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Maya calendar

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The Maya calendar is a system of distinct calendars and almanacs used by the Maya civilization of pre-Columbian Mesoamerica, and by some modern Maya communities in highland Guatemala.

These calendars can be synchronized and interlocked in many ways, their combinations giving rise to further, more extensive cycles. The essentials of the Maya calendric system are based upon a system which had been in common use throughout the region, dating back to at least the 6th century BCE. It shares many aspects with calendars employed by other earlier Mesoamerican civilizations, such as the Zapotec and Olmec, and contemporary or later ones such as the Mixtec and Aztec calendars. Although the Mesoamerican calendar did not originate with the Maya, their subsequent extensions and refinements of it were the most sophisticated. Along with those of the Aztecs, the Maya calendars are the best-documented and most completely understood.

By the Maya mythological tradition, as documented in Colonial Yucatec accounts and reconstructed from Late Classic and Postclassic inscriptions, the deity Itzamna is frequently credited with bringing the knowledge of the calendar system to the ancestral Maya, along with writing in general and other foundational aspects of Maya culture.[1]



[edit] General overview

v d e
Wide use Astronomical · Gregorian · Islamic · ISO
Calendar Types
Lunisolar · Solar · Lunar

Selected use Assyrian · Armenian · Attic · Aztec (TonalpohualliXiuhpohualli) · Babylonian · Bahá'í · Bengali · Berber · Bikram Samwat · Buddhist · Celtic · Chinese · Coptic · Egyptian · Ethiopian · Calendrier Républicain · Germanic · Hebrew · Hellenic · Hindu · Indian · Iranian · Irish · Japanese · Javanese · Juche · Julian · Korean · Lithuanian · Malayalam · Maya (Tzolk'inHaab') · Minguo · Nanakshahi · Nepal Sambat · Pawukon · Pentecontad calendar · Rapa Nui · Roman · Soviet · Tamil · Thai (LunarSolar) · Tibetan · Burmese . Vietnamese· Xhosa · Zoroastrian
Calendar Types
Runic · Mesoamerican (Long CountCalendar Round)
Christian variants
Julian calendar · Calendar of saints · Eastern Orthodox liturgical calendar · Liturgical year
Rarely used Darian calendar · Discordian calendar
Display types and applications Perpetual calendar · Wall calendar · Economic calendar

The most important of these calendars is one with a period of 260 days. This 260-day calendar was prevalent across all Mesoamerican societies, and is of great antiquity (almost certainly the oldest of the calendars). It is still used in some regions of Oaxaca, and amongst the Maya communities of the Guatemalan highlands. The Maya version is commonly known to scholars as the Tzolkin, or Tzolk'in in the revised orthography of the Academia de las Lenguas Mayas de Guatemala.[2] The Tzolk'in is combined with another 365-day calendar (known as the Haab, or Haab' ), to form a synchronized cycle lasting for 52 Haabs, called the Calendar Round. Smaller cycles of 13 days (the trecena) and 20 days (the veintena) were important components of the Tzolk'in and Haab' cycles, respectively.

A different form of calendar was used to track longer periods of time, and for the inscription of calendar dates (i.e., identifying when one event occurred in relation to others). This form, known as the Long Count, is based upon the number of elapsed days since a mythological starting-point.[3] According to the correlation between the Long Count and Western calendars accepted by the great majority of Maya researchers (known as the GMT correlation), this starting-point is equivalent to 11 August 3114 BCE in the proleptic Gregorian calendar or 6 September in the Julian calendar (−3113 astronomical). The Goodman-Martinez-Thompson correlation was chosen by Thompson in 1935 based on earlier correlations by Joseph Goodman in 1905 (11 August), Juan Martínez Hernández in 1926 (12 August), and John Eric Sydney Thompson in 1927 (13 August).[4][5] By its linear nature, the Long Count was capable of being extended to refer to any date far into the future (or past). This calendar involved the use of a positional notation system, in which each position signified an increasing multiple of the number of days. The Maya numeral system was essentially vigesimal (i.e., base-20), and each unit of a given position represented 20 times the unit of the position which preceded it. An important exception was made for the second place value, which instead represented 18 × 20, or 360 days, more closely approximating the solar year than would 20 × 20 = 400 days. It should be noted however that the cycles of the Long Count are independent of the solar year.

