Metonic cycle

The Metonic cycle is a special pattern that happens every almost exactly 19 years. After this time, the phases of the Moon, like when it is full or new, come back on the same dates each year. This idea was discovered by a person named Meton of Athens a long time ago, in the 5th century BC.

Even though the Metonic cycle is very close, it is not perfect. If you measure it very carefully, it is a little bit longer than 19 years by about 2 hours, 4 minutes, and 58 seconds. But using whole numbers makes it easier to create a special kind of calendar called a lunisolar calendar.

In a Metonic calendar, there are twelve years with 12 lunar months and seven years with 13 lunar months. This helps match up the Moon's phases with the seasons of the year.

Application in traditional calendars

The Metonic cycle is a special pattern that happens every 19 years. It helps match the lunar calendar, which follows the Moon, with the solar calendar, which follows the Sun. Ancient Babylonians and Hebrews used this cycle in their calendars. For example, in these calendars, certain years have an extra month to keep the calendar in sync.

This 19-year cycle was also important for deciding the date of Easter each year. The Greeks and Hebrews used it, and even a device called the Antikythera mechanism from ancient times showed knowledge of this cycle. The Metonic cycle was also used in other calendars, like the Celtic Coligny calendar and the Runic calendar.

Mathematical basis

The Metonic cycle is a way to match the time it takes for the Earth to go around the Sun (tropical year) with the time it takes for the Moon to go around the Earth (synodic month). This is done by adding an extra month to the calendar every few years.

A normal year based on the Moon is about 354 days, which is about eleven days shorter than a year based on the Sun. Over time, this difference adds up. It takes 19 years for the same moon phases to happen again at the same time of year.

This works because 19 years based on the Sun are almost the same as 235 months based on the Moon. To keep the calendar matching the seasons, seven extra months are added over 19 years. Some years have 12 months and some have 13. This keeps the calendar in line with the seasons.