400s | |||
20s | |||
1s | |||
Total(s) | 33 | 429 | 5125 |
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The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal (base-20) positional numeral system. The numerals are made up of three symbols: zero (a shell), [1] one (a dot) and five (a bar). For example, thirteen is written as three dots in a horizontal row above two horizontal bars; sometimes it is also written as three vertical dots to the left of two vertical bars. With these three symbols, each of the twenty vigesimal digits could be written.
Numbers after 19 were written vertically in powers of twenty. The Mayan used powers of twenty, just as the Hindu–Arabic numeral system uses powers of ten. [2]
For example, thirty-three would be written as one dot, above three dots atop two bars. The first dot represents "one twenty" or "1×20", which is added to three dots and two bars, or thirteen. Therefore, (1×20) + 13 = 33.
Upon reaching 202 or 400, another row is started (203 or 8000, then 204 or 160,000, and so on). The number 429 would be written as one dot above one dot above four dots and a bar, or (1×202) + (1×201) + 9 = 429.
Other than the bar and dot notation, Maya numerals were sometimes illustrated by face type glyphs or pictures. The face glyph for a number represents the deity associated with the number. These face number glyphs were rarely used, and are mostly seen on some of the most elaborate monumental carvings.
There are different representations of zero in the Dresden Codex, as can be seen at page 43b (which is concerned with the synodic cycle of Mars). [3] It has been suggested that these pointed, oblong "bread" representations are calligraphic variants of the PET logogram, approximately meaning "circular" or "rounded", and perhaps the basis of a derived noun meaning "totality" or "grouping", such that the representations may be an appropriate marker for a number position which has reached its totality. [4]
Adding and subtracting numbers below 20 using Mayan numerals is very simple. Addition is performed by combining the numeric symbols at each level:
If five or more dots result from the combination, five dots are removed and replaced by a bar. If four or more bars result, four bars are removed and a dot is added to the next higher row. This also means that the value of 1 bar is 5.
Similarly with subtraction, remove the elements of the subtrahend Symbol from the minuend symbol:
If there are not enough dots in a minuend position, a bar is replaced by five dots. If there are not enough bars, a dot is removed from the next higher minuend symbol in the column and four bars are added to the minuend symbol which is being worked on.
The "Long Count" portion of the Maya calendar uses a variation on the strictly vigesimal numerals to show a Long Count date. In the second position, only the digits up to 17 are used, and the place value of the third position is not 20×20 = 400, as would otherwise be expected, but 18×20 = 360 so that one dot over two zeros signifies 360. Presumably, this is because 360 is roughly the number of days in a year. (The Maya had however a quite accurate estimation of 365.2422 days for the solar year at least since the early Classic era.) [5] Subsequent positions use all twenty digits and the place values continue as 18×20×20 = 7,200 and 18×20×20×20 = 144,000, etc.
Every known example of large numbers in the Maya system uses this 'modified vigesimal' system, with the third position representing multiples of 18×20. It is reasonable to assume, but not proven by any evidence, that the normal system in use was a pure base-20 system. [6]
Several Mesoamerican cultures used similar numerals and base-twenty systems and the Mesoamerican Long Count calendar requiring the use of zero as a place-holder. The earliest long count date (on Stela 2 at Chiappa de Corzo, Chiapas) is from 36 BC. [a]
Since the eight earliest Long Count dates appear outside the Maya homeland, [7] it is assumed that the use of zero and the Long Count calendar predated the Maya, and was possibly the invention of the Olmec. Indeed, many of the earliest Long Count dates were found within the Olmec heartland. However, the Olmec civilization had come to an end by the 4th century BC, several centuries before the earliest known Long Count dates—which suggests that zero was not an Olmec discovery.
Mayan numerals codes in Unicode comprise the block 1D2E0 to 1D2F3
Mayan Numerals [1] [2] Official Unicode Consortium code chart (PDF) | ||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | |
U+1D2Ex | 𝋠 | 𝋡 | 𝋢 | 𝋣 | 𝋤 | 𝋥 | 𝋦 | 𝋧 | 𝋨 | 𝋩 | 𝋪 | 𝋫 | 𝋬 | 𝋭 | 𝋮 | 𝋯 |
U+1D2Fx | 𝋰 | 𝋱 | 𝋲 | 𝋳 | ||||||||||||
Notes |
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
In linguistics, a numeral in the broadest sense is a word or phrase that describes a numerical quantity. Some theories of grammar use the word "numeral" to refer to cardinal numbers that act as a determiner that specify the quantity of a noun, for example the "two" in "two hats". Some theories of grammar do not include determiners as a part of speech and consider "two" in this example to be an adjective. Some theories consider "numeral" to be a synonym for "number" and assign all numbers to a part of speech called "numerals". Numerals in the broad sense can also be analyzed as a noun, as a pronoun, or for a small number of words as an adverb.
0 (zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and consequently, division by zero has no meaning in arithmetic.
The Olmecs were the earliest known major Mesoamerican civilization, flourishing in the modern-day Mexican states of Veracruz and Tabasco from roughly 1200 to 400 BCE during Mesoamerica's formative period. They were initially centered at the site of their development in San Lorenzo Tenochtitlán, but moved to La Venta in the 10th century BCE following the decline of San Lorenzo. The Olmecs disappeared mysteriously in the 4th century BCE, leaving the region sparsely populated until the 19th century.
The Maya calendar is a system of calendars used in pre-Columbian Mesoamerica and in many modern communities in the Guatemalan highlands, Veracruz, Oaxaca and Chiapas, Mexico.
