Marketing Fragment 6 X 11.T65

Cambridge University Press 978-0-521-70238-6 - Calendrical Calculations, Third Edition Nachum Dershowitz and Edward M. Reingold Table of Contents More information

Contents

List of Frontispieces page xii List of Figures xiii List of Tables xiv Abbreviations xv Mathematical Notations xvi Preface xix Credits xxvii License and Limited Warranty and Remedy xxviii

1 Calendar Basics ...... 1 1.1 Calendar Units and Taxonomy 4 1.2 Fixed Day Numbers 9 1.3 Negative Years 12 1.4 Epochs 14 1.5 Julian Day Numbers 16 1.6 Mathematical Notation 17 1.7 Search 20 1.8 Dates and Lists 22 1.9 A Simple Calendar 24 1.10 Cycles of Days 27 1.11 Simultaneous Cycles 30 1.12 Cycles of Years 32 1.13 Warnings about the Calculations 39 References 41

I ARITHMETICAL CALENDARS 2 The Gregorian Calendar ...... 45 2.1 Structure 45 2.2 Implementation 48

vii

© Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-70238-6 - Calendrical Calculations, Third Edition Nachum Dershowitz and Edward M. Reingold Table of Contents More information

viii Contents

2.3 Alternative Formulas 52 2.4 The Zeller Congruence 56 2.5 Holidays 57 References 60 3 The Julian Calendar ...... 63 3.1 Structure and Implementation 63 3.2 Roman Nomenclature 65 3.3 Roman Years 69 3.4 Holidays 70 References 71 4 The Coptic and Ethiopic Calendars ...... 73 4.1 The Coptic Calendar 73 4.2 The Ethiopic Calendar 75 4.3 Holidays 76 References 77 5 The ISO Calendar ...... 79 Reference 81 6 The Islamic Calendar ...... 83 6.1 Structure and Implementation 83 6.2 Holidays 86 References 87 7 The Hebrew Calendar ...... 89 7.1 Structure and History 90 7.2 Implementation 95 7.3 Holidays and Fast Days 101 7.4 Personal Days 105 7.5 Possible Days of Week 108 References 110 8 The Ecclesiastical Calendars ...... 113 8.1 Orthodox Easter 114 8.2 Gregorian Easter 116 8.3 Astronomical Easter 119 8.4 Movable Christian Holidays 119 References 121 9 The Old Hindu Calendars ...... 123 9.1 Structure and History 123 9.2 The Solar Calendar 126 9.3 The Lunisolar Calendar 128 References 134

Contents ix

10 The Mayan Calendars ...... 137 10.1 The Long Count 138 10.2 The Haab and Tzolkin Calendars 139 10.3 The Aztec Calendars 145 References 150 11 The Balinese Pawukon Calendar ...... 153 11.1 Structure and Implementation 153 11.2 Conjunction Days 159 References 161 12 Generic Cyclical Calendars ...... 163 12.1 Single Cycle Calendars 163 12.2 Double Cycle Calendars 166 12.3 Summary 168

II ASTRONOMICAL CALENDARS 13 Time and Astronomy ...... 171 13.1 Position 172 13.2 Time 174 13.3 The Day 179 13.4 The Year 185 13.5 Astronomical Solar Calendars 192 13.6 The Month 193 13.7 Times of Day 207 References 214 14 The Persian Calendar ...... 217 14.1 Structure 217 14.2 The Astronomical Calendar 219 14.3 The Arithmetic Calendar 221 14.4 Holidays 226 References 227 15 The Baha’´ ´ı Calendar ...... 229 15.1 Structure 229 15.2 Western Version 231 15.3 The Future Baha’´ ´ı Calendar 233 15.4 Holidays 236 References 237 16 The French Revolutionary Calendar ...... 239 16.1 The Original Form 241 16.2 The Modiﬁed Arithmetical Form 242 References 244

x Contents

17 The Chinese Calendar ...... 247 17.1 Solar Terms 248 17.2 Months 251 17.3 Conversions to and from Fixed Dates 258 17.4 The Sexagesimal Cycle of Names 260 17.5 Common Misconceptions 263 17.6 Holidays 264 17.7 Chinese Age 266 17.8 Chinese Marriage Auguries 267 17.9 The Japanese Calendar 268 17.10 The Korean Calendar 269 17.11 The Vietnamese Calendar 271 References 272 18 The Modern Hindu Calendars ...... 275 18.1 Hindu Astronomy 281 18.2 Calendars 287 18.3 Sunrise 292 18.4 Alternatives 295 18.5 Astronomical Versions 299 18.6 Holidays 303 References 312 19 The Tibetan Calendar ...... 315 19.1 Calendar 315 19.2 Holidays 319 References 322 20 Astronomical Lunar Calendars ...... 325 20.1 Astronomical Easter 325 20.2 Lunar Crescent Visibility 326 20.3 The Observational Islamic Calendar 328 20.4 The Classical Hebrew Calendar 329 References 331 Coda ...... 333

III APPENDICES A Function, Parameter, and Constant Types ...... 337 A.1 Types 337 A.2 Function Types 342 A.3 Constant Types and Values 356 B Lisp Implementation ...... 361 B.1 Lisp Preliminaries 361

Contents xi

B.2 Basic Code 364 B.3 The Egyptian/Armenian Calendars 366 B.4 Cycles of Days 367 B.5 The Gregorian Calendar 367 B.6 The Julian Calendar 372 B.7 The Coptic and Ethiopic Calendars 375 B.8 The ISO Calendar 376 B.9 The Islamic Calendar 377 B.10 The Hebrew Calendar 378 B.11 The Ecclesiastical Calendars 385 B.12 The Old Hindu Calendars 386 B.13 The Mayan Calendars 388 B.14 The Balinese Pawukon Calendar 392 B.15 Time and Astronomy 395 B.16 The Persian Calendar 411 B.17 The Baha’´ ´ı Calendar 413 B.18 The French Revolutionary Calendar 416 B.19 The Chinese Calendar 417 B.20 The Modern Hindu Calendars 424 B.21 The Tibetan Calendar 435 B.22 Astronomical Lunar Calendars 437 Reference 439 C Sample Data ...... 441 References 447 Index 449 Envoi 477 About the Cover 479