scientist with beakers
There are two very different meanings for a golden number, depending on the context in which the phrase is used. A golden ratio in mathematics is often used to refer to the golden ratio, a way in which two quantities interact. A golden ratio 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 ancient times, 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 first 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 year 3, 5, 8, 11, 13, 16, and 19 of the cycle.
In modern times, the metonic cycle is rarely used, but it is still used. It was used, for example, 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 ratio and relying on the metonic cycle, is officially known as computus.
The golden ratio 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 ratio = X mod 19 + 1. For simplicity, this means we take the current year in the Christian era, such as 2009, divide it by nineteen, and then add one day. This extra day, known as saltus lunae, helps correct the discrepancy in the calendar caused by a slight difference between the lunar months and the solar year.
The golden ratio is important in this calculation because Easter must fall on a Sunday in the third week of a lunar month after the vernal equinox. This is a complex concept and can be difficult to understand, so the golden ratio helps to simplify the calculation of the month. In essence, the spring equinox is determined by the solar calendar and therefore falls on March 21. At the same time, the traditional system of months was based on the lunar months, and Easter is determined based on this lunar system.
Finding the golden number allows you to know exactly where the lunar month is in relation to March 21. Once you know which lunar month has its midpoint, or formal full moon, after March 21, you can take that Sunday and determine if it’s Easter. In other words: Within the solar calendar, which most of us use on a daily basis, Easter seems to fluctuate around the calendar between March 22 and April 25. But in the lunar system, which represents the golden number, Easter always falls on the third Sunday of the month of Easter each year.