are currently in. It can be determined by the formula: Golden number = X mod 19 + 1. For simplicity, this means we take the current year in the Christian era, such as 2009, and divide it by nineteen, and then add one day. This extra day, known as saltus lunae, helps to correct the discrepancy in the calendar caused by a slight difference between the lunar months and the solar year.