# Calendrical Calculations

## Nachum Dershowitz

Language: English

Pages: 512

ISBN: 0521702380

Format: PDF / Kindle (mobi) / ePub

A valuable resource for working programmers, as well as a fount of useful algorithmic tools for computer scientists, this new edition of the popular calendars book expands the treatment of the previous edition to new calendar variants: generic cyclical calendars and astronomical lunar calendars as well as the Korean, Vietnamese, Aztec, and Tibetan calendars. The authors frame the calendars of the world in a completely algorithmic form, allowing easy conversion among these calendars and the determination of secular and religious holidays. LISP code for all the algorithms are available on the Web.

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Calendar Basics Because our cycles always have length c > 0, the definition of the mod function guarantees that (yl mod c) ≥ 0, so we can drop that part of the inequality to get (yl mod c) < l. (1.69) For example, on the Julian calendar for years C.E. (see Chapter 3) we want l = 1 leap year in the cycle of c = 4 years; then year y > 0 is a leap year if (y mod 4) < 1, or, in other words, if (y mod 4) = 0. We can complicate the leap-year situation by insisting year 0 be in position in the cycle

present. Of course, the dates of most holidays will not be historically correct over that range. The astronomical code we use is not the best available, but it works quite well in practice, especially for dates near the present time, around which its approximations are centered. More precise code would be more time-consuming and complex and would not necessarily yield more accurate results for those calendars that depended on observations, tables, or less accurate calculations. Thus, the

Troesch, “Interprétation géométrique de l’algorithme d’Euclide et reconnaissance de segments,” Theoret. Comp. Sci., vol. 115, pp. 291–319, 1993. [33] B. L. van der Waerden, “Tables for the Egyptian and Alexandrian Calendar,” ISIS, vol. 47, pp. 387–390, 1956. If you steal from one author it’s plagiarism; if you steal from many, it’s research. —Attributed to Wilson Mizner Part I Arithmetical Calendars 43 44 Swedish almanac pages for February, 1712, showing a 30-day month. The Swedish date is

Maimonides [13, 7:8] ascribes this correction in the calendar of approximately half a day, on the average, to the need to better match the mean date of appearance of the new moon of the month of Tishri; al-B¯ır¯un¯ı [2] attributes it to astrological considerations. The real purpose of the delay is moot. 7.1 Structure and History 93 3. In some cases (about once in 30 years) an additional delaying factor may need to be employed to keep the length of a year within the allowable ranges. (It is

example, Spanish and Portuguese Jews never observe the anniversary of a common-year date in Adar I. As with birthdays, anniversaries in a given Gregorian year must be collected: def = yahrzeit-in-gregorian (death-date, g-year) (7.41) {date1 , date2 } ∩ gregorian-year-range (g-year) where jan1 = y = date1 = yahrzeit (death-date, y) date2 = yahrzeit (death-date, y + 1) gregorian-new-year (g-year) hebrew-from-fixed jan1 year 7.5 Possible Days of Week As described on page 92, the