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Cambridge University Press 978-0-521-88540-9 - Calendrical Calculations, Third Edition Nachum Dershowitz and Edward M. Reingold Index More information

First page of the index to Joseph Scaliger’s De Emendatione Temporum (Frankfort edition, 1593). (Courtesy of the University of Illinois, Urbana, IL.)

Index

. . . there will be few who will consider the industry, labor, vigils which we have bestowed upon [the index], or the profit and utility that may be gathered from our labors. For it is the equivalent of a whole book. —Joseph Scaliger: Letter to Isaac Casaubon (January 7, 1604)

It requires more scholarship to make a good index than to write the book that is indexed. —George Foote Moore: Address at a reception of the Harvard Graduate School of Arts and Sciences (1925) Function and constant names are given in boldface, and page numbers for a function are of four types: The page with the function definition is shown in boldface. The page with the type description is shown underlined. The page with the corresponding Lisp code is shown in italics. Pages of other occurrences are given in roman.

Names of people are indexed according to the guidelines of The Chicago Manual of Style: The Essential Guide for Writers, Editors, and Publishers, 14th ed., The University of Chicago Press, Chicago, 1993.

Symbols <= (Lisp relation), 361 (list construction), 22 = (Lisp relation), 361 [](list element selection), 22 > (Lisp relation), 361 (ceiling function), xvi, 17 >= (Lisp relation), 361 (floor function), xvi, 17 1+ (Lisp function), 362 π (pi), xvi 1- (Lisp function), 362 ||(absolute value function), xvi A || (list concatenation), 22 a.d. (= ante diem), 67 (summation operator), xvi, 20 Abdali, S. Kamal, 214, 331 * (Lisp function), 361 Abdollahy, Reza, 222 + (Lisp function), 361 Aberration, 189 - (Lisp function), 361 aberration, 189, 189, 342, 400 / (Lisp function), 361 Abraham ben David, 441 /= (Lisp relation), 361 Absolute value function (||), xvi < (Lisp relation), 361 Abu’l-Faraj, Gregory (= Bar Hebræus), 85

449

450 Index

AccessR ,79 representation, 24 A.D. (= Anno Domini), 10 solar depression, 212 Adam, 92 Annunciation (Orthodox holiday), 71 Adams, John Quincy, 239 Anomaly, 282, 283, 285 adar, 91, 91, 98, 107, 110, 356, 379 lunar, 199, 317 Adar (Hebrew month), 90, 91, 103, 106–108 solar, 199, 317 adarii, 91, 91, 98, 107, 356, 379 A.P. (= Anno Persico or Anno Persarum), 217 Adhika month (Hindu calendar), see Leap Apogee, 283, 317 months, Hindu apparent-from-local, 184, 184, 326, 342, Adjusted remainder function ( amod ), xvi, 397 19 approx-moment-of-depression, 208, 208, advent, 59, 59, 342, 372 209, 342, 408 Advent Sunday (Christian holiday), 59, 121 april, 48, 48, 115, 117, 270, 356, 368 Afghan Calendar, 217 Arabian Peninsula, 236 Africa, 5 Arc of light, 326 Afzal, Omar, 331 arccos-degrees, 342, 395 Age arcsin-degrees, 342, 395 Chinese, 266–267 arctan, 173, 186, 192, 213 Japanese, 269 arctan-degrees, 173, 342, 395 A.H. (= Anno Hegiræ), 84 Ari the Learned, 80 Ahargan.a (Hindu calendar), 124 Aries (constellation), 127, 186 Ahmad, Imad ad-Dean, 331 first point of, 174, 185, 186 Akrami, Mus¯ a,¯ 214 arithmetic-french-from-fixed, 243, 243, Al-Azhar University, 328 342, 417 Alaska, 47 arithmetic-french-leap-year?, 243, 243, Albumazar, see Falaki, Abu-Ma’shar al- 342, 416 Alexandria (Egypt), Church of, 113 arithmetic-persian-from-fixed, 224, 224, Ali, H. Amir, 282 342, 412 Ali-Ahyaie, Masahallah, 219 arithmetic-persian-leap-year?, 222, 222, Almagest, 25, 92, 282 342, 412 alt-fixed-from-gregorian, 54, 54–56, 65, arithmetic-persian-year-from-fixed, 224, 342, 370 224, 342, 412 alt-gregorian-from-fixed, 55, 55, 65, 342, Arithmetical calendars, 45–169, 221–225, 370 231–233, 242–244 alt-gregorian-year-from-fixed, 56, 56, 342, Armenian calendar, 5–6, 11, 25–26 370 days, 5 alt-hindu-sunrise, 298, 298, 301–303, 342, epagomenæ,26 429 epoch, 15, 25 alt-orthodox-easter, 116,116,342, 385 Lisp code, 366–367 A.M. months, 26 Anno Martyrum, 74 sample dates, 441 Anno Mundi, 91 armenian-date, 342, 366 a.m. (= ante meridiem), xv armenian-epoch, 25, 25, 26, 356, 366 amod, 342, 363 armenian-from-fixed, 26, 26, 342, 367 Amod function, see Adjusted remainder Arouet, Franc¸ois Marie (= Voltaire), 48 function arya-jovian-period, 125, 125, 126, 356, 386 Andhra Pradesh (India), 274 arya-lunar-day, 129, 129, 133, 134, 356, Anggara Kasih (Balinese holiday), 160 387 angle, 342, 396 arya-lunar-month, 129, 129, 131–134, 356, angle-from-degrees, 24, 24, 342, 366 387 Angles Arya-Siddh¯ anta¯ (First), 126

function definition function type Lisp code

Index 451

arya-solar-month, 126, 126–129, 131–134, Ayyappa Jyothi Darshanam (Hindu holiday), 356, 386 304 arya-solar-year, 125, 125–127, 131–133, Aztec calendar, 11, 29, 30, 138, 145–150, 479 356, 386 Lisp code, 390–392 Aryabhat¯ .a, 126 nemontemi, 146 Ascension Day (Christian holiday), 119 sample dates, 441 Ascension of ‘Abdu’l-Baha¯ (Bahá’í holiday), tonalpohualli, 145, 148–149 236 xihuitl, 145–147 Ascension of the Baha’u’ll¯ ah¯ (Bahá’í xiuhmolpilli, 149 holiday), 236 aztec-correlation, 146, 146–148, 356, 390 Ascensional difference, 293 aztec-tonalpohualli-correlation, 148, Ash Wednesday (Christian fast), 59, 119, 121 148–150, 356, 391 ‘Ashur¯ a’¯ (Islamic holiday), 87 aztec-tonalpohualli-date, 148, 343, 391 Aslaksen, Helmer, xxv, 265, 272 aztec-tonalpohualli-from-fixed, 148, 148, asr, 213, 213, 342, 410 149, 343, 391 Asr (Moslem prayer time), 213 aztec-tonalpohualli-name, 148, 343, 391 Assumption (Christian holiday), 59 aztec-tonalpohualli-number, 148, 343, 391 astro-hindu-calendar-year, 300, 300, 302, aztec-tonalpohualli-on-or-before, 149, 149, 342, 430 343, 391 astro-hindu-lunar-from-fixed, 301,301, aztec-tonalpohualli-ordinal, 148, 148–150, 303, 342, 431 343, 391 astro-hindu-solar-from-fixed, 300, 300, aztec-xihuitl-correlation, 147, 147, 150, 342, 430 356, 390 astro-hindu-sunset, 300, 300, 301, 342, 430 aztec-xihuitl-date, 147, 149, 343, 390 astro-lunar-day-from-moment, 301, aztec-xihuitl-day, 147, 343, 390 301–303, 342, 431 aztec-xihuitl-from-fixed, 147, 147, 149, 343, Astronomical calendars, 170–332 390 Astronomical day numbers, see Julian day aztec-xihuitl-month, 147, 149, 343, 390 numbers aztec-xihuitl-on-or-before, 147, 147, 149, Astronomical lunar calendars, 332 343, 391 classical Hebrew, 329–331 aztec-xihuitl-ordinal, 146, 146, 147, 150, Lisp code, 437–439 343, 390 observational Islamic, 328–329 aztec-xihuitl-tonalpohualli-on-or-before, astronomical-easter, 325, 325, 342, 438 149, 149, 343, 392 Astronomy, 171–213, 281–287 aztec-xiuhmolpilli-designation, 343, 391 Hindu, 281–287 aztec-xiuhmolpilli-from-fixed, 149, 149, Asura Maya, 275 343, 391 A.U.C. (= Ab Urbe Condita), 46, 69 aztec-xiuhmolpilli-name, 343, 391 auc-year-from-julian-year, 70, 70, 343, 373 aztec-xiuhmolpilli-number, 343, 391 Audette, Rodolphe, xxv august, 48, 48, 74, 76, 146, 270, 356, 368 B Augustine, Saint (= Aurelius Augustinus), Bab¯ (= Mirza¯ Ali Muhammad), 228, 229 174 Babylonian calendar, 6 autumn, 191,191,241,356, 400 Bach, Henri, 479 av, 90, 90, 104, 356, 379 Bahá’í calendar, 6, 11, 182, 229–237 Avanes, Armond, xxv days, 4, 13 Aveni, Anthony F., 150 epoch, 15 Avron, Haim, xxv future, 187, 192, 193, 218, 229, ayanamsha, 299, 299, 343, 430 236–237 ayyam-i-ha, 231, 231, 233, 235, 236, 356, holidays, 236–237 413 implementation, 231–233

function definition function type Lisp code

452 Index

leap-year rule, 229 bali-sangawara-from-fixed, 155, 158, 158, Lisp code, 413–415 344, 393 months, 230 bali-saptawara, 159, 344, 392 Near Eastern, 236–237 bali-saptawara-from-fixed, 155, 155, 157, New Year, 236, 237 344, 393 sample dates, 441 bali-triwara,344, 392 structure, 229–231 bali-triwara-from-fixed, 155, 155, 344, 393 weekdays, 229 bali-week-from-fixed, 157,157,344, 394 Western, 231–233 Balinese Pawukon calendar, 5, 11, 28, 29, Bahá’í New Year, see Feast of Naw-Ruz¯ 153–161 bahai-cycle, 343, 413 holidays, 155, 159–161 bahai-date, 343, 413 Lisp code, 392–394 bahai-day, 343, 413 sample dates, 441 bahai-epoch, 231, 231, 232, 235, 237, 356, balinese-date,344, 392 413 Balkh (Iran), 216 bahai-from-fixed, 232, 232, 343, 414 Ball, John A., 60 bahai-major, 343, 413 Banaras, see Var¯ an¯ asi¯ bahai-month, 343, 413 Bangladesh, 328 bahai-new-year, 236, 236, 343, 415 Bar Hebræus, see Abu’l-Faraj, Gregory bahai-year,344, 413 Bar mitzvah (Jewish event), 105 Baha’u’ll¯ ah¯ (= MirzaH¯ . oseyn Ali Nuri),¯ 229 Bar, Kfir, xxv Bahula, see Month, dark fortnight Bargeloní, Abraham bar H. iyya al- (= Bali, 5, 152, 153 Savasorda), 89, 92, 111 bali-asatawara,344, 392 Bat mitzvah (Jewish event), 105 bali-asatawara-from-fixed, 155, 158, 158, B.C. (= Before Christ), 14 344, 393 B.C.E. (= Before the Common Era), 14 bali-caturwara,344, 392 bce,344, 372 bali-caturwara-from-fixed, 155, 158, 158, B.E. (= Bahá’í Era), 231 344, 393 Beckwith, Roger T., 120 bali-dasawara,344, 393 Bede, Venerable, 12, 46, 113, 193 bali-dasawara-from-fixed, 155, 157,157, Beijing (China), 175, 250–252, 255 158, 344, 393 Belize, 137 bali-day-from-fixed, 155, 155, 157–160, Beltrami, Olivier, xxv 344, 393 Ben-Meir, Aaron, 93 bali-dwiwara,344, 392 Benediktsson, Jakob, 80 bali-dwiwara-from-fixed, 155, 157,157, Bengal (India), 288 344, 393 Berlekamp, Elwyn R., 110, 121 bali-epoch, 155, 155, 356, 393 Bernal, Ignacio, 150 bali-luang,344, 392 Berzin, Alexander, 315 bali-luang-from-fixed, 155, 158, 158, 344, Beyle, Marie-Henri (=Stendhal), 241 393 Bhutan calendar, 315 bali-on-or-before, 159, 159, 344, 394 Bible bali-pancawara, 159, 344, 392 Daniel, 441 bali-pancawara-from-fixed, 155, 155, 157, Exodus, 91 344, 393 Ezekiel, 166 bali-pawukon-from-fixed, 155, 155, 344, Leviticus, 90 394 Psalms, 4 bali-sadwara, 159, 344, 392 Bien, Reinhold, 121 bali-sadwara-from-fixed, 155, 155, 344, Bierce, Ambrose, 476 393 Bihar (India), 277 bali-sangawara,344, 392 binary-search, 21,344, 364

