A golden number is a number assigned to each year

Year

A year is the orbital period of the Earth moving around the Sun. For an observer on Earth, this corresponds to the period it takes the Sun to complete one course throughout the zodiac along the ecliptic....

 in sequence to indicate the year's position in a 19-year Metonic cycle

Metonic cycle

In astronomy and calendar studies, the Metonic cycle or Enneadecaeteris is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the solar year and the synodic month...

. They are used in the computus

Computus

Computus is the calculation of the date of Easter in the Christian calendar. The name has been used for this procedure since the early Middle Ages, as it was one of the most important computations of the age....

 (the calculation of the date of Easter

Easter

Easter is the central feast in the Christian liturgical year. According to the Canonical gospels, Jesus rose from the dead on the third day after his crucifixion. His resurrection is celebrated on Easter Day or Easter Sunday...

) and also in the Runic calendar

Runic calendar

A Runic calendar is a perpetual calendar based on the 19 year long Metonic cycle of the Moon. Runic calendars were written on parchment or carved onto staves of wood, bone, or horn. The oldest one known, and the only one from the Middle Ages, is the Nyköping staff, believed to date from the 13th...

. The golden number of any Julian

Julian calendar

The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...

 or Gregorian

Gregorian calendar

The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...

 calendar year can be calculated by dividing the year by 19, taking the remainder, and adding 1. (In mathematics this can be expressed as (year number modulo

Modulo operation

In computing, the modulo operation finds the remainder of division of one number by another.Given two positive numbers, and , a modulo n can be thought of as the remainder, on division of a by n...

 19) +1.)

For example, divided by 19 gives , remainder . Adding the number before to the number that you are using gives a golden number of .

The term golden number is first documented in Hildegard of Bingen

Hildegard of Bingen

Blessed Hildegard of Bingen , also known as Saint Hildegard, and Sibyl of the Rhine, was a German writer, composer, philosopher, Christian mystic, Benedictine abbess, visionary, and polymath. Elected a magistra by her fellow nuns in 1136, she founded the monasteries of Rupertsberg in 1150 and...

's Ordo Virtutum

Ordo Virtutum

Ordo Virtutum is an allegorical morality play, or liturgical drama, by Hildegard of Bingen, composed c. 1151...

(ca. 1151) and in the computistic poem Massa Compoti by Alexander de Villa Dei in 1200. Later, a scribe added it to tables originally composed by Abbo of Fleury

Abbo of Fleury

Abbo of Fleury , also known as Abbon or Saint Abbo was a monk, and later abbot, of the Benedictine monastery of Fleury sur Loire near Orléans, France....

in 988.