Many Maya Long Count inscriptions are supplemented by what is known as the Lunar Series, another calendar form which provides information on the lunar phase and position of the Moon in a half-yearly cycle of lunations.

A 584-day Venus cycle was also maintained, which tracked the appearance and conjunctions of Venus as the morning and evening stars. Many events in this cycle were seen as being inauspicious and baleful, and occasionally warfare was timed to coincide with stages in this cycle.

Other, less-prevalent or poorly-understood cycles, combinations and calendar progressions were also tracked. An 819-day count is attested in a few inscriptions; repeating sets of 9- and 13-day intervals associated with different groups of deities, animals and other significant concepts are also known.

[edit] Maya concepts of time

With the development of the place-notational Long Count calendar (believed to have been inherited from other Mesoamerican cultures), the Maya had an elegant system with which events could be recorded in a linear relationship to one another, and also with respect to the calendar ("linear time") itself. In theory, this system could readily be extended to delineate any length of time desired, by simply adding to the number of higher-order place markers used (and thereby generating an ever-increasing sequence of day-multiples, each day in the sequence uniquely identified by its Long Count number). In practice, most Maya Long Count inscriptions confine themselves to noting only the first 5 coefficients in this system (a b'ak'tun-count), since this was more than adequate to express any historical or current date (with an equivalent span of approximately 5125 solar years). Even so, example inscriptions exist which noted or implied lengthier sequences, indicating that the Maya well understood a linear (past-present-future) conception of time.

However, and in common with other Mesoamerican societies, the repetition of the various calendric cycles, the natural cycles of observable phenomena, and the recurrence and renewal of death-rebirth imagery in their mythological traditions were important and pervasive influences upon Maya societies. This conceptual view, in which the "cyclical nature" of time is highlighted, was a pre-eminent one, and many rituals were concerned with the completion and re-occurrences of various cycles. As the particular calendaric configurations were once again repeated, so too were the "supernatural" influences with which they were associated. Thus it was held that particular calendar configurations had a specific "character" to them, which would influence events on days exhibiting that configuration. Divinations could then be made from the auguries associated with a certain configuration, since events taking place on some future date would be subject to the same influences as its corresponding previous cycle dates. Events and ceremonies would be timed to coincide with auspicious dates, and avoid inauspicious ones.[6]

The completion of significant calendar cycles ("period endings"), such as a k'atun-cycle, were often marked by the erection and dedication of specific monuments such as twin-pyramid complexes such those in Tikal and Yaxha, but (mostly in stela inscriptions) commemorating the completion, accompanied by dedicatory ceremonies.

A cyclical interpretation is also noted in Maya creation accounts, in which the present world and the humans in it were preceded by other worlds (one to five others, depending on the tradition) which were fashioned in various forms by the gods, but subsequently destroyed. The present world also had a tenuous existence, requiring the supplication and offerings of periodic sacrifice to maintain the balance of continuing existence. Similar themes are found in the creation accounts of other Mesoamerican societies.[7]

[edit] Tzolk'in

Main article: Tzolk'in

Some Mayanists employ the name Tzolk'in (in modern Mayan orthography; also and formerly commonly written tzolkin) for the Maya Sacred Round or 260-day calendar. Tzolk'in is a neologism coined in Yukatek Maya, to mean "count of days" (Coe 1992). The actual names of this calendar as used by Precolumbian Maya peoples are still debated by scholars. The Aztec calendar equivalent was called Tonalpohualli, in the Nahuatl language.