function definition function type Lisp code

Index 453

binary-search (binary search macro), Building of the Cross (Coptic holiday), 77 364 Burgess, Ebenezer, 282, 312 Birashk, Ahmad, 85, 87, 217–219, 221, 222, Burgess, James, 134, 312 225, 227 Burnaby, Sherrard B., 87, 111 Birkath ha-H. ama (Jewish event), 105 Bushwick, Nathan, 111 birkath-ha-hama, 105, 105, 344, 382 Birth of ‘Abdu’l-Baha¯ (Bahá’í holiday), 236 C Birth of the Bab¯ (Bahá’í holiday), 236, 237 C (computer language), 18, 19, 40, 365 Birth of the Baha’u’ll¯ ah¯ (Bahá’í holiday), C++ (computer language), 18, 19, 40, 365 236, 237 Caching, 40 Birthday of Krishna (Hindu holiday), 306 Cæsar, Julius, 46, 62, 69 Birthday of Rama¯ (Hindu holiday), 306, 309 Cæsarea (Israel), 46 B¯ırun¯ ¯ı, Abu-Raih¯ .an¯ Muh.ammad ibn ’Ah.mad Cairo (Egypt), 328 al-, 1, 82, 92, 94, 110, 123, 129, Cajori, Florian, 112 134, 226, 275, 278, 295 Calendar Bissextile years, see Leap years Afghan, 217 Bissextus (leap day), 66 arithmetical, 45–169, 221–225, Blackburn, Bonnie, 41, 71 231–233, 242–244 Bloch, Abraham P., 447 Armenian, 5–6, 11, 15, 25–26 Blue moon, 195 astronomical, 170–332 Bodde, Derk, 273 lunar, 325–332 bogus, 102, 144, 145, 149, 208–212, 266, Aztec, 11, 29, 30, 138, 145–150, 479 342–346, 352–355, 357, 362,446 tonalpohualli, 145, 148–149 Bohras, 85 xihuitl, 145–147 Bolshevik Revolution, 47 xiuhmolpilli, 149 Bonaparte, Louis Napoleon (= Napoleon Babylonian, 6 III), 239 Bahá’í, 4, 6, 11, 15, 182, 229–237 Bonaparte, Napoleon, 239 future, 187, 192, 193, 218, 229, Boncompagni, Ugo, see Gregory XIII, Pope 236–237 Bornstein, H. ayyim Y., 89, 111 Near Eastern, 236–237 Bowditch, Charles P., 150 Western, 231–233 Brady, John, 244 Balinese Pawukon, 5, 11, 28, 29, Brainerd, George W., 150 153–161 Bramsen, William, 272 Bhutan, 315 Brand, Stewart, 324 Chinese, xxii, 5–7, 11, 15, 28, 30–32, Braude, Morris, 9 89, 182, 187, 193, 195, 207, Bredon; Juliet, 272 247–273, 275, 299, 316, 333–334 Bresenham, Jack E., 32 Coptic, 6, 7, 9–11, 15, 73–77, 105, Bretagnon, Pierre, 214 164–165, 217 Brewer, David, xxi diurnal, 4 Brisson, James F., 479 ecclesiastical, 113–121 Bromberg, Irvin L., xxv, 96 Egyptian, 6, 7, 10, 11, 15, 24–25, 140 Browne, Gerald M., xxv Ethiopic, 6, 7, 9–11, 15, 75–76, 217 Brownfield, Marla, xxv French Revolutionary, xxii, 4, 6, 7, 10, Buda-Cemeng (Balinese holiday), 160 11, 15, 182, 207, 239–244 Buda-Keliwon (Balinese holiday), 160 modified, 242–244 Buddha’s Birthday (Buddhist holiday), 264, original, 187, 192, 193, 239–242 306, 321 Generic cyclical, 163–168 Buddha’s Descent (Buddhist holiday), 322 Gregorian, xx, 1, 6, 7, 10, 11, 15, 16, Buddha’s Enlightenment (Buddhist holiday), 45–61, 70, 94–95, 104, 233, 234, 322 275

function definition function type Lisp code

454 Index

Hebrew, 1, 4, 6, 7, 10, 11, 15, 89–112, Chakravarty, Apurba K., 312 123, 182, 207 Chamberlain, Basil H., 268 classical, 326, 329–331 Chandramana Ugadi, see New Year, Hindu Hindu, xxii, 6, 10, 11, 15, 28, 89, lunisolar 123–135, 182, 185, 186, 195, 207, Chandran, Sharat, xxv 247, 255, 275–313, 315 Chatterjee, S. K., 312 modern, 7, 182, 185, 195, 275–313 Chaturvedi, Anoop, xxv old, 7, 123–135, 275, 277, 289 Chen, Jiujin, 272 Icelandic, 80 Chen, Shigang, xxv Islamic, 4, 6, 7, 10, 11, 15, 83–87, 89, Chesterfield, Earl of, see Stanhope, Philip D. 102, 182, 217, 222, 275 China, see also Beijing, Nanjing, Shanxˇ ¯ı, observational, 11, 86, 328–329 and X¯ıan,¯ 247, 268 ISO, 6, 11, 15, 79–81 Chinese calendar, xxii, 5–7, 11, 28, 30–32, Jalal¯ ¯ı, 217 89, 182, 187, 193, 195, 207, Japanese, 268–269 247–273, 316, 333–334 Julian, 6, 7, 9–11, 15, 48, 57, 63–71, age, 266–267 105, 217, 479 celestial stem names, 260 revised, 47, 70 days, 13 Karaite, 329 epoch, 15, 258 Korean, 269–271 holidays, 264–266 lunar, 6, 326–329 implementation, 258–260 lunisolar, 6, 35, 329–331 Lisp code, 417–423 Mayan, xxii, 10, 11, 15, 28, 29, 137–151 marriage auguries, 267–268 haab, 139–142, 144–145, 147 misconceptions, 263–264 long count, 138–139 month numbering, 252–258 round, 144–145, 149 New Year, xxii, 248, 263–264, 266, tzolkin, 5, 30–31, 142–145, 148 271, 332 Mongolian, 315 sample dates, 441 Native American, 6, 239 sexagesimal cycle of names, 260–263 Nepali, 277 solar terms, 248–251 Persian, 6, 7, 9–11, 15, 217–227 structure, 251–252 arithmetic, 221–225 terrestrial branch names, 261 astronomical, 182, 187, 192, 193, chinese-age, 266, 266, 269, 344, 422 219–221 chinese-branch,344, 421 Roman nomenclature, 11, 65–69 chinese-cycle, 345, 417 Sherpa, 315 chinese-date, 345, 417 solar, 6, 236 chinese-day, 345, 417 taxonomy, 4–9 chinese-day-name-epoch, 262, 262, 357, Tibetan, 6, 10, 12, 15, 315–322 422 Tsurphu, 315 chinese-day-name-on-or-before, 262, 262, Vietnamese, 271–272 345, 422 Zoroastrian, 15, 26, 217 chinese-epoch, 258, 258–260, 264, 266, Casaubon, Isaac, 449 357, 419 Caso, Alfonso, 150 chinese-from-fixed, 259, 259, 260, 267, Cassini, Jacques, 46 345, 420 Catholic Church, 121 chinese-leap, 345, 417 C.E. (= Common Era), 10 chinese-location, 248, 248, 250–252, 269, ce,344, 372 345, 417 Ceiling function (), xvi, 17 chinese-month, 345, 417 cfs-alert, 211,211 chinese-month-name-epoch, 262, 262, 357, Chaˆıne, Marius, 77 421

function definition function type Lisp code

Index 455

chinese-name, 345, 421 Constantine the Great (= Flavius Valerius chinese-name-difference, 261, 261, 262, Constantinus), 113 345, 421 Conversions, time of day of, 12 chinese-name-of-day, 262, 262, 345, 422 Conway, John H., 110, 121 chinese-name-of-month, 262, 262, 345, 421 Cook, Michael A., 83 chinese-name-of-year, 261,261,345, 421 Cope, Leona, 41 chinese-new-moon-before, 252, 252, 255, Copeland, Jeffrey L., xxv 258, 259, 345, 418 Copernicus, Nicolaus (= Mikolaj Kopernik), chinese-new-moon-on-or-after, 251,251, 179 253, 258–260, 345, 418 Coptic calendar, 6, 7, 9–11, 33, 35, 36, 38, chinese-new-year, 264,264,345, 419 46, 73–77, 105, 164–165, 217 chinese-new-year-in-sui, 257, 257–259, days, 13, 73, 74 345, 419 epagomenæ,73,165 chinese-new-year-on-or-before, 258, 258, epoch, 15, 74 260, 264, 345, 419 holidays, 76–77 chinese-no-major-solar-term?, 253, 253, implementation, 74–75 255, 258, 259, 345, 419 leap-year rule, 74 chinese-prior-leap-month?, 255, 255, 259, Lisp code, 375–376 345, 421 months, 73 chinese-sexagesimal-name, 261, 261, 262, sample dates, 441 345, 421 structure, 73–74 chinese-solar-longitude-on-or-after, 250, coptic-christmas, 77, 77, 345, 376 250, 251, 271, 345, 418 coptic-date, 345, 375 chinese-stem, 345, 421 coptic-epoch, 74, 74–76, 357, 375 chinese-winter-solstice-on-or-before 251 , , coptic-from-fixed, 74, 74, 76, 77, 105, 346, 251, 258, 259, 345, 419 376 chinese-year, 345, 417 coptic-in-gregorian, 76, 76, 77, 105, 346, chinese-year-marriage-augury, 267,267, 376 345, 422 coptic-leap-year?, 74, 74, 346, 375 christmas, 59, 59, 345, 371 Corpus Christi (Christian holiday), 121 Christmas (Christian holiday), 47, 59, 70–71, Corr, Franz, xxv 77 Cortés, Hernán, 30, 146 Christmas Fast (Orthodox fast), 71 cosine-degrees, 346, 395 Cicero, Marcus Tullius, 79 Cox, Nicholas J., xxv Cidenas, 92 Coyne, George V., 60 Clamen, Stewart M., xxv, xxvi, 137 Craun, Edwin D., 42 classical-passover-eve, 331,331,345, 439 Cross, John, xxv Clavius, Christopher (= Christoph Clau), 114, 116 Crossley, John N., 273 clock-from-moment, 23, 23, 24, 345, 366 current-major-solar-term, 248, 248, 253, COBOL (computer language), xx 346, 417 Cody, Aelred, 77 current-minor-solar-term, 250, 250, 268, Cohn, Berthold, 212, 214 346, 418 Common Lisp, see Lisp Cycles Compline (Christian prayer time), 213 of days, 27–30, 367 cond (Lisp function), 364 of years, 32–39 Conditional expressions, 18 simultaneous, 5, 30–32, 142–145, Congo, 5 153–161, 261–262 Congress of the Orthodox Oriental Cyprus, 101 Churches, 47, 70 Conjunction, see Moon, new D

