## Calendrical CalculationsThis new edition of the successful calendars book is being published at the turn of the millennium and expands the treatment of the previous edition to new calendars and variants. As interest grows in the impact of seemingly arbitrary calendrical systems upon our daily lives, this book frames the world in a completely algorithmic form. The book gives a description of twenty-five calendars and how they relate to one another: the Gregorian (current civil), ISO (International Organization for Standardization), Egyptian (and nearly identical Armenian), Julian (old civil), Coptic, Ethiopic, Islamic (Moslem), modern Persian (both astronomical and arithmetic forms), Baha'i (both present and future forms), Hebrew (Jewish), Mayan (long count, haab, and tzolkin), Balinese Pawukon, French Revolutionary (both astronomical and arithmetic forms), Chinese (and nearly identical Japanese), old Hindu (solar and lunisolar), and modern Hindu (solar and lunisolar). Easy conversion among these calendars is a by-product of the approach, as is the determination of secular and religious holidays. Calendrical Calculations makes accurate calendrical algorithms readily available for computer use with LISP, Mathematica, and Java code for all the algorithms included on the CD, and updates are available on the Web. This book will be a valuable resource for working programmers as well as a fount of useful algorithmic tools for computer scientists. In addition, the lay reader will find the historical setting and general calendar descriptions of great interest. |

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#### LibraryThing Review

User Review - Garzo - LibraryThingI didn't know there was such a thing as a Calendar Nerd until I read this book. Calendrical Calculations has complete and reliable details on major calendar systems. It mixes culture with maths in a heady mix that will put your brain in epicycles. Read full review

#### Review: Calendrical Calculations

User Review - Enrico - GoodreadsVery well written and exceptionally implemented. Focus is on clarity, from approximation to correct value. Read full review

### Contents

Introduction | 3 |

11 Calendar Units and Taxonomy | 7 |

12 Fixed Day Numbers | 11 |

13 Negative Years | 15 |

15 Julian Day Numbers | 18 |

16 Mathematical Notation | 19 |

17 Search | 21 |

18 Dates and Lists | 23 |

129 Astronomical Lunisolar Calendars | 207 |

References | 208 |

The Persian Calendar | 211 |

131 Structure | 212 |

132 The Astronomical Calendar | 213 |

133 The Arithmetic Calendar | 215 |

134 Holidays | 220 |

References | 221 |

19 A Simple Calendar | 24 |

110 Cycles of Days | 27 |

111 Simultaneous Cycles | 30 |

112 Cycles of Years | 32 |

113 Warnings about the Calculations | 39 |

References | 41 |

Arithmetical Calendars | 45 |

The Gregorian Calendar | 47 |

22 Implementation | 50 |

23 Alternative Formulas | 55 |

24 Holidays | 58 |

References | 60 |

The Julian Calendar | 63 |

32 Roman Nomenclature | 66 |

33 Holidays | 70 |

References | 72 |

The Coptic and Ethiopic Calendars | 75 |

42 The Ethiopic Calendar | 77 |

43 Holidays | 78 |

References | 80 |

The ISO Calendar | 83 |

Reference | 84 |

The Islamic Calendar | 87 |

62 Holidays | 90 |

References | 92 |

The Hebrew Calendar | 95 |

71 Structure and History | 96 |

72 Implementation | 101 |

73 Holidays and Fast Days | 106 |

74 Personal Days | 111 |

References | 114 |

The Ecclesiastical Calendars | 117 |

81 Orthodox Easter | 118 |

82 Gregorian Easter | 120 |

83 Astronomical Easter | 122 |

References | 124 |

The Old Hindu Calendars | 127 |

92 The Solar Calendar | 130 |

93 The Lunisolar Calendar | 132 |

References | 139 |

The Mayan Calendars | 141 |

101 The Long Count | 142 |

102 The Haab and Tzolkin Calendars | 144 |

References | 150 |

The Balinese Pawukon Calendar | 153 |

112 Conjunction Days | 160 |

References | 162 |

Astronomical Calendars | 163 |

Time and Astronomy | 165 |

121 Position | 166 |

122 Time | 168 |

123 The Day | 175 |

124 The Year | 179 |

125 The Month | 185 |

126 Times of Day | 197 |

127 Astronomical Solar Calendars | 203 |

128 Astronomical Lunar Calendars | 204 |

The Bahai Calendar | 223 |

142 Western Version | 226 |

143 Future Calendar | 228 |

144 Holidays | 230 |

References | 231 |

The French Revolutionary Calendar | 233 |

151 The Original Form | 235 |

152 The Modified Form | 237 |

References | 239 |

The Chinese Calendar | 241 |

161 Solar Terms | 242 |

162 Months | 246 |

163 Conversions to and from Fixed Dates | 254 |

164 The Sexagesimal Cycle of Names | 256 |

165 Common Misconceptions | 259 |

166 Holidays | 260 |

167 Chinese Age | 261 |

168 The Japanese Calendar | 262 |

References | 263 |

The Modern Hindu Calendars | 267 |

171 Hindu Astronomy | 271 |

172 Calendars | 277 |

173 Sunrise | 283 |

174 Alternatives | 287 |

175 Holidays | 288 |

References | 295 |

Coda | 299 |

Appendices | 301 |

Function Parameter and Constant Types | 303 |

A2 Function Types | 306 |

A3 Constant Types and Values | 312 |

Lisp Implementation | 317 |

B2 Basic Code | 322 |

B3 The EgyptianArmenian Calendars | 323 |

B4 Cycles of Days | 324 |

B5 The Gregorian Calendar | 325 |

B6 The Julian Calendar | 330 |

B7 The Coptic and Ethiopic Calendars | 333 |

B8 The ISO Calendar | 335 |

B9 The Islamic Calendar | 336 |

B10 The Hebrew Calendar | 337 |

B11 The Ecclesiastical Calendars | 343 |

B12 The Old Hindu Calendars | 344 |

B13 The Mayan Calendars | 346 |

B14 The Balinese Pawukon Calendar | 349 |

B15 Time and Astronomy | 352 |

B16 The Persian Calendar | 369 |

B17 The Bahai Calendar | 372 |

B18 The French Revolutionary Calendar | 375 |

BI9 The Chinese Calendar | 377 |

B20 The Modern Hindu Calendars | 383 |

Reference | 392 |

Sample Data | 395 |

401 | |

403 | |

Envoi | 423 |

### Common terms and phrases

algorithms angle approx approximate arithmetic arya-lunar-month arya-solar-month astronomical b-date Baha'i bahai-date balinese-date begin bogus boolean C.E. Julian calculations Chinese calendar compute Coptic Coptic calendar days 30 days days in prior defconstant defun determine Easter epoch equation equinox Ethiopic fixed-from-gregorian fixed-from-hebrew fixed-from-julian fN fN formula French Revolutionary French Revolutionary calendar function g-year january given Gregorian calendar gregorian-date g-year gregorian-year fixed-date gregorian-year-from-fixed haab Hebrew calendar hebrew-date hebrew-year Hindu calendar holidays integer Islamic calendar janl Julian calendar Julian day number Julian-date kalends leap day leap month leap-year length Lisp list-of-fixed-dates longitude lunar day lunar month lunisolar calendar March 21 Mayan mean mean-tropical-year midnight month day new-year noon number of days old Hindu Pawukon Persian calendar positive-integer quotient R.D. date rational-moment roman-date sidereal sin-degrees solar month solar term solar-longitude solstice standard-day standard-month standard-year Sunday sunrise sunset Tishri TYPE fixed-date TYPE gregorian-year tzolkin