A vigesimal or base-20 (base-score) numeral system is based on twenty. Vigesimal is derived from the Latin adjective vicesimus, meaning 'twentieth'.
A numerical digit or numeral is a single symbol used alone or in combinations, to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal digits.
The tzolkʼin is the 260-day Mesoamerican calendar used by the Maya civilization of pre-Columbian Mesoamerica.
The calendrical systems devised and used by the pre-Columbian cultures of Mesoamerica, primarily a 260-day year, were used in religious observances and social rituals, such as divination.
Maya script, also known as Maya glyphs, is historically the native writing system of the Maya civilization of Mesoamerica and is the only Mesoamerican writing system that has been substantially deciphered. The earliest inscriptions found which are identifiably Maya date to the 3rd century BCE in San Bartolo, Guatemala. Maya writing was in continuous use throughout Mesoamerica until the Spanish conquest of the Maya in the 16th and 17th centuries. Though modern Mayan languages are almost entirely written using the Latin alphabet rather than Maya script, there have been recent developments encouraging a revival of the Maya glyph system.
The Isthmian script is an early set of symbols found in inscriptions around the Isthmus of Tehuantepec, dating to c. 500 BCE – 500 CE, though with dates subject to disagreement. It is also called the La Mojarra script and the Epi-Olmec script.
Mesoamerica, along with Mesopotamia and China, is one of three known places in the world where writing is thought to have developed independently. Mesoamerican scripts deciphered to date are a combination of logographic and syllabic systems. They are often called hieroglyphs due to the iconic shapes of many of the glyphs, a pattern superficially similar to Egyptian hieroglyphs. Fifteen distinct writing systems have been identified in pre-Columbian Mesoamerica, many from a single inscription. The limits of archaeological dating methods make it difficult to establish which was the earliest and hence the progenitor from which the others developed. The best documented and deciphered Mesoamerican writing system, and the most widely known, is the classic Maya script. Earlier scripts with poorer and varying levels of decipherment include the Olmec hieroglyphs, the Zapotec script, and the Isthmian script, all of which date back to the 1st millennium BC. An extensive Mesoamerican literature has been conserved, partly in indigenous scripts and partly in postconquest transcriptions in the Latin script.
The Mesoamerican Long Count calendar is a non-repeating base-20 and base-18 calendar used by pre-Columbian Mesoamerican cultures, most notably the Maya. For this reason, it is often known as the MayaLong Count calendar. Using a modified vigesimal tally, the Long Count calendar identifies a day by counting the number of days passed since a mythical creation date that corresponds to August 11, 3114 BCE in the proleptic Gregorian calendar. The Long Count calendar was widely used on monuments.
San Andrés is an Olmec archaeological site in the present-day Mexican state of Tabasco. Located 5 km northeast of the Olmec ceremonial center of La Venta in the Grijalva river delta section of the Tabasco Coastal Plain, San Andrés is considered one of its elite satellite communities, with evidence of elite residences and other elite activities. Several important archaeological finds have been made at San Andrés, including the oldest evidence of the domesticated sunflower, insight into Olmec feasting rituals, didactic miniatures, and possible evidence of an Olmec writing system.
Olmec hieroglyphs are a set of glyphs developed within the Olmec culture. The Olmecs were the earliest known major Mesoamerican civilization, flourishing during the formative period in the tropical lowlands of the modern-day Mexican states of Veracruz and Tabasco. The subsequent Epi-Olmec culture, was a successor culture to the Olmec and featured the Isthmian script, which has been characterized as a full-fledged writing system, though with its partial decipherment being disputed.
The Maya civilization was a Mesoamerican civilization that existed from antiquity to the early modern period. It is known by its ancient temples and glyphs (script). The Maya script is the most sophisticated and highly developed writing system in the pre-Columbian Americas. The civilization is also noted for its art, architecture, mathematics, calendar, and astronomical system.
Las Choapas is a recently found archaeological site located within the municipality of Las Choapas, in the southeastern border of the Veracruz State, inside the San Miguel de Allende Ejido, bordering the municipalities of Huimanguillo, Tabasco and Ostuacán, in Chiapas.
Maya astronomy is the study of the Moon, planets, Milky Way, Sun, and astronomical phenomena by the Precolumbian Maya civilization of Mesoamerica. The Classic Maya in particular developed some of the most accurate pre-telescope astronomy in the world, aided by their fully developed writing system and their positional numeral system, both of which are fully indigenous to Mesoamerica. The Classic Maya understood many astronomical phenomena: for example, their estimate of the length of the synodic month was more accurate than Ptolemy's, and their calculation of the length of the tropical solar year was more accurate than that of the Spanish when the latter first arrived. Many temples from the Maya architecture have features oriented to celestial events.
Muisca numerals were the numeric notation system used by the Muisca, one of the civilizations of the Americas before the Spanish conquest of the Muisca. Just like the Mayas, the Muisca had a vigesimal numerical system, based on multiples of twenty. The Muisca numerals were based on counting with fingers and toes. They had specific numbers from one to ten, yet for the numbers between eleven and nineteen they used "foot one" (11) to "foot nine" (19). The number 20 was the 'perfect' number for the Muisca which is visible in their calendar. To calculate higher numbers than 20 they used multiples of their 'perfect' number; gue-muyhica would be "20 times 4", so 80. To describe "50" they used "20 times 2 plus 10"; gue-bosa asaqui ubchihica, transcribed from guêboʒhas aſaqɣ hubchìhicâ. In their calendar, which was lunisolar, they only counted from one to ten and twenty. Each number had a special meaning, related to their deities and certain animals, especially the abundant toads.