function definition function type Lisp code

456 Index

d’Églantine, Fabre (= Philippe Franc¸ois daytime-temporal-hour, 211,211,213,346, Nazaire Fabre), 239 410 da Silva, Hezekiah ben David, 94 de Blois, Franc¸ois C., 87, 227 Dabal, Ehssan, xxv de Madariaga, Salvador, 30 Daivajna, Gan.esa, 285 de Ossorio, Buenaventura Francisco, 112 Dalai Lama, see Gyatso, Tenzin de Santillana, Giorgio, 258 Danki system (Korean calendar), 270 december, 48, 48, 50, 59, 64, 71, 80, 316, Dasra (Hindu holiday), 306 357, 368 Date line, international, 47 Deckers, Michael H., xxv, xxvii, 54 Dawn, 25, 207–213 Declaration of the Bab¯ (Bahá’í holiday), astronomical, 212 236, 237 Islamic, 212 Declercq, Georges, 121 Jewish, 212 Declination, 174, 186 sample dates, 441 declination, 186, 186, 205, 209, 213, 346, dawn, 209, 209, 210, 298, 346, 409 400 Day, 4–6, 17, 177, 179–185 defconstant (Lisp construct), 361 Armenian, 5 Deferent, 282, 283, 285 Bahá’í, 13 defun (Lisp construct), 362 Chinese, 13 deg, 346, 395 civil, 207 degrees, 346, 395 Coptic, 13, 73, 74 degrees-from-radians, 346, 395 ecclesiastical, 13 degrees-minutes-seconds, 346, 396 Ethiopic, 13, 75 Delrina Technology, xxi expunged, 278, 303, 304, 307, 316 Deo, Narsingh, 42, 61 French Revolutionary, 4 Depression angles, 212 Gregorian, 13, 45, 218 Dershowitz, Erga, xxv Hebrew, 4, 13, 89 Dershowitz, Idan, xxv Hindu, 4, 13, 124, 276 Dershowitz, Nachum, iii, xxvi, 214, 312 intercalated, 278 Deuteronomy Rabbah, 70 Islamic, 4, 13, 83 Dharamsala (India), 315 Julian, 13, 45 Dickson, Stewart P., 324 Korean, 270 Dˆıkshit, S. Bâlkr.ishn.a, 135, 277, 306, 312 leap, 49, 64, 66, 278, 281, 289, 290, Diocletian (Roman emperor), 74 303, 316 Dionysian cycle, 115 lunar, 129, 133, 134, 278, 286, 290, Dionysius Exiguus, 46, 113, 114 298, 303–305, 307, 309 direction, 173, 173, 346, 396 nautical, 13 Dirichlet box principle, 253 of week, determination, 27, 56–57 diwali, 308, 308, 346, 434 Persian, 13, 26, 218 Diwali (Hindu holiday), 306, 308 sidereal, 185, 187, 207, 294 Doggett, LeRoy E., 41, 60, 71, 214, 273 solar, 174, 177, 185, 187, 294 Double-ninth Festival (Chinese holiday), 264 subdivisions, 207 Douglass, Robert H., xxv tropical, 185 Dragon Festival (Chinese holiday), 264 day-number, 52, 52, 346, 370 dragon-festival, 266, 266, 346, 422 day-of-week-from-fixed, 27, 27, 56, 81, 103, Dù, Shírán, 273 104, 109, 346, 362 DurgaAsht¯ .am¯ı (Hindu holiday), 306 Daylight saving, United States, 59 Durrani, Muhibullah, 331 daylight-saving-end, 59, 59, 346, 371 Dusk, 207–213 daylight-saving-start, 59, 59, 346, 371 astronomical, 212 days-in-hebrew-year, 98, 98, 346, 381 Islamic, 212 days-remaining, 52, 52, 346, 370 Jewish, 212

function definition function type Lisp code

Index 457

dusk, 210, 210, 211, 213, 300, 326, 346, 409 elul, 91, 91, 98, 110, 357, 379 Dutka, Jacques, 60 Emerson, Ralph Waldo, 333 dynamical-from-universal, 179, 179, 346, end, 346, 365 399 Epacts, 114 Epagomenæ E Armenian calendar, 26 Earth, 4, 173, 174, 177, 179, 185–187, 193, Coptic calendar, 73, 165 195, 282, 283, 294, 317 Egyptian calendar, 24 equator, 186 Persian calendar, 26 orbit, 182, 186 Ephemeris, 299 easter, 117, 117, 121, 346, 385 ephemeris-correction, 177, 177, 179–181, Easter (Christian holiday), xxii, 7, 10, 47, 59, 346, 398 70, 77, 112–121, 325–326 Epicycle, 282, 283, 285, 286, 298, 312 astronomical, 117–119, 325–326 epiphany, 59, 59, 346, 372 Gregorian, 116–117 Lisp code, 385–386 Epiphany (Christian holiday), 59, 71, 77 Orthodox, 10, 33, 114–116 epoch (Lisp constant), 363 sample dates, 441 Epochs, 12, 14 eastern-orthodox-christmas, 71, 71, 346, Armenian, 15, 25 385 Bahá’í, 15, 231 Eccentricity, 197 Chinese, 15, 258 Ecclesiastical calendar, 113–121 Coptic, 15, 74 days, 13 Egyptian, 15, 25 Lisp code, 385–386 Ethiopic, xxii, 15, 76 Ecliptic, 174, 186, 276, 278 French Revolutionary, 15, 239, 242 Eco, Umberto, 22 Gregorian, 15, 48 Edmundson, Munro S., 150 Hebrew, 15, 92, 95 E.E. (= Ethiopic Era), 76 Hindu, 15, 123, 124, 284, 288, 289 Egypt, see also Alexandria, Cairo, Medinet Islamic, 15, 84 Habu, and Thebes, 5, 24, 328 ISO, 15, 79 Egyptian calendar, 6, 7, 10, 11, 24–25, 140 Julian, 15, 64 epagomenæ,24 julian day number, 15 epoch, 15, 25 Mayan, 15, 138 Lisp code, 366–367 modified julian day number, 15 sample dates, 441 Persian, 15, 217 egyptian-date, 346, 366 Tibetan, 15, 316 egyptian-epoch, 25, 25, 26, 357, 366 Zoroastrian, 15 egyptian-from-fixed, 25, 25, 26, 346, 366 equal (Lisp relation), 362 eighth (Lisp function), 361 Equation of center, 283 Eiseman, Fred B., Jr., 161 Eiseman, Margaret, 161 Equation of motion, 286 Ekholm, Gordon F., 150 Equation of time, 182–185, 294 Election Day (U. S. event), 59 equation-of-time, 183, 183, 184, 346, 397 election-day, 59, 59, 346, 371 Equator elevation, 346, 396 celestial, 186 Elevation of the Life-giving Cross (Orthodox Earth, 185 holiday), 71 Equinox, 6, 21, 163, 171, 186, 187, 190, 191, Eliyahu ben Shelomo Zalman (= Vilna 300 Gaon), 212 autumnal, 105, 239, 241 Elkins, James, 41 dynamical, 187 Elongation, 199, 326 sample dates, 441

function definition function type Lisp code

458 Index

vernal, 46, 105, 113, 114, 119, 185, 192, Finland, 115 217–219, 229, 233, 234, 236, 241, first (Lisp function), 361 304, 325, 329 first-kday, 58, 58, 59, 347, 371 Era first-quarter, 202, 202, 326, 357, 405 Alexander, 16 Fixed day numbers, 9 Seleucid, 16, 89 fixed-from-arithmetic-french, 243, 243, Esslemont, John E., 229 244, 347, 416 estimate-prior-solar-longitude, 193, 193, fixed-from-arithmetic-persian, 223, 220, 234, 241, 251, 346, 401 223–226, 347, 412 Ethiopic calendar, 6, 7, 9–11, 75–76, 217 fixed-from-armenian, 25, 25, 347, 366 days, 13, 75 fixed-from-astro-hindu-lunar, 302, 302, epoch, xxii, 15, 76 347, 431 holidays, 77 fixed-from-astro-hindu-solar, 301,301, implementation, 76 347, 431 Lisp code, 376 fixed-from-bahai, 231, 231–233, 347, 413 months, 75 fixed-from-chinese, 260, 260, 266, 267, 347, sample dates, 441 420 structure, 75–76 fixed-from-coptic, 74, 74–77, 347, 375 ethiopic-date,347, 376 fixed-from-egyptian, 25, 25, 347, 366 ethiopic-epoch, 76, 76, 357, 376 fixed-from-ethiopic, 76, 76, 347, 376 ethiopic-from-fixed, 76, 76, 347, 376 fixed-from-french, 242, 242, 347, 416 Euclid, 31 fixed-from-future-bahai, 234, 234, 236, Europe, 175 237, 347, 414 Eusebius, 46, 113 fixed-from-gregorian, see also Eve, 92 alt-fixed-from-gregorian, 49, evening, 210,210,357, 409 49–53, 55, 57–59, 64, 117, 179, evenp (Lisp function), 361 191, 211, 231, 232, 236, 242, 258, Everett, Steven M., 42 264, 266, 270, 316, 347, 368 ExcelR , xxi, 79 fixed-from-hebrew, 99, 99–104, 106, 107, 110, 331, 347, 381 F fixed-from-hindu-fullmoon, 297, 297, 347, Falaki, Abu-Ma’shar al- (= Albumazar), 216 429 false, 66, 208, 357, 362 fixed-from-hindu-lunar, 291, 291, 297, 298, Fast of the Apostles (Orthodox fast), 121 307, 347, 427 Fast of the Repose of the Virgin Mary fixed-from-hindu-solar, 289, 289, 347, 426 (Orthodox fast), 71 fixed-from-islamic, 85, 85–87, 347, 377 Fausett, Donald W., xxv fixed-from-iso, 80, 80, 347, 377 Fayyumi,¯ Sa’adia ben Joseph al- (= Sa’adia fixed-from-jd,17,18, 18, 25, 138, 155, 347, Gaon), 89, 93 363 Feast of Naw-Ruz¯ (Bahá’í New Year), 233, fixed-from-julian, 64, 64, 65, 68, 71, 74, 76, 236, 237 84, 95, 115, 124, 146, 217, 347, Feast of Orthodoxy (Orthodox holiday), 121 372 Feast of Rid.van¯ (Bahá’í holiday), 236, 237 fixed-from-mayan-long-count, 139, 139, feast-of-ridvan, 237,237,347, 415 347, 388 february, 48, 48, 68, 124, 258, 357, 367 fixed-from-mjd, 17,17,347, 363 Feinstein, Moses, 108 fixed-from-moment, 18, 18, 208, 213, 296, Feldman, William M., 111 308, 347, 365 Fienberg, Richard T., 214 fixed-from-observational-hebrew, 331, fifth (Lisp function), 361 331, 347, 439 Filipowski, Herschell, 111 fixed-from-observational-islamic, 328, final,347, 364 328, 347, 438

function definition function type Lisp code

Index 459

fixed-from-old-hindu-lunar, 134, 134, 348, future-bahai-new-year-on-or-before, 234, 387 234–236, 348, 415 fixed-from-old-hindu-solar, 127,127,348, 386 G fixed-from-persian, 220, 220, 221, 226, Gorke,¨ Winfried, xxv 348, 411 Galloway, Thomas, 41 fixed-from-roman, 66, 68, 68, 69, 348, 375 Galungan (Balinese holiday), 160 fixed-from-tibetan, 317, 317–319, 321, 348, Galungan Days (Balinese period), 161 436 Gane¯sa´ Chaturth¯ı (Hindu holiday), 306 Fleet, John F., 134 Gangooly, Phanindralal, 312 Flesner, Molly, xxv Ganz, Solomon, 111, 331 Fliegel, Henry F., 60 Gardner, Martin, back cover, 185 floor (Lisp function), 363 Gauss, Carl F., xxi, xxvi, 95, 102, 111, 113, Floor function (), xvi, 17 121 Flower Festival (Japanese holiday), 266 Gautama Buddha, 264, 306, 321 Forsythe, George E., 337 Gcd function, see Greatest common divisor Fotheringham, John K., xxvii, 60, 71, 121 function fourth (Lisp function), 361 Geertz, Clifford, 153, 159 Fractional part function, 18 Gelasius, xxvii France, see also Paris, 174 Generic cyclical calendars, 163–168 Francou, Gérard, 214 double cycle, 166–167 single cycle, 163–166 Frazer, James G., 139 George, Alan, 337 Freeman-Grenville, Greville S. P., 87 Germany, 47, 119 French Revolutionary calendar, xxii, 6, 7, 10, Gezer (Israel), 239 11, 182, 207, 239–244 Gilbert, Martin, 447 days, 4 Gilbert, William S., 45 decades, 240 Gillispie, Charles C., 134, 312 epoch, 15, 242 Gingerich, Owen, back cover Lisp code, 416–417 Ginzel, Friedrich K., 9, 41, 60, 77 modified, 242–244 GNU Emacs, xix, xxvi, 2, 42 implementation, 243–244 Go-Chosun (Korea), 270 leap year rule, 242–243 Godman, Frederick D., 150 months, 240 Goharian, Nazli, xxv original, 187, 192, 193, 239–242 Golb, Norman, 111 implementation, 241–242 Goldberg, Mayer, xxv structure, 239–241 Golden number, 114 sample dates, 441 Good Friday (Christian holiday), 59, 119 sansculottides, 240 Goodman, John T., 137, 138, 150 french-date, 348, 416 Goodman-Martinez-Thompson correlation french-epoch, 242, 242, 243, 357, 416 (Mayan calendar), 137, 138 french-from-fixed, 242, 242, 348, 416 Graetz, Heinrich H., 447 french-new-year-on-or-before, 241,241, Grafton, Anthony T., xxvii, 16, 41 242, 348, 416 Graham, Ronald L., 41 friday, 27, 27, 60, 104, 109, 110, 357, 362 Great Britain, see also Greenwich and Friday the Thirteenth, 60 London, 47 Friedlander,¨ Michael, 111 Great Night of Shiva (Hindu holiday), 306, Frisch, Christian, 119 309 Fritsche, Hermann P. H., 263, 273 Greatest common divisor function, xvi, 19 full, 202, 202, 326, 357, 405 Greaves, John, 14, 85 future-bahai-from-fixed, 235, 235, 348, 415 Greece, 70