The Tzolk'in calendar combines twenty day names with the thirteen numbers of the trecena cycle to produce 260 unique days. It is used to determine the time of religious and ceremonial events and for divination. Each successive day is numbered from 1 up to 13 and then starting again at 1. Separately from this, each day is given a name in sequence from a list of 20 day names:

Tzolk'in calendar: named days and associated glyphs
No. 1
Name 2
example 3
16th C.
Yucatec 4
Classic Maya 5
No. 1
Name 2
example 3
16th C.
Yucatec 4
Classic Maya 5
01 Imix' Imix Imix (?) / Ha' (?) 11 Chuwen Chuen (unknown)
02 Ik' Ik Ik' 12 Eb' Eb (unknown)
03 Ak'b'al Akbal Ak'b'al (?) 13 B'en Ben (unknown)
04 K'an Kan K'an (?) 14 Ix Ix Hix (?)
05 Chikchan Chicchan (unknown) 15 Men Men (unknown)
06 Kimi Cimi Cham (?) 16 K'ib' Cib (unknown)
07 Manik' Manik Manich' (?) 17 Kab'an Caban Chab' (?)
08 Lamat Lamat Ek' (?) 18 Etz'nab' Etznab (unknown)
09 Muluk Muluc (unknown) 19 Kawak Cauac (unknown)
10 Ok Oc (unknown) 20 Ajaw Ahau Ajaw
  1. The sequence number of the named day in the Tzolk'in calendar
  2. Day name, in the standardised and revised orthography of the Guatemalan Academia de Lenguas Mayas[2]
  3. An example glyph (logogram) for the named day. Note that for most of these several different forms are recorded; the ones shown here are typical of carved monumental inscriptions (these are "cartouche" versions)
  4. Day name, as recorded from 16th century Yukatek Maya accounts, principally Diego de Landa; this orthography has (until recently) been widely used
  5. In most cases, the actual day name as spoken in the time of the Classic Period (ca. 200–900) when most inscriptions were made is not known. The versions given here (in Classic Maya, the main language of the inscriptions) are reconstructed based on phonological evidence, if available; a '?' symbol indicates the reconstruction is tentative.[8]

Some systems started the count with 1 Imix', followed by 2 Ik', 3 Ak'b'al, etc. up to 13 B'en. The trecena day numbers then start again at 1 while the named-day sequence continues onwards, so the next days in the sequence are 1 Ix, 2 Men, 3 K'ib', 4 Kab'an, 5 Etz'nab', 6 Kawak, and 7 Ajaw. With all twenty named days used, these now began to repeat the cycle while the number sequence continues, so the next day after 7 Ajaw is 8 Imix'. The repetition of these interlocking 13- and 20-day cycles therefore takes 260 days to complete (that is, for every possible combination of number/named day to occur once).

[edit] Divination

Each day of the Tzolk'in has a Patron Spirit who influences events. Ah K'in, the Mayan shaman-priest, whose title means "Day Keeper", read the Tzolk'in to determine the answers to yes/no questions as well as more complex questions involving health, wealth and family. The Sacred Calendar is also used to set the most auspicious dates for household, lineage, and community rituals.

When a child is born, the day keeper interprets the Tzolk'in cycle to identify the baby’s character (similarly done today with a natal chart). For example, a child born on the day of Ak'b'al is thought to be feminine, wealthy, and verbally skillful. The birthday of Ak'b'al (along with several other days) is also thought to give the child the ability to receive messages with the supernatural world through somatic twitches of "blood lightning", so he or she might become a Shaman-priest or a Marriage Spokesman.

There are several forms of Maya Calendar divination employing the sacred coral seeds which each Calendar diviner carries in a small bag with crystals and 'other small things' (Tozzer 1941).

The Precolumbian Maya practiced a form of Bibliomancy, in which they would cast the seeds upon a calendar to determine the good and bad days for the year.

Precolumbian Maya employed and Modern Maya Ah K'in employ Sortilage, in which piles of four or five beans are counted from the current calendar day of the Sacred Round to arrive at the result.

