Calendrical Calculations

by Nachum Dershowitz , Edward M. Reingold

• ISBN13: 9780521702386
• ISBN10: 0521702380
• Edition: 3rd
• Format: Paperback
• Copyright: 2007-12-10
• Publisher: Cambridge University Press

Summary

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. As interest grows in the impact of seemingly arbitrary calendrical systems upon our daily lives, this book frames the calendars of the world in a completely algorithmic form. 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 and Java code for all the algorithms available on the Web. This book is 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.

Table of Contents

List of Frontispieces	p. xii
List of Figures	p. xiii
List of Tables	p. xiv
Abbreviations	p. xv
Mathematical Notations	p. xvi
Preface	p. xix
Credits	p. xxvii
License and Limited Warranty and Remedy	p. xxviii
Calendar Basics	p. 1
Calendar Units and Taxonomy	p. 4
Fixed Day Numbers	p. 9
Negative Years	p. 12
Epochs	p. 14
Julian Day Numbers	p. 16
Mathematical Notation	p. 17
Search	p. 20
Dates and Lists	p. 22
A Simple Calendar	p. 24
Cycles of Days	p. 27
Simultaneous Cycles	p. 30
Cycles of Years	p. 32
Warnings about the Calculations	p. 39
References	p. 41
Arithmetical Calendars
The Gregorian Calendar	p. 45
Structure	p. 45
Implementation	p. 48
Alternative Formulas	p. 52
The Zeller Congruence	p. 56
Holidays	p. 57
References	p. 60
The Julian Calendar	p. 63
Structure and Implementation	p. 63
Roman Nomenclature	p. 65
Roman Years	p. 69
Holidays	p. 70
References	p. 71
The Coptic and Ethiopic Calendars	p. 73
The Coptic Calendar	p. 73
The Ethiopic Calendar	p. 75
Holidays	p. 76
References	p. 77
The ISO Calendar	p. 79
Reference	p. 81
The Islamic Calendar	p. 83
Structure and Implementation	p. 83
Holidays	p. 86
References	p. 87
The Hebrew Calendar	p. 89
Structure and History	p. 90
Implementation	p. 95
Holidays and Fast Days	p. 101
Personal Days	p. 105
Possible Days of Week	p. 108
References	p. 110
The Ecclesiastical Calendars	p. 113
Orthodox Easier	p. 114
Gregorian Easter	p. 116
Astronomical Easter	p. 119
Movable Christian Holidays	p. 119
References	p. 121
The Old Hindu Calendars	p. 123
Structure and History	p. 123
The Solar Calendar	p. 126
The Lunisolar Calendar	p. 128
References	p. 134
The Mayan Calendars	p. 137
The Long Count	p. 138
The Haab and Tzolkin Calendars	p. 139
The Aztec Calendars	p. 145
References	p. 150
The Balinese Pawukon Calendar	p. 153
Structure and Implementation	p. 153
Conjunction Days	p. 159
References	p. 161
Generic Cyclical Calendars	p. 163
Single Cycle Calendars	p. 163
Double Cycle Calendars	p. 166
Summary	p. 168
Astronomical Calendars
Time and Astronomy	p. 171
Position	p. 172
Time	p. 174
The Day	p. 179
The Year	p. 185
Astronomical Solar Calendars	p. 192
The Month	p. 193
Times of Day	p. 207
References	p. 214
The Persian Calendar	p. 217
Structure	p. 217
The Astronomical Calendar	p. 219
The Arithmetic Calendar	p. 221
Holidays	p. 226
References	p. 227
The Baha'i Calendar	p. 229
Structure	p. 229
Western Version	p. 231
The Future Baha'i Calendar	p. 233
Holidays	p. 236
References	p. 237
The French Revolutionary Calendar	p. 239
The Original Form	p. 241
The Modified Arithmetical Form	p. 242
References	p. 244
The Chinese Calendar	p. 247
Solar Terms	p. 248
Months	p. 251
Conversions to and from Fixed Dates	p. 258
The Sexagesimal Cycle of Names	p. 260
Common Misconceptions	p. 263
Holidays	p. 264
Chinese Age	p. 266
Chinese Marriage Auguries	p. 267
The Japanese Calendar	p. 268
The Korean Calendar	p. 269
The Vietnamese Calendar	p. 271
References	p. 272
The Modern Hindu Calendars	p. 275
Hindu Astronomy	p. 281
Calendars	p. 287
Sunrise	p. 292
Alternatives	p. 295
Astronomical Versions	p. 299
Holidays	p. 303
References	p. 312
The Tibetan Calendar	p. 315
Calendar	p. 315
Holidays	p. 319
References	p. 322
Astronomical Lunar Calendars	p. 325
Astronomical Easter	p. 325
Lunar Crescent Visibility	p. 326
The Observational Islamic Calendar	p. 328
The Classical Hebrew Calendar	p. 329
References	p. 331
Coda	p. 333
Appendices
Function, Parameter, and Constant Types	p. 337
Types	p. 337
Function Types	p. 342
Constant Types and Values	p. 356
Lisp Implementation	p. 361
Lisp Preliminaries	p. 361
Basic Code	p. 364
The Egyptian/Armenian Calendars	p. 366
Cycles of Days	p. 367
The Gregorian Calendar	p. 367
The Julian Calendar	p. 372
The Coptic and Ethiopic Calendars	p. 373
The ISO Calendar	p. 376
The Islamic Calendar	p. 377
The Hebrew Calendar	p. 378
The Ecclesiastical Calendars	p. 385
The Old Hindu Calendars	p. 386
The Mayan Calendars	p. 388
The Balinese Pawukon Calendar	p. 392
Time and Astronomy	p. 395
The Persian Calendar	p. 411
The Baha'i Calendar	p. 413
The French Revolutionary Calendar	p. 416
The Chinese Calendar	p. 417
The Modern Hindu Calendars	p. 424
The Tibetan Calendar	p. 435
Astronomical Lunar Calendars	p. 437
Reference	p. 439
Sample Data	p. 441
References	p. 447
Index	p. 449
Envoi	p. 477
About the Cover	p. 479
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