function definition function type Lisp code

460 Index

greenwich, 172,172 H Greenwich (England), xv, 172, 174, 177, 299 Haab (Mayan calendar), 139–142, 144–145, Gregorian calendar, xx, 1, 6, 7, 10, 11, 16, 147 45–61, 70, 94–95, 104, 233, 234, Hademer, Nathan ben Meir, 479 275 Hai ben Sherira (= Hai Gaon), 89 adoption of, 47 haifa, 234, 234, 357, 415 days, 13, 45, 218 Haifa (Israel), 234, 236 Easter, 116–117 H. alaqim (Hebrew calendar), 92, 207 epoch, 15, 48 Hale, Wayne, xx history, 46–47 Halevy, Schulamith C., xxv holidays, 57–59 Halkin, Abraham S., xxvii implementation, 48–52 Halmos, Paul, 17 leap-year rule, 45 Hamer, Mick, 244 Lisp code, 367–372 Hania (Crete), 336 months, 45 Hannah, Robert, xxvii New Year, xx, xxi, 47 Hanoi (Vietnam), 271 sample dates, 441 Hansch, Michael G., 119 structure, 45 H. anukkah (Jewish holiday), 101, 103 year, 47–48 Harris, Mitchell A., xxv, 41 Gregorian reform, 45, 47, 114 Harvey, Oswald L., 41 gregorian-date, 348, 367 Haryana (India), 277 gregorian-date-difference, 52, 52, 178, 179, Hastings, James, 41, 42, 60, 111 348, 369 Heaslet, Maxwell A., 61, 121 gregorian-epoch, 48, 48–50, 55, 56, 357, Hebrew calendar, 1, 6, 7, 10, 11, 33, 35, 36, 367 89–112, 123, 182, 207 gregorian-from-fixed, see also bar mitzvah, 105 alt-gregorian-from-fixed, 51,51, bat mitzvah, 105 53, 60, 67, 348, 369 birthdays, 105–106 gregorian-leap-year?, 49, 49, 51, 67, 231, classical, 326, 329–331 348, 368 days, 4, 13, 89 gregorian-new-year, 50, 50, 51, 70, 77, 81, delays, 92–93, 96–98, 100–101 86, 106, 108, 179, 271, 304, 306, epoch, 15, 92, 95 308, 309, 325, 330, 348, 369 history, 89, 93–95 gregorian-year-end, 50, 50, 52, 81, 321, holidays and fast days, 101–105 348, 369 implementation, 95–101 gregorian-year-from-fixed, see also Karaite, 329 alt-gregorian-year-from-fixed, leap-year rule, 91 50, 50–52, 55, 80, 101–104, 178, Lisp code, 378–385 179, 226, 232, 237, 250, 264, lo iddo rosh, 92, 108, 109 266, 268, 330, 331, 348, 369 molad, 92, 95–97, 479 gregorian-year-range, 50, 50, 70, 76, 86, months, 90 106, 108, 160, 308, 309, 311, 321, nah.ala, 105–108 348, 369 New Year, see Rosh ha-Shanah Gregory XIII, Pope (= Ugo Boncompagni), possible weekdays, 108–110 45, 47 sabbatical year, 91 Gregory, Ruth W., 60 sample dates, 441 Guatemala, see also Tikal, 137, 140, 142 structure, 90–93 Guinot, Bernard, 214 week, 89 Guy, Richard K., 110, 121 weekdays, 89 Guyot, Laurent, 238 yahrzeit, 105–108 Gyatso, Tenzin (= Dalai Lama), 315 hebrew-birthday, 106, 106, 348, 383

function definition function type Lisp code

Index 461

hebrew-birthday-in-gregorian, 106, 106, structure, 275–281 348, 383 naks.atras, 312 hebrew-calendar-elapsed-days, 96, 96–98, old, 7, 123–135, 275, 277 100, 348, 380 history, 123–124 hebrew-date, 348, 378 leap month, 123, 128, 129 hebrew-epoch, 95, 95, 97–99, 101–104, 357, Lisp code, 386–388 379 lunisolar, 37–39, 128–134, 167 hebrew-from-fixed, 99, 99, 106, 108, 331, solar, 7, 126–128 348, 381 structure, 123–126 hebrew-leap-year?, 91, 91, 98, 107, 348, 379 old lunisolar hebrew-new-year, 98, 98, 99, 348, 380 implementation, 129–134 hebrew-sabbatical-year?, 91, 91, 348, 379 Lisp code, 386–388 hebrew-year-length-correction, 97, 97, 98, sample dates, 441 348, 380 structure, 128–129 Heilbron, John L., 121 old solar Henderson, Helene, 42 implementation, 126–128 Henning, Edward, xxv, 315, 322 Lisp code, 386 Herran, Nicolas, xxv sample dates, 441 Herschel, John W. F., 16, 42 structure, 126 Hezekiah ben David da Silva, 94 Panchang, 312 Hillel II (= Hillel ben Judah), 89 solar Hillis, W. Daniel, back cover, 324 holidays, 304 Hindu calendar, xxii, 6, 10, 11, 28, 89, Lisp code, 425–426 123–135, 182, 185, 186, 195, 207, New Year, 126, 304, 305 247, 255, 275–313 sample dates, 441 astronomical, 299–303 tithi, 129, 278, 290, 292, 306, 312 Lisp code, 429–432 yogas, 312 sample dates, 441 hindu-anomalistic-month, 285, 285, 286, days, 4, 13, 124, 276 357, 425 epoch, 15, 123, 124, 284, 288, 289 hindu-anomalistic-year, 285, 285, 286, holidays, xxiv, 303–312 294, 295, 357, 425 karan.as, 312 hindu-arcsin, 283, 283–285, 293, 348, 424 lunisolar, 315, 316 hindu-ascensional-difference, 293, 293, holidays, 304–309 295, 296, 348, 427 Lisp code, 426–427 hindu-calendar-year, 287, 287, 288, 290, lunar day, 129, 133, 134, 278, 286, 349, 426 290, 298, 303–305, 309 hindu-creation, 284, 284, 357, 424 New Year, 133, 285, 305–306 hindu-daily-motion, 294, 294, 295, 349, sample dates, 441 428 modern, 7, 182, 185, 195, 275–313 hindu-date-occur, 307, 307, 308, 349, 433 alternatives, 295–299 hindu-day-count, 124, 124, 126, 127, 133, expunged day, 278, 303, 304 349, 386 expunged month, 277, 281, 287, 303, hindu-epoch, 124, 124, 127, 134, 284, 287, 306 289, 291, 293, 300–302, 357, 386 history, 275 hindu-equation-of-time, 295, 295, 296, implementation, 287–295 349, 428 intercalated day, 278 hindu-expunged?, 297, 298, 298, 349, 429 leap day, 278, 289 hindu-fullmoon-from-fixed, 297, 297, 349, leap month, 277–279, 287, 289, 290, 429 303, 304, 306, 307 hindu-locale, 292, 292, 295, 296, 298, 300, Lisp code, 424–435 357, 429

function definition function type Lisp code

462 Index

hindu-lunar-date, 349, 426 hindu-sunrise, 288–290, 292, 295, 295, see hindu-lunar-day, 349, 426 also alt-hindu-sunrise, 296, 298, hindu-lunar-day-at-or-after, 305, 305, 306, 305, 306, 309, 350, 429 308, 309, 311, 349, 432 hindu-sunset, 296, 296, 350, 430 hindu-lunar-day-from-moment, 286, 286, hindu-synodic-month, 276, 276, 287, 305, 290–292, 305, 349, 425 357, 424 hindu-lunar-era, 289, 289–291, 302, 357, hindu-tithi-occur, 308, 308, 309, 350, 434 426 hindu-tropical-longitude, 293, 293, 294, hindu-lunar-event, 309, 309, 349, 434 350, 428 hindu-lunar-from-fixed, 289, 289, 292, hindu-true-position, 285, 285, 286, 350, 297, 298, 307–309, 312, 349, 426 424 hindu-lunar-holiday, 308, 308, 349, 434 hindu-zodiac, 286, 286–290, 350, 425 hindu-lunar-leap-day, 349, 426 Hồ Ngọc Đức, 271, 273 hindu-lunar-leap-month, 349, 426 Hoang, Peter (Pierre), 273, 333 hindu-lunar-longitude, 286, 286, 309, 311, Hoffman, Roy E., 331 349, 425 Hoffrichter, Burghart, xxv hindu-lunar-month, 349, 426 Hohenkerk, Catherine Y., 215 hindu-lunar-new-year, 305, 305, 349, 433 Holford-Strevens, Leofranc, 41, 71 Holi (Hindu holiday), 306 hindu-lunar-on-or-before?, 307, 307, 349, Holidays 433 Bahá’í, 236–237 hindu-lunar-phase, 286, 286, 287, 305, 308, Balinese, 155, 159–161 349, 425 Chinese, 264–266 hindu-lunar-station, 309, 309, 349, 432 Christian, 70–71, 113–121, 325–326 hindu-lunar-year, 349, 426 Coptic, 76–77 hindu-mean-position, 284, 284, 285, 294, Easter, 47, 70, 113–121, 325–326 295, 349, 424 Ethiopic, 77 hindu-new-moon, 305 Gregorian, 57–59 hindu-new-moon-before, 287, 287, 290, Hindu, xxiv, 303–312 349, 425 Islamic, 86–87 hindu-rising-sign, 294, 294, 349, 428 Jewish, 101–105, 326, 331 hindu-sidereal-month, 276, 276, 286, 357, Julian, 70–71 424 Korean, 271 hindu-sidereal-year, 276, 276, 284, 286, Orthodox, 70–71, 121 287, 289, 291, 294, 295, 304, 357, Persian, 226 424 Tibetan, 319–322 hindu-sine, 283, 283, 285, 293–295, 349, Hoot, Charles, xxv 424 Horæ temporales, see Hour, temporal hindu-sine-table, 282, 282–284, 294, 350, Horizon 424 geometric, 208 hindu-solar-date, 350, 425 visible, 210 hindu-solar-era, 288, 288, 289, 300, 301, Hoshana Rabba (Jewish holiday), 92, 102 357, 425 Hoskin, Michael A., 60 hindu-solar-from-fixed, 288, 288, 350, 425 hour, 350, 365 hindu-solar-longitude, 286, 286–288, 291, Hour angle, 185 293, 304, 311, 350, 425 Hour, temporal (= seasonal), 92, 207, 211, hindu-solar-longitude-at-or-after, 304, 306 304, 306, 350, 432 Howse, Derek, 214 hindu-solar-sidereal-difference, 294, hr, 350, 395 294–296, 350, 428 Huángdì (Chinese emperor), 263 hindu-sundial-time, 296, 296, 297, 350, 430 Hube, Douglas P., 214

