Calendrical Calculations

List of Frontispieces 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 Calendar Basics 1(44) Calendar Units and Taxonomy 4(5) Fixed Day Numbers 9(3) Negative Years 12(2) Epochs 14(2) Julian Day Numbers 16(1) Mathematical Notation 17(3) Search 20(2) Dates and Lists 22(2) A Simple Calendar 24(3) Cycles of Days 27(3) Simultaneous Cycles 30(2) Cycles of Years 32(7) Warnings about the Calculations 39(6) References 41(4) I. ARITHMETICAL CALENDARS The Gregorian Calendar 45(18) Structure 45(3) Implementation 48(4) Alternative Formulas 52(4) The Zeller Congruence 56(1) Holidays 57(6) References 60(3) The Julian Calendar 63(10) Structure and Implementation 63(2) Roman Nomenclature 65(4) Roman Years 69(1) Holidays 70(3) References 71(2) The Coptic and Ethiopic Calendars 73(6) The Coptic Calendar 73(2) The Ethiopic Calendar 75(1) Holidays 76(3) References 77(2) The ISO Calendar 79(4) Reference 81(2) The Islamic Calendar 83(6) Structure and Implementation 83(3) Holidays 86(3) References 87(2) The Hebrew Calendar 89(24) Structure and History 90(5) Implementation 95(6) Holidays and Fast Days 101(4) Personal Days 105(3) Possible Days of Week 108(5) References 110(3) The Ecclesiastical Calendars 113(10) Orthodox Easter 114(2) Gregorian Easter 116(3) Astronomical Easter 119(1) Movable Christian Holidays 119(4) References 121(2) The Old Hindu Calendars 123(14) Structure and History 123(3) The Solar Calendar 126(2) The Lunisolar Calendar 128(9) References 134(3) The Mayan Calendars 137(16) The Long Count 138(1) The Haab and Tzolkin Calendars 139(6) The Aztec Calendars 145(8) References 150(3) The Balinese Pawukon Calendar 153(10) Structure and Implementation 153(6) Conjunction Days 159(4) References 161(2) Generic Cyclical Calendars 163(8) Single Cycle Calendars 163(3) Double Cycle Calendars 166(2) Summary 168(3) II. ASTRONOMICAL CALENDARS Time and Astronomy 171(46) Position 172(2) Time 174(5) The Day 179(6) The Year 185(7) Astronomical Solar Calendars 192(1) The Month 193(14) Times of Day 207(10) References 214(3) The Persian Calendar 217(12) Structure 217(2) The Astronomical Calendar 219(2) The Arithmetic Calendar 221(5) Holidays 226(3) References 227(2) The Baha'i Calendar 229(10) Structure 229(2) Western Version 231(2) The Future Baha'i Calendar 233(3) Holidays 236(3) References 237(2) The French Revolutionary Calendar 239(8) The Original Form 241(1) The Modified Arithmetical Form 242(5) References 244(3) The Chinese Calendar 247(28) Solar Terms 248(3) Months 251(7) Conversions to and from Fixed Dates 258(2) The Sexagesimal Cycle of Names 260(3) Common Misconceptions 263(1) Holidays 264(2) Chinese Age 266(1) Chinese Marriage Auguries 267(1) The Japanese Calendar 268(1) The Korean Calendar 269(2) The Vietnamese Calendar 271(4) References 272(3) The Modern Hindu Calendars 275(40) Hindu Astronomy 281(6) Calendars 287(5) Sunrise 292(3) Alternatives 295(4) Astronomical Versions 299(4) Holidays 303(12) References 312(3) The Tibetan Calendar 315(10) Calendar 315(4) Holidays 319(6) References 322(3) Astronomical Lunar Calendars 325(124) Astronomical Easter 325(1) Lunar Crescent Visibility 326(2) The Observational Islamic Calendar 328(1) The Classical Hebrew Calendar 329(8) References 331(2) Coda 333(4) III. APPENDICES Function, Parameter, and Constant Types 337(24) Types 337(5) Function Types 342(14) Constant Types and Values 356(5) Lisp Implementation 361(80) Lisp Preliminaries 361(3) Basic Code 364(2) The Egyptian/Armenian Calendars 366(1) Cycles of Days 367(1) The Gregorian Calendar 367(5) The Julian Calendar 372(3) The Coptic and Ethiopic Calendars 375(1) The ISO Calendar 376(1) The Islamic Calendar 377(1) The Hebrew Calendar 378(7) The Ecclesiastical Calendars 385(1) The Old Hindu Calendars 386(2) The Mayan Calendars 388(4) The Balinese Pawukon Calendar 392(3) Time and Astronomy 395(16) The Persian Calendar 411(2) The Baha'i Calendar 413(3) The French Revolutionary Calendar 416(1) The Chinese Calendar 417(7) The Modern Hindu Calendars 424(11) The Tibetan Calendar 435(2) Astronomical Lunar Calendars 437(2) References 439(2) Sample Data 441(8) References 447(2) Index 449(28) Envoi 477(2) About the Cover 479