Modern Maya Ah K'in also employ Cartomancy, in which the fifty two cards of the poker deck represent the fifty two Year Bearers of the Maya Calendar Round.

Maya shamans also perform a wide variety of divinatory arts which do not specifically depend upon a mastery of the sacred calendar, including crystal, mirror, and water gazing; and spirit possession, among others.

[edit] Origin of the Tzolk'in

The exact origin of the Tzolk'in is not known, but there are several theories. One theory is that the calendar came from mathematical operations based on the numbers thirteen and twenty, which were important numbers to the Maya. The numbers multiplied together equal 260. Another theory is that the 260-day period came from the length of human pregnancy. This is close to the average number of days between the first missed menstrual period and birth, unlike Naegele's rule which is 40 weeks (280 days) between the last menstrual period and birth. It is postulated that midwives originally developed the calendar to predict babies' expected birth dates.

A third theory comes from understanding of astronomy, geography and paleontology. The mesoamerican calendar probably originated with the Olmecs, and a settlement existed at Izapa, in southeast Chiapas Mexico, before 1200 BCE. There, at a latitude of about 15° N, the Sun passes through zenith twice a year, and there are 260 days between zenithal passages, and gnomons (used generally for observing the path of the Sun and in particular zenithal passages), were found at this and other sites. The sacred almanac may well have been set in motion on August 13, 1359 BCE, in Izapa. Vincent H. Malmström, a geographer who suggested this location and date, outlines his reasons:

(1) Astronomically, it lay at the only latitude in North America where a 260-day interval (the length of the "strange" sacred almanac used throughout the region in pre-Columbian times) can be measured between vertical sun positions -- an interval which happens to begin on the 13th of August -- the day the peoples of the Mesoamerica believed that the present world was created; (2) Historically, it was the only site at this latitude which was old enough to have been the cradle of the sacred almanac, which at that time (1973) was thought to date to the 4th or 5th centuries B.C.; and (3) Geographically, it was the only site along the required parallel of latitude that lay in a tropical lowland ecological niche where such creatures as alligators, monkeys, and iguanas were native -- all of which were used as day-names in the sacred almanac.[9]

Malmström also offers strong arguments against both of the former explanations.

A fourth theory is that the calendar is based on the crops. From planting to harvest is approximately 260 days.

[edit] Haab'

Haab' Months[10]
Name Meaning
Pop mat
Wo black conjunction
Sip red conjunction
Sotz' bat
Sek ?
Xul dog
Yaxk'in new sun
Mol water
Ch'en black storm
Yax green storm
Sac white storm
Keh red storm
Mak enclosed
K'ank'in yellow sun
Muwan owl
Pax planting time
K'ayab' turtle
Kumk'u granary
Wayeb' five unlucky days
Jones 1984
Main article: Haab'

The Haab' was the Maya solar calendar made up of eighteen months of twenty days each plus a period of five days ("nameless days") at the end of the year known as Wayeb' (or Uayeb in 16th C. orthography). Bricker (1982) estimates that the Haab' was first used around 550 BCE with the starting point of the winter solstice.

The Haab' month names are known today by their corresponding names in colonial-era Yukatek Maya, as transcribed by 16th century sources (in particular, Diego de Landa and books such as the Chilam Balam of Chumayel). Phonemic analyses of Haab' glyph names in pre-Columbian Maya inscriptions have demonstrated that the names for these twenty-day periods varied considerably from region to region and from period to period, reflecting differences in the base language(s) and usage in the Classic and Postclassic eras predating their recording by Spanish sources.[11]

Each day in the Haab' calendar was identified by a day number in the month followed by the name of the month. Day numbers began with a glyph translated as the "seating of" a named month, which is usually regarded as day 0 of that month, although a minority treat it as day 20 of the month preceding the named month. In the latter case, the seating of Pop is day 5 of Wayeb'. For the majority, the first day of the year was 0 Pop (the seating of Pop). This was followed by 1 Pop, 2 Pop as far as 19 Pop then 0 Wo, 1 Wo and so on.