function definition function type Lisp code

Index 463

Hungry Ghosts (Chinese holiday), 264 islamic-date, 350, 377 Husain, Muzhar, 86 islamic-epoch, 84, 84, 85, 329, 357, 377 islamic-from-fixed, 85, 85, 86, 350, 378 I islamic-in-gregorian, 86, 86, 87, 350, 378 ‘Id-al-’Ad¯ .h.a¯ (Islamic holiday), 87 islamic-leap-year?, 84, 84, 85, 350, 377 ‘Id-al-Fit¯ .r (Islamic holiday), 87 islamic-locale, 328, 328, 329, 357, 438 Ides, 65–67 ISO calendar, 6, 11, 79–81 ides, 65, 65, 68, 357, 374 epoch, 15, 79 ides-of-month, 66, 66, 68, 350, 374 Lisp code, 376–377 if (Lisp function), 364 sample dates, 441 Ilyas, Mohammad, 87, 214 iso-date, 350, 376 in-range?, 350, 365 iso-day, 350, 377 Independence Day (U. S. holiday), 57 iso-from-fixed, 80, 80, 350, 377 independence-day, 57, 57, 350, 371 iso-long-year?, 81, 81, 350, 377 India, see also Andhra Pradesh, Bengal, iso-week, 350, 376 Bihar, Dharamsala, Haryana, iso-year, 350, 377 Kashmir, Madhya Pradesh, Israel, see also Cæsarea, Haifa, Mount Nadia, Rajasthan, Ujjain, and Carmel, and Jerusalem, 93, 105, Uttar Pradesh, 6, 85, 122, 123, 228, 236, 237 128, 274, 275, 299, 328 Israel Independence Day, 104 Ingerman, Peter Zilahy, xxv Italy, see also Rome, 47 International Astronomical Union (IAU), 172 iyyar, 90, 90, 98, 104, 357, 378 International Organization for Standardization (ISO), 79 J International Telecommunications Union, 175 j2000, 179, 179, 185, 196, 197, 357, 397 Interpolation, 282–284, 298 Jacob ben Meir (= Rabbenu Tam), 212 interval, 350, 365 Jacobi, Hermann G., 134, 290, 292, 312 Inui, Shiho, xxv Jacobson, Howard, xxv, xxvii, 10 invert-angular, 350, 364 J.A.D. (= julian astronomical day), 16 Iran, see also Isfahan, Khurasan, Shiraz, and jaffa, 330, 330, 331, 357, 439 Tehran, 236 Jaffa (Israel), 330 Ise (Japan), 440 Jalal¯ ¯ı calendar, 217 Isfahan (Iran), 219 Janmasht¯ .am¯ı, see Birthday of Krishna Ishigami, Yoshiyasu, xxv Janson, Svante, xxv, 315, 322 Islamic calendar, 6, 7, 10, 11, 33–36, 83–87, january, 48, 48, 50, 59, 65, 178, 191, 270, 182, 217, 222, 275 357, 367 days, 4, 13, 83, 84, 89 Japan, see also Ise and Tokyo, 5, 268 epoch, 15, 84 Japanese calendar, 268–269 holidays, 86–87 age, 269 implementation, 85–86 eras, 268 leap-year rule, 85 kigen, 268 Lisp code, 377–378 Lisp code, 423 months, 84 nengo,¯ 268 New Year, 86, 87, 263 japanese-location, 268, 268, 269, 350, 423 observational, 11, 86, 328–329 Jaritz, Gerhard, 46 sample dates, 441 JD (= julian day), 16 structure, 83–85 jd-epoch, 17,17,357, 362 week, 83–84 jd-from-fixed, 18, 18, 350, 363 Islamic Shura Council of North America, jd-from-moment, 17, 17, 18, 350, 363 328 jerusalem, 173, 173, 326, 357, 396

function definition function type Lisp code

464 Index

Jerusalem (Israel), 70, 92, 94, 96, 103, 172, kajeng-keliwon, 160, 160, 351, 394 173, 177, 441, 446 Kajeng-Keliwon (Balinese holiday), 155, 160 Jesus’s Circumcision (Coptic holiday), 77 Kak, Subhash, xxv Jesus’s Transfiguration (Coptic holiday), 77 Kalacakra¯ calendar, see Tibetan calendar jewish-dusk, 211,211,350, 409 Kalends, 65–67, 69, 70 jewish-morning-end, 213,213,350, 410 kalends, 65, 65, 68, 69, 358, 374 jewish-sabbath-ends, 211,211,351, 409 Kaler, James B., 214 Jiéqì (Chinese calendar), 248, 249 Kali Yuga (Hindu calendar), 15, 123, 124, Jimmu Tenno¯ (Japanese Emperor), 269 129, 284, 288, 289 Johnson, Samuel, xxvi Kamasan (Bali), 152 Jones, William, 303 Kaneko, Hikotaro, 440 Joshi, Murli Manohar, 123 Kang¯ X¯ı (Chinese emperor), 332 Jovian cycle (Hindu calendar), 125–126, 316 Kantor, Mattis, 92 jovian-year, 126, 126, 351, 386 Karaite calendar, 329 Julian astronomical day, see Julian day Karan.a numbers Hindu, 309–312 Julian calendar, 6, 7, 9–11, 14, 33–36, 46, 48, Tibetan, 319, 320 57, 63–71, 105, 217, 479 karana, 309, 309, 310, 351, 434 days, 13, 45 Karthikai Deepam (Hindu holiday), 306 epoch, 15, 64 Kasher, Menahem M., 111 history, 46–47 Kashmir (India), 277 holidays, 70–71 Kazoe doshi (Japanese age), 269 implementation, 63–65 kday-after, 29, 29, 58, 115–117, 325, 351, leap-year rule, 63 367 Lisp code, 372–374 kday-before, 29, 29, 58, 104, 351, 367 months, 45 kday-nearest, 29, 29, 59, 351, 367 revised, 47, 70 kday-on-or-after, 29, 29, 60, 312, 351, 367 Roman nomenclature, 65–69 kday-on-or-before, 27, 27, 29, 262, 351, 367 sample dates, 441 Keiper, Jerry B., 42 structure, 63 Kelly, Richard P., xxv Julian century, 179, 184, 189 Kepler, Johannes, xxv, 119, 170, 282 Julian day numbers, 9, 11, 15–17 Khayyam, Omar, see Omar Khayyam modified, 11, 15, 17 Khinchin, Aleksandr Ya., 42 sample dates, 441 Khowarizm¯ ¯ı, Abu Ja‘far Mohammed ibn julian-centuries, 179, 179, 183, 186, 189, Mus¯ a¯ al-, 89, 111 190, 192, 199, 203, 205, 351, 396 Khurasan (Persia), 216 julian-date,351, 372 Kielhorn, Franz, 312 julian-epoch, 64, 64, 358, 372 Kigen (Japanese calendar), 268 julian-from-fixed, 64, 64, 65, 69, 70, 351, Kinkelin, Hermann, 121 373 Kirchner, Claude, xxv julian-in-gregorian, 70, 70, 71, 351, 373 kislev, 91, 91, 98, 107, 110, 358, 379 julian-leap-year?, 63, 63–65, 68, 351, 372 Klein, Hyman, 111, 331 julian-year-from-auc-year, 69, 69, 351, 373 Klotz, Irene, xx Julius Cæsar, see Cæsar, Julius Knuth, Donald E., xxiv, 41, 47, 121, 361 july, 48, 48, 57, 66, 84, 178, 264, 358, 368 Koolish, Richard M., xxv june, 48, 48, 358, 368 Koran, 83, 328 Jupiter, 5, 124, 125, 199, 282 Korea, see also Go-Chosun and Seoul, 269 Justeson, John S., 150 Korea Astronomy Observatory, 272 Korean calendar, 269–271 K celestial stem names, 270 Kaiss, Daher, xxv holidays, 271

function definition function type Lisp code

Index 465

Lisp code, 423 Leap seconds, 177 solar terms, 270 Leap years, 7, 32–39 terrestrial branch names, 270 Coptic, 73, 74, 105 korean-location, 269, 269, 351, 423 French Revolutionary, 240, 243 korean-year, 270, 270, 351, 423 Gregorian, xx, 45, 49, 94, 275 Kratesis (Roman festival), 70 Hebrew, 90–94, 97, 100, 103, 105–107, Kshaya month (Hindu calendar), see Month, 109 expunged Islamic, 84 Kudlek, Manfred, 161 Julian, 45, 49, 63, 64 Kull-i-Shay (Bahá’í calendar), 231 Persian, 218, 223 Kuningan Day (Balinese holiday), 160 Least common multiple function, xvi, 19 K.Y.(=KaliYuga),124 Jungmin Lee, xxv Leffler, Jonathan, xxv L Leiden (The Netherlands), 162 Labor Day (U. S. holiday), 58 Lent (Christian fast), 121 labor-day, 58, 58, 351, 371 Lerner, Alon, xxv Lagrenée, Jean-Jacques, the younger, 238 let* (Lisp construct), 363 Lahiri, Nirmal C., 298 Levi, Leo, 111, 214 Lailat-al-Bara’a¯ (Islamic holiday), 87 Levin, Daniel Z., 214 Lailat-al-Kadr (Islamic holiday), 87 L˘ıYăn,273 Lailat-al-Mi‘raj¯ (Islamic holiday), 87 License, xxviii–xxix Lalla, 126 Lilius, Aloysius (= Luigi Lilio Ghiraldi), 45, Lamport, Leslie, 60 116 Langermann, Tzvi, 111 Line drawing, 32 Lantern Festival (Chinese holiday), 264 Linnæus, see von Linne, Carl last-day-of-hebrew-month, 98, 98–100, Lisp (computer language), xix, xxvi, 2, 42, 351, 381 361–364, 382, 424, 439 last-kday, 58, 58, 351, 371 list-range,351, 365 last-month-of-hebrew-year, 91, 91, 99, 103, Lists, 22–24 106, 107, 351, 379 concatenation of (||), 22 last-quarter, 202, 202, 358, 405 construction of ( ), 22 Lata, 275 element selection ( []), 22 Latitude empty, 22 celestial, 174, 187 Liú Baolín,ˇ 247, 273 terrestrial, 172, 174, 293 Liu, Chung Laung, 60, 273 latitude,351, 396 Lo iddo rosh (Hebrew calendar rule), 92, Laud (Christian prayer time), 213 108, 109 Lcm function, see Least common multiple local-from-apparent, 184, 184, 185, 208, function 351, 397 Lê Thành Lân, 273 local-from-standard, 177,177,351, 398 Leap days local-from-universal, 175, 175, 177, 326, Gregorian, 49 351, 398 Hindu, 278, 281, 289, 290, 303 location,351, 396 Julian, 49, 64, 66 Loewinger, Yaaqov, xxv Tibetan, 316 London (England), 172, 182, 207 Leap months, 7, 35 Long count (Mayan calendar), 138–139 Chinese, 253–255, 257, 262, 263 Long Now Foundation, 324 Hebrew, 90, 91 long-marheshvan?, 98, 98, 107, 351, 380 Hindu, 123, 128–133, 277–279, 287, Longitude 289, 290, 303, 304, 306, 307 celestial, 174, 186, 187, 276, 278, 282, Tibetan, 316 284, 286, 293

