Tag Archives: calendar

Hebrew Calendar

click to enlarge monthsThe Jewish calendar is based on both the lunar and the solar cycles and is used for computing Jewish holidays. Hebrew days begin at sunset when three stars are visible. An ordinary year has 12 months, and a leap year has 13 months. Every month starts approximately on the day of a new moon. There are three year lengths for ordinary years and three for leap years.


Year type Ordinary Year Leap Year
deficient 353 383
regular 354 384
complete 355 385

In a regular year, months alternate between 29 and 30 days.

The Jewish New Year starts on 1 Tishri, called Rosh Hashana, which celebrates the creation of the world (assumed to be 3761 BC). There is a rather complicated set of 5 rules for determining the date of Rosh Hashana. A formula for computing Rosh Hashana is given by Berlekamp et al. (1982), and a Lisp program for computing the Jewish calendar by Reingold and Dershowitz (1989).



Sunset is the time at which the trailing limb of the Sun first sets below the horizon. The effect of refraction in the Earth’s atmosphere lifts the image of the Sun about half a degree at the horizon, making sunset about two minutes later than would be expected from the actual position of the Sun in space. Refraction and the fact that sunrise and sunset are calculated from the limb (and not the center) slightly lengthen “day” relative to “night.”


Berlekamp, E. R.; Conway, J. H.; and Guy, R. K. Winning Ways, For Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, p. 800, 1982.

Dershowitz, N. and Reingold, E. M. Calendrical Calculations: The Millennium Edition. Cambridge, England: Cambridge University Press, 1999.

Reingold, E. M. and Dershowitz, N. “Calendrical Calculations.” Technical Report UIUCCDCS-R-89-1541. Department of Computer Science, Univ. Illinois, Urbana-Champaign, IL, 1989. ftp://a.cs.uiuc.edu/.

Ross, K. L. “The Jewish and Moslem Calendars and the Era of Nabonassar.” http://www.friesian.com/calendar.htm#nabo.

Ross, K. L. “The Jewish Calendar.” http://www.friesian.com/calendar.htm#jewish.

Tøndering, C. “Frequently Asked Questions about Calendars.” http://www.tondering.dk/claus/calendar.html.

Vardi, I. Computational Recreations in Mathematica. Redwood, CA: Addison-Wesley, p. 240, 1991.

© 1996-2007 Eric W. Weisstein

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calendar in three

 The number of days less in a 400-year period after the adoption of the Gregorian calendar, created by Pope Gregory XIII in 1582 to reform the old Julian calendar.

The minimum number of complete (full) weeks in a month.
The number of months in a quarter of a year.
March’s birthstone is aquamarine, jasper or bloodstone (for wisdom). 
March’s flower is violet or jonquil.
March’s full moon is named “Sap Moon”.
The number of U.S. states which do not use Daylight Saving Time: Arizona, Hawaii and Indiana, which has 3 different time zones.
The number of different time zones used by the state of Indiana:
[1] 76 counties using Eastern Time Zone all year, excluding 16 counties bordering other states,
[2] Six counties near Chicago, Illinois and 5 near Evansville, Indiana use in Central Time Zone together with Daylight Saving Time, and
[3] Two counties near Cincinnati, Ohio and 3 near Louisville, Kentucky use Eastern Time Zone together with Daylight Saving Time.
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The Mayan Calendar

Mayan pyramid

Mayan pyramid

Among their other accomplishments, the ancient Mayas invented a calendar of remarkable accuracy and complexity. At right is the ancient Mayan Pyramid Chichen Itza, Yucatan, Mexico. The Pyramid of Kukulkan at Chichén Itzá, constructed circa 1050 was built during the late Mayan period, when Toltecs from Tula became politically powerful. The pyramid was used as a calendar: four stairways, each with 91 steps and a platform at the top, making a total of 365, equivalent to the number of days in a calendar year. 

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