The Jewish Leap Year - Jewish Calendar

The Jewish "leap year", which occurs seven times in a 19-year cycle, has 13 months instead of the regular year's 12. This is so that the lunar-based Jewish year should remain aligned with the solar seasons (12 lunar months make up a total of 354 days -- slightly more than 11 days short of the 365.25 day solar cycle). The added month is called "Adar I" and is inserted before the month of Adar (termed "Adar II" in leap years).

See The 19-Year Marriage.

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The Jewish Year

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July 19, 2012

Calculation

To determine whether a Jewish year is a leap year, one must find its position in the 19-year Metonic cycle. This position is calculated by dividing the Jewish year number by 19 and finding the remainder. For example, Jewish year 5771 divided by 19 results in a remainder of 14, indicating that it is year 14 of the Metonic cycle. Since there is no year 0, a remainder of 0 indicates that the year is year 19 of the cycle. (See also Golden number (time).)

Years 3, 6, 8, 11, 14, 17, and 19 the Metonic cycle are leap years.

Frank
Yonkers, NY

February 21, 2011

calendar calculation algorithms

I am a software engineer/ mathematician and I was wondering if there are algorithms to calculate the calendar accurately. I have tried to follow all the evolution of the calendar during the centuries, it is very interesting but it appears to me that there is always some human decision in the definition of the calendar even today. Pardon my ignorance on the subject, my interest is purely mathematical algorithmic. Can someone give me some references or directions about it. Any help will be highly appreciated. Thank You,

Walter
Babylon, NY/USA