function definition function type Lisp code

466 Index

lunar, 198, 202, 283, 286, 309, 311, 446 Mardi Gras (Christian holiday), 119 sidereal, 186, 191–192 marheshvan, 91, 91, 98, 107, 110, 358, 379 solar, 187–193, 195, 202, 234, Marriage auguries (Chinese calendar), 248–250, 286, 304, 311, 441, 446 267–268 terrestrial, 172, 174 Mars, 5, 124, 282 longitude,351, 396 Marshack, Alexander, 42 losar, 321,321,351, 437 Martial (= Marcus Valerius Martialis), 477 Losar (Tibetan holiday), 320–321 Martinez-Hernandez, Juan, 137, 138 LotusR 1-2-3R , xxi Martyrdom of the Bab¯ (Bahá’í holiday), 236, Lounsbury, Floyd G., 138, 150 237 Lovering, Joseph, 239 Mary’s Announcement (Coptic holiday), 77 Lozowski, Edward P., 214 Mason, Charles W., 42 Luang (Balinese calendar), 158 Matins (Christian prayer time), 213 Lun, Anthony W.-C., 273 Maundy Thursday (Christian holiday), 119 Lunar mansions, see Lunar stations Mawlid an-Nab¯ı (Islamic holiday), 87 Lunar stations, 216, 278, 309 mawlid-an-nabi, 87, 87, 352, 378 lunar-altitude, 203, 203, 205–207, 326, 351, MAX, xvi, 20, 99, 198, 318, 319, 364 406 may, 48, 48, 58, 66, 358, 368 lunar-anomaly, 199, 201, 201, 203, 205, Mayan calendar, xxii, 10, 11, 28, 29, 137–151 403 317, 351, epoch, 15, 138 lunar-diameter, 328, 328, 351, 438 Goodman-Martinez-Thompson lunar-distance, 205, 205–207, 328, 351, 407 correlation, 137 lunar-elongation, 199, 201, 201, 203, 205, haab, 139–142, 144–145, 147 351, 403 Lisp code, 388–390 lunar-latitude, 202, 202, 204, 205, 326, long count, 138–139 351, 405 New Year, 136 lunar-longitude, 199, 199–201, 204, 352, round, 144–145, 149 404 sample dates, 441 lunar-parallax, 206, 206, 207, 352, 408 Spinden’s correlation, 138 lunar-phase, 198, 201, 201, 202, 299, 301, 326, 327, 352, 405 tzolkin, 5, 30–31, 142–145, 148 lunar-phase-at-or-after, 202, 202, 326, year bearer, 144, 149 352, 405 mayan-baktun, 352, 388 lunar-phase-at-or-before, 202, 202, 352, mayan-calendar-round-on-or-after,145 405 mayan-calendar-round-on-or-before, 145, Lunation, see Month 145, 352, 390 mayan-epoch, 138, 138–140, 142, 358, 388 M mayan-haab-date, 352, 388 McCarthy, Daniel P., 46 mayan-haab-day, 352, 389 McCarthy, Dennis D., 214 mayan-haab-epoch, 140, 140–142, 145, 358, Macler, Frédéric, 42 389 Madhya Pradesh (India), 277 mayan-haab-from-fixed, 140, 140, 144, Maha Shivaratri, see Great Night of Shiva 352, 389 Mahler, Eduard, 87 mayan-haab-month, 352, 389 Maimonides, Moses (= Rambam), xix, xxvii, mayan-haab-on-or-before, 141,141,144, 89, 92, 95, 111, 212, 331 352, 389 Main, Andrew, xxv mayan-haab-ordinal, 140, 140, 141, 145, major-solar-term-on-or-after, 250, 250, 352, 389 352, 418 mayan-katun, 352, 388 march, 48, 48, 51, 55, 57, 59, 65, 66, 68, 217, mayan-kin, 352, 388 231, 232, 236, 266, 270, 358, 367 mayan-long-count-date, 352, 388

function definition function type Lisp code

Index 467

mayan-long-count-from-fixed, 139, 139, Michels, Agnes K., 41, 60, 71 352, 388 Microsoft, 85 mayan-tun, 352, 388 OfficeR , xxi mayan-tzolkin-date, 352, 389 OutlookR , xxi mayan-tzolkin-epoch, 142, 142, 144, 145, WindowsR , xxi 358, 389 Mid-Autumn Festival (Chinese holiday), 264 mayan-tzolkin-from-fixed, 142, 142, 144, midday, 185, 185, 213, 219, 352, 397 352, 389 midday-in-tehran, 219, 219, 220, 352, 411 mayan-tzolkin-name, 352, 389 Midnight, 17, 45, 174, 182, 207, 213 mayan-tzolkin-number, 352, 389 civil, 247 mayan-tzolkin-on-or-before, 144, 144, 352, true (= apparent), 4, 184, 241 390 midnight, 184, 184, 213, 241, 353, 397 mayan-tzolkin-ordinal, 142, 144, 144, 145, midnight-in-china, 250, 251, 251, 252, 353, 352, 389 419 mayan-uinal, 352, 388 midnight-in-paris, 241,241,353, 416 mayan-year-bearer-from-fixed, 144,144, Midrash Tanh.uma, xxvii 352, 390 Milankovitch, Milutin, 47 Mayr, Joachim, 87 Milbrath, Susan, 150 mean-lunar-longitude, 199, 200, 200, 203, Milford-Lutzker, Mary-Ann, 152 352, 403 MIN, xvi, xvii, 20–22, 100, 193, 198, 219, mean-sidereal-year, 187, 187, 300–302, 234, 241, 251, 284, 287–289, 292, 358, 399 301, 303, 307, 327, 364 mean-synodic-month, 193, 193, 196, 198, M¯ına (Hindu month), 129, 133 201, 202, 258, 259, 327, 329, minor-solar-term-on-or-after, 251,251, 358, 401 266, 353, 418 mean-tropical-year, 187, 187, 191, 193, 220, minute, 353, 365 235, 242, 259, 260, 358, 399 Mitrophanow, Igor, 272 mecca, 173, 173, 358, 396 Mizner, Wilson, 42 Mecca (Saudi Arabia), 173, 328 MJD (= modified julian day), 17 Medina (Saudi Arabia), 84 mjd-epoch, 17, 17, 358, 363 Medinet Habu (Egypt), 72 mjd-from-fixed, 17, 17, 353, 363 Meeus, Jean, 60, 121, 214 mod (Lisp function), 363 Meletios IV, 70 Modified Julian day numbers, 17 Melhado, Evan M., 240 sample dates, 441 member (Lisp relation), 361 Modulus function, xvi, 18 Memoization, 40 Mohammed, 82, 84 Memorial Day (U. S. holiday), xxi, 58 molad, 95, 95–97, 353, 379 memorial-day, 58, 58, 352, 371 Molad (Hebrew calendar), see also Moon, Meng, Zhuo, xxv new, 92, 95–97, 109, 479 Mercury, 5, 124, 282 Moment, 10 Meridian, 174, 185 moment-from-jd, 17, 17, 18, 353, 363 lower, 182 moment-of-depression, 209, 209, 210, 353, upper, 182 408 Mesha sam. kranti¯ (Hindu Vernal equinox), monday, 27, 27, 58, 110, 358, 361 see New Year, Hindu solar Mongolian calendar, 315 mesha-samkranti, 300, 304,304,352, 433 Montezuma II (= Moctezuma Xocoyotzin), Meton, 7 30 Metonic cycle, 7, 91, 114, 116, 267 Month, 4, 6, 193–207 Metz (France), 479 anomalistic, 195 Mexico, 137, 146, 479 Armenian, 26 Mexico City (Mexico), 146, 479 Bahá’í, 230

function definition function type Lisp code

468 Index

bright fortnight, 129, 277 N Chinese, 251–258, 262 Nabonassar (Chaldean king), 25 Coptic, 73 Nabonassar era, 25 dark fortnight, 129, 277 Nadia (India), 303 Ethiopic, 75 Naga¯ Pancham¯ı (Hindu holiday), 305 expunged, 277, 281, 287, 303, 306 Nah.ala (Jewish event), 105–108 French Revolutionary, 240 Nakayama, Shigeru, 273 Gregorian, 45 Naks.atras, see also Lunar stations Hebrew, 90 Hindu, 312 Islamic, 84 Tibetan, 319, 320 Korean, 270 Nanjing (China), 247 leap, 7, 35, 91, 123, 129–133, 195, Napoleon, see Bonaparte, Napoleon 253–255, 262, 263, 272, 287, Napoleon III, see Bonaparte, Louis Napoleon 289, 303, 304, 306, 316 NASA, xx lunar, 7, 123, 124, 128, 129, 133, 247, Naser El-deen, Nabeel, xxv 248, 252–255, 276–279, 281, 303, National Spiritual Assembly, 233 315 Native American calendar, 6, 239 Persian, 218 Nativity of the Virgin Mary (Orthodox sidereal, 195, 276, 278, 283 holiday), 71 solar, 126, 128, 129, 133, 195, 247, Naw Ruz 253, 276, 277, 281, 292 Bahá’í, 233, 236, 237 Persian, 123, 226, 237 synodic, 193, 195, 247, 276, 281 naw-ruz, 226, 226, 353, 413 Tibetan, 315 Needham, Joseph, 247, 273 Vietnamese, 272 Negative years, 12–14 Moon, 5, 6, 95, 174, 179, 187, 195, 283 Nemontemi (Aztec calendar), 146 blue, 195 Nengo¯ (Japanese calendar), 268 first quarter, 202 Nepal, 314 full, 6, 113–115, 119, 195, 202, 305, Nepali calendar, 277 325 Neugebauer, Otto, 24, 42, 111, 331 last quarter, 202 Neumann, Peter G., xxvi new, 6, 86, 91, 92, 95, 96, 114, 123, new, 202, 202, 326, 358, 405 128, 129, 137, 171, 193, 195–202, New moon, see Moon, new 247, 251, 253, 263, 277, 292, 305, New Year 329 Bahá’í, 234, 236, 237 sample dates, 441 Chinese, xxii, 248, 263–264, 266, 271, Paschal, 115 332 phase, 278 Gregorian, xx, xxi, 47, 271 visibility, 326–328 Hebrew, see Rosh ha-Shanah moon-node, 199, 201, 201, 203, 205, 353, Hindu lunisolar, 133, 285, 305–306 403 Hindu solar, 126, 304, 305 Moore, George F., 449 Islamic, 86, 87, 263 Moreno-Riano,˜ Gerson, 46 Jewish, see Rosh ha-Shanah Morley, Sylvanus G., 150 Korean, 271 morning, 209, 209, 358, 409 Mayan, 136 Moshe ben Maimon, see Maimonides, Persian, see Naw Ruz Moses Tibetan, see Losar Mount Carmel (Israel), 228 New York City, xxi Moyer, Gordon, 61, 121 New Zealand, xxi mt, 353, 395 new-moon-at-or-after, 198, 198, 251, 302, Mumm, Christine, xxv 353, 403

function definition function type Lisp code

Index 469

new-moon-before, 198, 198, 252, 302, 353, October Revolution, 47 403 old-hindu-lunar-date, 353, 386 new-year,39 old-hindu-lunar-day, 353, 387 Newton, Isaac, 293 old-hindu-lunar-from-fixed, 133, 133, 353, next, 353, 364 387 Nián (Chinese calendar), 248 old-hindu-lunar-leap, 353, 387 Nicæa, Council of, 113–114 old-hindu-lunar-leap-year?, 131,131,353, Nievergelt, Jurg, 42, 61 387 nighttime-temporal-hour, 212,212,213, old-hindu-lunar-month, 353, 387 353, 410 old-hindu-lunar-year, 353, 387 nil (Lisp constant), 361, 362 old-hindu-solar-from-fixed, 127,127,353, ninth (Lisp function), 361 386 nisan, 90, 90, 99, 102, 110, 331, 358, 378 Olson, Donald W., 214 Nisan (Hebrew month), 90, 331 Omar Khayyam, 217 Nishizawa, Yus¯ o,¯ 273 omer, 102, 102, 354, 382 Nizamiah Observatory, 86 Omer (Jewish period), 102 None (Christian prayer time), 213 Ore, Øystein, 42, 150 Nones, 65–67 orthodox-easter, see also nones, 65, 65, 68, 358, 374 alt-orthodox-easter, 115,115, nones-of-month, 66, 66, 68, 353, 374 354, 385 Noon, 14, 182, 213, 218, 237 Ottoman Empire, 83 true (= apparent), 184 North Pole, 186, 283 P Norway, 360 Pakistan, 328 Nothmann, Gerhard A., xxv Palaioemerologitai, 70 november, 48, 48, 59, 358, 368 Palm Sunday (Christian holiday), 119 nth (Lisp function), 361 Panchang (Hindu calendar), 299, 312 nth-kday, 58, 58, 59, 79, 80, 353, 371 Parallax, 205 nth-new-moon, 195, 195, 197, 198, 201, 202, paris, 241, 241, 358, 416 353, 401 Paris (France), 174, 175, 238, 239, 241, 441, Numa (= Numa Pompilius), 63 446, 479 Nunavut (Canada), 211 Paris Commune, 239 Nutation, 187, 189 Parise, Frank, xxi, xxvi, 9, 42, 273 nutation, 189, 189, 199, 353, 398 Parker, Richard A., 42 Nyatri Tsenpo, 316 Pascal (computer language), 18 Nychthemeron, see Day Pascal, Blaise, xxvi Nyepi (Balinese holiday), 153 Passion Sunday (Christian holiday), 119 passover, 102, 102, 354, 382 O Passover (Jewish holiday), xxi, xxii, 70, 89, O’Beirne, Thomas H., 119, 121 100–103, 113, 326, 331 O’Malley, Michael, 214 Pasternak, Ofer, xxv Obermann, Julian, 111, 331 Patashnik, Oren, 41 Obliquity, 182, 184, 186 Pawukon (Balinese calendar), 153–161 obliquity, 184, 186, 186, 187, 353, 400 Pedersen, Olaf, 60 observational-hebrew-from-fixed, 330, Pengembang (Balinese holiday), 160 330, 353, 439 pentecost, 121,121,354, 386 observational-hebrew-new-year, 330, 330, Pentecost (Christian holiday), 119 331, 353, 439 Pepperdine, Andy, xxv observational-islamic-from-fixed, 329, Perigee, 195, 317 329, 353, 438 Perihelion, 263, 277 october, 48, 48, 66, 95, 358, 368 Persia, see Iran