As a calendar for keeping track of the seasons, the Haab' was crude and inaccurate, since it treated the year as having 365 days, and ignored the extra quarter day (approximately) in the actual tropical year. This meant that the seasons moved with respect to the calendar year by a quarter day each year, so that the calendar months named after particular seasons no longer corresponded to these seasons after a few centuries. The Haab' is equivalent to the wandering 365-day year of the ancient Egyptians. Some argue that the Maya knew about and compensated for the quarter day error, even though their calendar did not include anything comparable to a leap year, a method first implemented by the Romans.

[edit] Wayeb'

The five nameless days at the end of the calendar called Wayeb' were thought to be a dangerous time. Foster (2002) writes "During Wayeb, portals between the mortal realm and the Underworld dissolved. No boundaries prevented the ill-intending deities from causing disasters." To ward off these evil spirits, the Maya had customs and rituals they practiced during Wayeb'. For example, people avoided leaving their houses or washing or combing their hair.

[edit] Calendar Round

Neither the Tzolk'in nor the Haab' system numbered the years. The combination of a Tzolk'in date and a Haab' date was enough to identify a date to most people's satisfaction, as such a combination did not occur again for another 52 years, above general life expectancy.

Because the two calendars were based on 260 days and 365 days respectively, the whole cycle would repeat itself every 52 Haab' years exactly. This period was known as a Calendar Round. The end of the Calendar Round was a period of unrest and bad luck among the Maya, as they waited in expectation to see if the gods would grant them another cycle of 52 years.

[edit] Long Count

Detail showing three columns of glyphs from 2nd century CE La Mojarra Stela 1.  The left column gives a Long Count date of, or 156 CE. The two right columns are glyphs from the Epi-Olmec script.
Detail showing three columns of glyphs from 2nd century CE La Mojarra Stela 1. The left column gives a Long Count date of, or 156 CE. The two right columns are glyphs from the Epi-Olmec script.

Since Calendar Round dates can only distinguish in 18,980 days, equivalent to around 52 solar years, the cycle repeats roughly once each lifetime, and thus, a more refined method of dating was needed if history was to be recorded accurately. To measure dates, therefore, over periods longer than 52 years, Mesoamericans devised the Long Count calendar.

The Mayan name for a day was k'in. Twenty of these k'ins are known as a winal or uinal. Eighteen winals make one tun. Twenty tuns are known as a k'atun. Twenty k'atuns make a b'ak'tun.

The Long Count calendar identifies a date by counting the number of days from August 11, 3114 BCE. But instead of using a base-10 (decimal) scheme like Western numbering, the Long Count days were tallied in a modified base-20 scheme. Thus is equal to 25, and is equal to 40. As the winal unit resets after only counting to 18, the Long Count consistently uses base-20 only if the tun is considered the primary unit of measurement, not the k'in; with the k'in and winal units being the number of days in the tun. The Long Count represents 360 days, rather than the 400 in a purely base-20 (vigesimal) count.

Table of Long Count units
Days Long Count period Long Count period Approx solar years
1 = 1 K'in
20 = 20 K'in = 1 Winal 1/18th
360 = 18 Winal = 1 Tun 1
7,200 = 20 Tun = 1 K'atun 20
144,000 = 20 K'atun = 1 B'ak'tun 395

There are also four rarely-used higher-order cycles: piktun, kalabtun, k'inchiltun, and alautun.

Since the Long Count dates are unambiguous, the Long Count was particularly well suited to use on monuments. The monumental inscriptions would not only include the 5 digits of the Long Count, but would also include the two tzolk'in characters followed by the two haab' characters.

