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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2400000.5, which counts days from midnight, Wednesday, November 17, 1858 (Gregorian). This is equivalent to defining mjd-epoch def = R.D. fixed-from-mjd (mjd) mjd-from-fixed (date) 678576 (1.6) def = mjd + mjd-epoch (1.7) def date − mjd-epoch (1.8) = We do not use modified julian days directly because we want positive numbers for dates within recent history. 1.6 Mathematical Notation The best notation is no notation. —Paul Halmos: How to Write Mathematics (1970) We use the

particular, when y = 1, x mod 1 is the fractional part of x, allowing us to obtain the time of day as a fraction from a moment by time-from-moment (t) def = t mod 1 (1.16) In programming languages (including C, C++, and Pascal) without a built-in remainder function that works for nonintegers, the definition given in (1.15) must be used instead. 1.6 Mathematical Notation 19 There are five important consequences of definition (1.15). First, if y > 0, then x mod y ≥ 0, for all x, even for

Philadelphia, 1983. [12] J. Hastings, ed., Encyclopædia of Religion and Ethics, Charles Scribner’s Sons, New York, 1908–1922. 42 1 Calendar Basics [13] H. Henderson and B. Puckett, Holidays & Festivals Index, Omnigraphics, Inc., Detroit, MI, 1995. [14] H. Henderson and S. E. Thompson, Holidays, Festivals & Celebrations of the World Dictionary, 2nd ed., Omnigraphics, Inc., Detroit, MI, 1997. [15] J. F. W. Herschel, Outlines of Astronomy, 3rd ed., Longman, Brown, Green, Longmans, and Roberts,

The Solar Calendar 127 Table 9.2: Hindu solar (saura) months, named after the signs of the zodiac corresponding to the position of the mean sun. Vedic (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Sanskrit Madhu M¯adhava ´ Sukra ´ Suchi Mes.a Vr.s.abha Mithuna Karka Sim . ha Kany¯a Tul¯a Vr.s´cika Dhanus Makara Kumbha M¯ına Nabhas Nabhasya Issa ¯ Urja Sahas Sahasya Tapas Tapasya c Zodiacal Sign Lunisolar Month Aries Taurus Gemini Cancer Leo Virgo Libra Scorpio Sagittarius Capricorn

Calendar Basics A learned man once asked me regarding the eras used by different nations, and regarding the difference of their roots, that is, the epochs where they begin, and of their branches, that is, the months and years, on which they are based; further regarding the causes which led to such difference, and the famous festivals and commemoration-days for certain times and events, and regarding whatever else one nation practices differently from another. He urged me to give an explanation,