function definition function type Lisp code

470 Index

Persian calendar, 6, 7, 9–11, 33, 217–227 Poznanski,´ Samuel A., 111 arithmetic, 221–225 Precession, 185–186, 293 arithmetic leap year rule, 221–223 precession, 191, 191, 192, 300, 354, 401 astronomical, 182, 187, 192, 193, Presentation of Christ in the Temple 219–221 (Orthodox holiday), 71 days, 13, 26, 218 Presentation of the Virgin Mary in the epagomenæ,26 Temple (Orthodox holiday), 71 epoch, 15, 217 Pridie (= day before), 66 holidays, 226 Prime (Christian prayer time), 213 Lisp code, 411–413 Ptolemy (Claudius Ptolmæus), 25, 92, 282 months, 218 Ptolemy III Euergetes, 76 New Year, 226 Puckett, Barry, 42 sample dates, 441 Purewal, Pal Singh, xxv structure, 217–222 purim, 103, 103, 354, 382 week, 218 Purim (Jewish holiday), 103 Persian Gulf, 236 Purple Mountain Observatory (Nanjing), persian-date, 354, 411 247, 273 persian-epoch, 217, 217, 220, 223, 226, 358, 411 Q persian-from-fixed, 220, 220, 354, 411 Qibla, 174 persian-new-year-on-or-before, 219,219, Q¯ıng dynasty, 207, 247 220, 354, 411 qing-ming, 266, 266, 354, 422 Peters, Francis E., 447 Q¯ıngmíng (Chinese solar term/holiday), 266 Peters, Tom, xxv Qˇıqiaoˇ (Chinese holiday), 264 Peterson, Arthur E., 214 Q¯ıx¯ı (Chinese holiday), 264 phasis-on-or-after, 327, 327, 330, 354, 437 Quadragesima, see Lent phasis-on-or-before, 327, 327, 329–331, Quartodecimans, 113 354, 437 Quiché, 140 Philippines, 47 Quinn, Terry J., 214 Phugpa calendar, see Tibetan calendar Quintus Curtius Rufus, 217 Phukluk calendar, see Tibetan calendar quotient, 354, 363 pi, 358 Pigeon-hole principle, 253 R Pillai, Dewan Bahadur L. D. Swamikannu, Rabbenu Tam, see Jacob ben Meir 277,287,312 radians-from-degrees, 354, 395 Pingree, David, 134, 312 Rajasthan (India), 277 Pirkei Avoth, 192 rama, 309, 309, 354, 434 Pisces (constellation), 186, 276 Rama¯ Navam¯ı, see Birthday of Rama¯ Pleiades (star cluster), 6 Ramadan¯ (Islamic fast), 87, 328 Plutarch, 69 Ramasubramanian, K., xxv p.m. (= post meridiem), xv Rambam, see Maimonides, Moses Polaris (star), 186 Ramses III, 72 poly, 354, 364 Rashi, see Solomon ben Isaac poly (polynomial evaluation macro), 364 Rata Die, 10 Pongal, see Ayyappa Jyothi Darshanam R.D.(=RataDie),10 Poole, Robert, 61 rd, 11, 11, 354, 362 Portugal, 47 rd (Lisp function), 363 Position, 172–174 Read, Kay, 145, 150 positions-in-range, 160, 160, 354, 394 Recursion, 40 possible-hebrew-days, 109, 109, 110, 354, Reese, Ronald L., 42 384 Regulagedda, Akshay, xxv

function definition function type Lisp code

Index 471

Reingold, Deborah H., xxv Routh, Martin, 168 Reingold, Edward M., iii, xxvi, 41, 42, 61, Ruggles, Clive L. N., 80 214, 227, 312 Russia, 5, 47, 70 Reingold, Eve M., xxv Reingold, Leah S., 471 S Reingold, Rachel N., xxv Sa’adia Gaon, see Fayyumi,¯ Sa’adia ben Reingold, Ruth N., xxv Joseph al- Remainder function, see Modulus function Sabbath (Jewish), 211 Repose of the Virgin Mary (Orthodox Sachau, C. Edward, 110, 123, 134 holiday), 71 sacred-wednesdays, 311,311,354, 435 Resnikoff, Louis A., 111 sacred-wednesdays-in-range, 311,311,312, rest (Lisp function), 361 354, 435 Revat¯ı (star), 276, 279 Sagarin, Jeff, xxv Rhodes, Ida, xxvi Sahill˙ıoglu,ˇ Hal˙ıl, 83 Richards, Edward G., back cover, 42, 71 Saka´ Era (Hindu calendar), 288 Richards, Nigel, xxv Sakai, Ko,¯ xxv Rickey, V. Frederick, 61 Salama, Ahmed, 331 Rieb, Jean-Pierre, 479 Salvin, Osbert, 150 Right ascension, 174, 186 Sam. kranti¯ (Hindu calendar), 304 right-ascension, 186, 186, 205, 354, 401 Samoa, 47 Roegel, Denis B., xxv Sampson, Russell D., 214 Rogation Sunday (Christian holiday), 119 Samuel, Alan E., 71 Rolf, John C., xxvii Samvatsara, see Jovian cycle Rolle, Theodore M., xxv Sansculottides (French Revolutionary Roman calendar calendar), 240 days of the month, 65–69 Sarasvat¯ı (Hindu deity), 306 ides, 65–66 Sarasvat¯ı Puja (Hindu holiday), 306 kalends, 65–66 Satterwaite, Linton, 150 Lisp code, 374–375 saturday, 27, 27, 103, 108, 110, 358, 362 nones, 65–66 Saturn, 5, 124, 282 pridie, 66 Saturnalia (Roman festival), 70 sample dates, 441 Saudi Arabia, see Mecca and Medina, 328 years, 69–70 Saunders, Robert A., xxv Roman Republic, 5 Savasorda, see Bargeloní, Abraham bar roman-count, 354, 374 H. iyya al- roman-date, 354, 374 Savoie, Denis, 214 roman-event, 354, 374 Saw, Swee-Hock, 273 roman-from-fixed, 66, 68, 68, 354, 374 Scaliger, Joseph Justus, xxii, xxvii, 0, 16, 62, roman-leap, 354, 374 63, 90, 162, 448, 449 roman-month, 354, 374 Scaliger, Julius Cæsar, 16 roman-year, 354, 374 Schram, Robert G., 9, 42, 123, 135, 312 Rome (Italy), 46, 74 Schuh, Dieter, 322 Romme, Gilbert, 242 S.E.(=Saka´ Era), 288 Rosh ha-Shanah (Jewish holiday), xxi, Search, 20–22, 40, 364 90–93, 98–102, 108 bisection, 20–22, 287, 304, 328 Rosh H. odesh (Jewish holiday), 104 linear, 20 Roth, Arthur J., xxv Season, 191 Roth, Cecil, 111, 447 sec, 354, 395 round,24 second (Lisp function), 361 Round (Mayan calendar), 144–145, 149 Second Empire (France), 239 Round function, xvi, 18 seconds, 354, 365

function definition function type Lisp code

472 Index

secs, 354, 396 Singer, Isidore, 111, 447 Seidelmann, P. Kenneth, back cover, 41, 60, Sinnott, Roger W., 214 71,214,215,273 Sirius (star), 6 Sengupta, Prabodh C., 312 Sivakumar, G., xxv Seoul (Korea), 269 sivan, 90, 90, 358, 378 september, 48, 48, 58, 242, 358, 368 Sıvıs¸ year (Ottoman Empire), 83 Septuagesima Sunday (Christian holiday), sixth (Lisp function), 361 119, 121 Skeel, Robert D., 42 Serbia, 70 Skiena, Steven S., xxv seventh (Lisp function), 361 Slonimski, H. ayyim S., 111 Sewell, Robert, 134, 135, 277, 306, 312 Sobel, Dava, 215 Sexagesima Sunday (Christian holiday), 119, Sodhya (Hindu calendar), 285 121 Sohn, Sangmo, 269 Sext (Christian prayer time), 213 Solar cycle, 105 Sh’ela (Jewish event), 105 Solar terms sh-ela, 105, 105, 354, 383 Chinese calendar, 239, 248–251 Shakespeare, William, 20, 27, 32, 65, 163, Japanese pronunciation, 248 325, 329 Korean calendar, 270 Shallit, Jeffery O., 61 solar-anomaly, 199, 201, 201, 203, 205, Shanks, Thomas G., 214 355, 403 Shanxˇ ¯ı (China), 246 solar-longitude, 189, 189–193, 201, 209, Sharma, Shriramana, xxv 213, 219, 234, 241, 248, 250, 251, Shaukat, S. Khalid, xxv, 326–328, 331 299, 355, 399 Shavuot (Jewish holiday), 70, 102 solar-longitude-after, 190, 190, 191, 250, Shemini Az.eret (Jewish holiday), 102 325, 330, 355, 400 Sherpa calendar, 315 Solomon ben Isaac (= Rashi), 185 shevat, 91, 91, 107, 110, 358, 379 Solstice, 6, 21, 163, 171, 187, 190, 191, 441 shift-days, 109, 109, 354, 385 sample dates, 441 Shiraz (Persia), 228 winter, 247, 251, 304 shiva, 309, 309, 354, 434 Sornes, Rasmus, 360 Shiva (Hindu deity), 306 Sosigenes, 46 short-kislev?, 98, 98, 107, 354, 380 Soviet Union, 47 Shrove Monday (Christian holiday), 119, 121 Sowramana Ugadi, see New Year, Hindu Shrove Sunday (Christian holiday), 119, 121 solar Shrove Tuesday (Christian holiday), 119, 121 Spain, 47 Shushan Purim (Jewish holiday), 103 Spectrum (of a real number), 36 sidereal-from-moment, 185, 185, 205, 354, Spica (star), 276 397 Spier, Arthur, 111 sidereal-solar-longitude, 192, 192, 299, Spinden, Herbert J., 137, 138, 150, 151 300, 302, 354, 401 spring, 191, 191, 219, 220, 234, 325, 330, sidereal-start, 192, 300, 300, 358, 430 358, 400 sidereal-zodiac, 300, 300–302, 355, 430 Spuler, Bertold, 87 sigma, 355, 364 Stallman, Richard M., xxvi, 42 sigma (summation macro), 364 standard-day, 355,364,365 Sign function, xvi, 18 standard-from-local, 177, 177, 184, 185, Signum, 18 209, 210, 355, 398 Simh.at Torah (Jewish holiday), 102 standard-from-sundial, 212, 212, 213, 296, Simon, Jean-Louis, 214 308, 355, 410 sin-degrees, 355, 395 standard-from-universal, 177,177,191, sine-offset, 208, 209, 209, 355, 408 250–252, 355, 398 Singer, Isaac Bashevis, 325 standard-month, 355,364,364

