The term “golden number” can refer to the golden ratio in mathematics or to a number used in the Metonic cycle, an astrological sequence discovered by Meton of Athens. The Metonic cycle is used to calculate the date of Easter and is still used in some situations today. The golden number helps determine which lunar month Easter falls in, simplifying the calculation. Easter always falls on the third Sunday of the Easter month in the lunar system.
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 usually 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. A number of surviving calendar systems, notably the Jewish calendar, continue to be based on a 1-year cycle. Since twelve lunar months are substantially less than a true tropical year, the Metonic cycle included additional months in the 19th year, 3rd year, 5th year, 8th year, 11th year, 13th year and 16th year of the cycle.
In modern times, the metonic cycle is seldom used, but still has some use. It has, for example, been used to calculate launch windows for lunar missions. It is also notably used to calculate the date of Easter for the Christian calendar, in both the Eastern Orthodox faith and the Roman Catholic faith. This calculation, which uses the golden number and is based on the metonic cycle, is officially known as the computus.
The golden number is a key part in determining the date of Passover, 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. To simplify, this means we take the current year in the Christian era, such as 2009, and divide it by nineteen, then add one day. This extra day, known as the saltus lunae, helps correct the discrepancy in the calendar caused by a slight difference between the lunar months and the solar year.
The golden number is important in this calculation because Easter must fall on a Sunday within the third week of a lunar month that falls after the vernal equinox. This is a complex concept and can be difficult to understand, so the golden number helps by simplifying the calculation of the month. Essentially, the vernal equinox is determined by the solar calendar, and therefore falls on March 21st. At the same time, the traditional system of months was based on lunar months, and Easter is determined according to this lunar system.
Finding the golden number allows you to understand where exactly the lunar month is in relation to March 21st. Once you know which lunar month has its midpoint, or formal full moon, after March 21, you can take that Sunday and determine that it is Easter. To put it another way: Within the solar calendar, which most of us use on a daily basis, Easter appears to move around the calendar between March 22nd and April 25th. But in the lunar system, represented by the golden number, Easter always falls on the third Sunday of the Easter month, every year.
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