The Mesoamerican Long Count calendar forms the basis for a New Age belief, first forecast by José Argüelles, that a cataclysm will take place on or about 21 December 2012, a forecast that mainstream Mayanist scholars consider a mis-interpretation.[12]

[edit] Venus Cycle

Main article: Transits of Venus

Another important calendar for the Maya was the Venus cycle. The Maya were skilled astronomers, and could calculate the Venus cycle with extreme accuracy. There are six pages in the Dresden Codex (one of the Maya codices) devoted to the accurate calculation of the location of Venus. The Maya were able to achieve such accuracy by careful observation over many years. There are various theories as to why Venus cycle was especially important for the Mayans, including the belief that it was associated with war and used it to divine good times (called electional astrology) for coronations and war. Maya rulers planned for wars to begin when Venus rose. The Maya also possibly tracked other planets’ movements, including those of Mars, Mercury, and Jupiter.

[edit] See also

[edit] Notes

  1. ^ See entry on Itzamna, in Miller and Taube (1993), pp.99-100.
  2. ^ a b Academia de las Lenguas Mayas de Guatemala. Lenguas Mayas de Guatemala: Documento de referencia para la pronunciación de los nuevos alfabetos oficiales. Guatemala City: Instituto Indigenista Nacional. . Refer citation in Kettunen and Hemke (2005:5) for details and notes on adoption among the Mayanist community.
  3. ^ "Mythological" in the sense that when the Long Count was first devised sometime in the Mid- to Late Preclassic, long after this date; see for e.g. Miller and Taube (1993, p.50).
  4. ^ Finley (2002), Voss (2006, p.138)
  5. ^ Malmström (1997): "Chapter 6: The Long Count: The Astronomical Precision".
  6. ^ Coe (1992), Miller and Taube (1993).
  7. ^ Miller and Taube (1993, pp.68-71).
  8. ^ Classic-era reconstructions are as per Kettunen and Helmke (2005), pp.45–46..
  9. ^ Malmström (1997), and
  10. ^ Kettunen and Helmke (2005), pp.47–48
  11. ^ Boot (2002), pp.111–114.
  12. ^ Susan Milbrath, Curator of Latin American Art and Archaeology , Florida Museum of Natural History, quoted in USA Today, Wednesday, March 28, 2007, p. 11D.
    "For the ancient Maya, it was a huge celebration to make it to the end of a whole cycle," says Sandra Noble, executive director of the Foundation for the Advancement of Mesoamerican Studies, Inc. in Crystal River, Florida. To render December 21, 2012, as a doomsday or moment of cosmic shifting, she says, is "a complete fabrication and a chance for a lot of people to cash in." (Quoted in USA Today, Wednesday, March 28, 2007, p. 11D.)