function definition function type Lisp code

Index 473

standard-year, 355,364,365 Tamerlane (Mongol conqueror), 14 Stanhope, Philip D. (= Fourth Earl of tammuz, 90, 90, 98, 358, 378 Chesterfield), xxiv, 171 Táng (Chinese dynasty), 246 start, 355, 365 tangent-degrees, 355, 395 Stavroulakis, Nicholas, 336 Tantzen, Robert G., 61 Steel, Duncan, 42 Taqizdeh, Seyyid H., 218, 219, 227 Steele, Guy L., Jr., xxvi, 42, 439 Tarvainen, Tapani, 47 Stein, Michael R., xxv Tasmania, xxi Stendhal, see Beyle, Marie-Henri tehran, 219, 219, 358, 411 Stephenson, F. Richard, 215, 273 Tehran (Iran), 192, 219, 233, 236 Stern, Sacha, 89, 111 tenth (Lisp function), 361 Stewart, Ian, back cover Terce (Christian prayer time), 213 Stillingfleet, Benjamin, 240 Teresi, Dick, 46 Stolz, Otto, xxv tevet, 91, 91, 98, 107, 110, 358, 379 Suddha, see Month, bright fortnight Thanksgiving Day Suì (Chinese calendar), 252 Korean holiday, 271 Sukkot (Jewish holiday), 70, 102 U. S. holiday, xxi, 27 Sullivan, Arthur, 45 Thebes (Egypt), 72 sum, 355, 363 third (Lisp function), 361 sum (summation macro), 363, 364 Thompson, J. Eric S., 136–138, 151 Summation operator ( ), xvi, 20, 40 Thompson, Sue E., 42 summer, 191, 191, 358, 400 thursday, 27, 27, 81, 104, 108, 110, 358, 362 Sun, 4, 5, 95, 174, 179, 185–187 Tibetan calendar, 6, 10, 12, 315–322 Sun Yat-sen, 263 animal totems, 314, 316 sunday, 27, 27, 59, 80, 103, 104, 108–110, epoch, 15, 316 115–117, 325, 358, 361 expunged day, 316 Sunrise, 4, 12, 124, 126–129, 134, 138, 182, holidays, 319–322 207–213, 217, 276, 278, 292–295, karan.as, 319, 320 298, 305, 309 leap day, 316 Hindu, 292–295 leap month, 316 sample dates, 441 Lisp code, 435–437 sunrise, 210,210,212,355, 409 months, 315 Sunset, 4, 12, 73, 83, 84, 87, 89, 182, naks.atras, 319, 320 207–213, 229, 233, 237, 441 sample dates, 441 sample dates, 441 weekdays, 316 sunset, 210, 210–212, 234, 330, 355, 409 yogas, 319 sunset-in-haifa, 234, 234, 355, 415 tibetan-date, 355, 435 Surya-Siddh¯ anta¯ (present), 275, 276, 282, tibetan-day, 355, 435 284, 285, 293, 295, 298, 299, tibetan-epoch, 316, 316–318, 358, 435 306, 312 tibetan-from-fixed, 318,318,321,355, 436 Sweden, 44, 47, 79, 119 tibetan-leap-day, 355, 435 Switzerland, 47 tibetan-leap-month, 355, 435 tibetan-leap-month?, 321,321,355, 437 T tibetan-month, 355, 435 t (Lisp constant), 361 tibetan-moon-equation, 317,317,318,355, Ta’anit Esther (Jewish fast), 103 436 ta-anit-esther, 103, 103, 355, 382 tibetan-new-year, 321,321,355, 437 Taiwan, 16 tibetan-sun-equation, 317,317,318,355, Talmud 435 Babylonian, 9, 163, 207 tibetan-year, 355, 435 Jerusalem, 101 Tika (Balinese calendar), 157, 158

function definition function type Lisp code

474 Index

Tikal (Guatemala), 144 tuesday, 27, 27, 59, 108, 110, 359, 361 Time, 174–179 tumpek, 160, 160, 355, 394 apparent, 184 Tumpek (Balinese holiday), 155, 160 durations, 23–24 Tumpek Kandang (Balinese holiday), 160 Dynamical, 174, 177–179 Tumpek Krulut (Balinese holiday), 160 ephemeris, 174 Tumpek Kuningan (Balinese holiday), 160 intervals, 22–23 Tumpek Landep (Balinese holiday), 160 leap seconds, 175 Tumpek Ringgit (Balinese holiday), 160 local mean, 175, 177, 184 Tumpek Uduh (Balinese holiday), 160 sidereal, 174, 185 Tun, Li-Ch’en, 273 actual, 187 Turkey, 47 mean, 187 Turning of the Wheel of Dharma (Buddhist solar, 174–175, 177 holiday), 322 apparent, 182 Twilight, 212 mean, 182 Tykocinski, Jehiel M., 212 standard, 175, 177 Type declarations, 337–359, 362 terrestrial, see Time, Dynamical Tzolkin (Mayan calendar), 30–31, 142–145, Universal, 174–175, 177 148 zones, 175–177 Tzom Gedaliah (Jewish fast), 103 time-from-clock, 23, 23, 355, 365 Tzom Tammuz (Jewish fast), 103 time-from-moment, 18, 18, 23, 211, 355, Tzom Tevet (Jewish fast), 103, 104 365 time-of-day, 355, 365 U Tishah be-Av (Jewish fast), 92, 101, 103 Uayeb (Mayan calendar), 139, 140 tishah-be-av, 103, 103, 355, 382 Uchida, Masao, 273 tishri, 91, 91, 95, 97, 99, 101, 331, 358, 379 ujjain, 292, 292, 295, 296, 308, 359, 429 Tishri (Hebrew month), 90–92, 95, 96, Ujjain (India), 292, 295, 300 98–103 Ulisano, Benita, xxv Tithi (Hindu calendar), 129, 278, 290, 292, Ulugh Beg, 14, 85 306, 312 ‘Umar, Caliph, 84 Titus Vespasianus, 92 Underhill, Muriel M., 313 Toe-Wang-Yong-Sa (Korean calendar), 271 United States of America, see also Alaska, Tokyo (Japan), 268 Hawaii, New York, and Urbana, Tonalpohualli (Aztec calendar), 145, 27, 47, 59, 121, 175, 328 148–149 Naval Observatory, xxii Tondering, Claus, xxv Universal House of Justice, 233 topocentric-lunar-altitude, 207, 207, 328, universal-from-dynamical, 179, 179, 195, 355, 408 356, 399 Trajan (= Marcus Ulpius Traianus), 101 universal-from-local, 175,175,177,184, Trần Đức Ngọc, xxv 209, 300, 356, 398 Trần Tiến Bình, 273 universal-from-standard, 177,177,213, Transfiguration (Orthodox holiday), 71 219, 234, 241, 248, 250, 251, 326, Trepidation, 293 330, 356, 398 Trinity Sunday (Christian holiday), 121 Unix, xxii Troesch, Albert, 42 unlucky-fridays-in-range, 60, 60, 356, 372 true, 66, 208, 359, 362 urbana, 172,172,191,211 Tseng, Karen, xxiii Urbana (Illinois), 0, 170, 172, 174, 191, 211, Tsuchihashi, Paul Y., 273 448 Tsurphu calendar, 315 urbana-sunset, 211,211 Tsybulsky, Vladimir V., 87 urbana-winter, 191,191 Tu-B’Shevat (Jewish holiday), 103, 110 Urip (Balinese calendar), 157

function definition function type Lisp code

Index 475

Uspensky, James V., 61, 121 Waupotitsch, Roman, xxv Uttar Pradesh (India), 277 wednesday, 27, 27, 104, 109, 110, 312, 359, 362 V Week, 4–5 Vah¯ .id (Bahá’í calendar), 230 Hebrew, 89 Vaikunta Ekadashi (Hindu holiday), 306 Islamic, 83–84 Vais´akha¯ (Hindu month), 278, 306, 321 Persian, 218 van Dalen, Benno, 87, 227 Weekdays van der Waerden, Bartel L., 42 Armenian, 5 van Flandern, Thomas C., 60 Bahá’í, 229 van Gent, Robert H., xxv, 119, 180, 181, 188, Coptic, 74 194 Ethiopic, 75 van Vlijmen, Oscar, xxv Hebrew, 89 van Wijk, Walther E., 124, 126, 128, 135, Hindu, 124 275, 292, 299, 313 Islamic, 83, 84 Varalakshmi Vratam (Hindu holiday), 306 Persian, 218 Var¯ an¯ asi¯ (= Banaras) (India), 303 sample dates, 441 Varro (= Marcus Terentius Varro), 46 Tibetan, 316 Vatican Council, Second, 121 Welch, Windon C., 273 V.E. (= Vikrama Era), 290 Whitmundy (Christian holiday), 119 Vedic months, 239 Whitney, William D., 312 Vega (star), 186 Whitsunday (Christian holiday), 119 Venus, 5, 124, 199, 282 Widiarki, Ni Made, 152 Verne, Jules, 172 Wiesenberg, Ephraim J., 111, 331 Vesper (Christian prayer time), 213 Wildmann, Helmut, xxv Victorian cycle, 115 Wilhelm, Robert, 479 Vietnamese calendar, 271–272 Willey, Gordon R., 150 celestial stem names, 272 winter, 191,191,251,359, 400 Lisp code, 423 Woodworth, Joyce, xxv months, 272 Woolhouse, Wesley S. B., 41, 87 terrestrial branch names, 272 World Council of Churches, 119, 121, 325, vietnamese-location, 271, 271, 356, 423 331 Vikrama Era (Hindu calendar), 289 World Wide Web, xxiv, 2, 361 Vilhjálmsson, Porsteinn, 80 Wynn, Peter, 42 Vilna Gaon, see Eliyahu ben Shlomo Zalman Vishnu (Hindu deity), 306 X visible-crescent, 326, 326, 327, 356, 438 X¯ıan¯ (China), 246 Vollers, Karl, 326 Xihuitl (Aztec calendar), 145–147 Voltaire, see Arouet, Franc¸ois Marie Xiuhmolpilli (Aztec calendar), 149 von Dechend, Hertha, 258 Xú X¯ıqí, 247, 273 von Lieven, Carl Christoph, 52 von Linne, Carl, 239 Y Y10K problem, 39 W Y2K problem, xx Wustenfeld,¨ Ferdinand, 87 Yadav, Bhuri S., 312 Wada, Eiiti, xxv yahrzeit, 107, 107, 108, 356, 383 Wallis, Faith, 46 Yahrzeit (Jewish event), 105–108 Wallis, John, 116 yahrzeit-in-gregorian, 108, 108, 356, 384 Warnings, 39–41 Yallop, Bernard D., 215 Wassef, Cérès W., 77 Yáng Guangxi¯ an,¯ 248 Wauchope, Robert, 150 Yaqob, Daniel, xxv

function definition function type Lisp code

476 Index

Yarshater, Ehsan, 227 Yoh.anan ben Zakkai, 70 Year, 4, 6–9, 185–236 Yom ha-Shoah (Holocaust Memorial Day), A.U.C., 69–70 104 embolismic (Hebrew calendar), 90 Yom ha-Zikkaron (Israel Memorial Day), equinoctial, 222, 226 104 gravid (Hebrew calendar), 90 Yom Kippur (Jewish holiday), 92, 101, 103 Gregorian calendar, 47–48 yom-ha-zikkaron, 104, 104, 356, 383 Hebrew sabbatical, 91 yom-kippur, 101, 101, 356, 382 leap, 7, 32–39, 45, 49, 63, 64, 73, 74, Yucatan (Mexico), 137, 140 90–94, 97, 100, 103, 105–107, 109, 218, 223, 240, 243, 275 Z negative, 12–14 Zarineba, Fariba, xxv Roman, 69–70 Zeller’s congruence, 53, 56–57 sıvıs¸ (Ottoman Empire), 83 Zeller, J. Christian J., 56–57, 61 sabbatical (Hebrew calendar), 91 Zhongqì¯ (Chinese calendar), 248, 249 sidereal, 125, 187, 276, 284 Zodiac, 6, 88, 123, 126, 127, 130, 186, 195, solar, 7, 146, 195, 241 248, 274, 276–278, 280, 286, 287, tropical, 46, 105, 140, 187, 195, 247 305 Year bearer (Mayan calendar), 144, 149 Zomorodian, Afra, xxv year-rome-founded, 69, 69, 70, 359, 373 zone, 356, 396 Yoga zone-from-longitude, 175, 175, 295, 356, Hindu, 311–312 398 Tibetan, 319 Zoroastrian calendar, 26, 217 yoga, 311,311,356, 435 epoch, 15

The covers of this book are too far apart. —Attributed to Ambrose Bierce

function definition function type Lisp code