[edit] References

Aveni, Anthony F. (2001). Skywatchers, Revised and updated edition of: Skywatchers of Ancient Mexico [1980], Austin: University of Texas Press. ISBN 0-292-70502-6. OCLC 45195586.
Boot, Erik (2002). A Preliminary Classic Maya-English/English-Classic Maya Vocabulary of Hieroglyphic Readings (PDF), Mesoweb. Retrieved on 2006-11-10.
Bricker, Victoria R. (February 1982). "The Origin of the Maya Solar Calendar". Current Anthropology 23 (1): 101. Chicago, IL: University of Chicago Press, sponsored by Wenner-Gren Foundation for Anthropological Research. doi:10.1086/202782. ISSN 0011-3204. OCLC 62217742.
Coe, Michael D. (1987). The Maya, 4th edition (revised), London; New York: Thames & Hudson. ISBN 0-500-27455-X. OCLC 15895415.
Coe, Michael D. (1992). Breaking the Maya Code. London: Thames and Hudson. ISBN 0-500-05061-9. OCLC 26605966.
Finley, Michael (2002). The Correlation Question. The Real Maya Prophecies: Astronomy in the Inscriptions and Codices. Maya Astronomy. Retrieved on 2007-05-11.
Foster, Lynn V. (2002). Handbook to Life in the Ancient Maya World, with Foreword by Peter Mathews, New York: Facts on File. ISBN 0-8160-4148-2. OCLC 50676955.
Ivanoff, Pierre (1971). Mayan Enigma: The Search for a Lost Civilization, Elaine P. Halperin (trans.), English translation of Découvertes chez les Mayas, New York: Delacorte Press. ISBN 0-440-05528-8. OCLC 150172.
Jacobs, James Q. (1999). Mesoamerican Archaeoastronomy: A Review of Contemporary Understandings of Prehispanic Astronomic Knowledge. Mesoamerican Web Ring. Retrieved on 2007-11-26.
Jones, Christopher (1984). Deciphering Maya Hieroglyphs, Carl P. Beetz (illus.), 2nd edition, prepared for Weekend Workshop April 7 and 8, 1984, Philadelphia: University Museum, University of Pennsylvania. OCLC 11641566.
Kettunen, Harri; and Christophe Helmke (2005). Introduction to Maya Hieroglyphs: 10th European Maya Conference Workshop Handbook (PDF), Leiden: Wayeb and Leiden University. Retrieved on 2006-06-08.
Malmström, Vincent H. (1997). Cycles of the Sun, Mysteries of the Moon: The Calendar in Mesoamerican Civilization, online reproduction by author, Austin: University of Texas Press. ISBN 0-292-75197-4. OCLC 34354774. Retrieved on 2007-11-26.
Miller, Mary; and Karl Taube (1993). The Gods and Symbols of Ancient Mexico and the Maya: An Illustrated Dictionary of Mesoamerican Religion. London: Thames and Hudson. ISBN 0-500-05068-6. OCLC 27667317.
Robinson, Andrew (2000). The Story of Writing: Alphabets, Hieroglyphs and Pictograms. London; New York: Thames and Hudson. ISBN 0-500-28156-4. OCLC 59432784.
Schele, Linda; and David Freidel (1990). A Forest of Kings: The Untold Story of the Ancient Maya, Reprint, New York: Harper Perennial. ISBN 0-688-11204-8. OCLC 145324300.
Tedlock, Barbara (1982). Time and the Highland Maya. Albuquerque: University of New Mexico Press. ISBN 0-826-30577-6. OCLC 7653289.
Tedlock, Dennis (trans.) (1985). Popol Vuh: the Definitive Edition of the Mayan Book of the Dawn of Life and the Glories of Gods and Kings. New York: Simon and Schuster. ISBN 0-671-45241-X. OCLC 11467786.
Thomas, Cyrus (1897). "Day Symbols of the Maya Year", in J. W. Powell (ed.): Sixteenth Annual Report of the Bureau of American Ethnology to the Secretary of the Smithsonian Institution, 1894–1895 (Project Gutenberg EBook online reproduction), Washington DC: Bureau of American Ethnology, Smithsonian Institution; U.S. Government Printing Office, pp.199–266. OCLC 14963920.
Thompson, J. Eric S. (1971). Maya Hieroglyphic Writing; An Introduction, 3rd edition, Civilization of the American Indian Series, No. 56, Norman: University of Oklahoma Press. ISBN 0-806-10447-3. OCLC 275252.
Tozzer, Alfred M.; (ed., notes and trans.) (1941). Landa's Relación de las cosas de Yucatán: a translation, Charles P. Bowditch and Ralph L. Roys (additional trans.), English translation of Diego de Landa's Relación de las cosas de Yucatán [orig. ca. 1566], with notes, commentary, and appendices incorporating translated excerpts of works by Gaspar Antonio Chi, Tomás López Medel, Francisco Cervantes de Salazar, and Antonio de Herrera y Tordesillas., Papers of the Peabody Museum of American Archaeology and Ethnology, Harvard University vol. 18, Cambridge, MA: Peabody Museum of Archaeology and Ethnology. OCLC 625693.
Voss, Alexander (2006). "Astronomy and Mathematics", in Nikolai Grube (ed.): Maya: Divine Kings of the Rain Forest, Eva Eggebrecht and Matthias Seidel (assistant eds.), Cologne, Germany: Könemann Press, pp.130–143. ISBN 3-8331-1957-8. OCLC 71165439.

[edit] External links

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