Mayan numerals.

The Pre-Columbian Maya civilization used a vigesimal (base-twenty) numeral system. A numeral system (or system of numeration) is a Mathematical notation for representing numbers of a given set by symbols in a consistent manner The Hindu-Arabic numeral system is a Positional Decimal Numeral system first documented in the ninth century The arabic numerals (often capitalized are the ten Digits (0 1 2 3 4 5 6 7 8 9 which—along with the system The Eastern Arabic numerals (also called Arabic-Indic numerals and Arabic Eastern Numerals) are the symbols used to represent the Hindu-Arabic numeral system Khmer numerals are the numerals used in the Khmer language of Cambodia. Most of the positional Base 10 Numeral systems in the world have originated from India, which first developed the concept of positional numerology The Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens Thai numerals (เลขไทย are a set of numerals traditionally used in Thailand, although the Arabic numerals are more common Chinese numerals are characters for writing Numbers in Chinese. The Suzhou numerals or huama is a Numeral system used in China before the introduction of Arabic numerals. Counting rods ( Japanese: 算木 sangi are small bars typically 3-14 cm long used by mathematicians for calculation in China, Japan The Korean language has two regularly used sets of numerals a Sino-Korean system and a native Korean system The Abjad numerals are a decimal Numeral system in which the 28 letters of the Arabic alphabet are assigned numerical values The system of Armenian numerals is a historic Numeral system created using the Majuscules (uppercase letters of the Armenian alphabet. Cyrillic numerals was a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. Ge'ez (gez ግዕዝ) also called Ethiopic, is an Abugida script that was originally developed to write Ge'ez, a Semitic language The system of Hebrew numerals is a quasi-decimal alphabetic Numeral system using the letters of the Hebrew alphabet. ʹ the numeral sign redirects here For the accent ´ see Acute accent. The Āryabhaṭa numeration is a system of numerals based on Sanskrit phonemes. Attic numerals were used by the ancient Greeks, possibly from the 7th century BC Babylonian numerals were written in cuneiform, using a wedge-tipped reed Stylus to make a mark on a soft Clay tablet which would be exposed The system of Ancient Egyptian numerals was a Numeral system used in ancient Egypt aka Kemet The Etruscan numerals were used by the ancient Etruscans The system was adapted from the Greek Attic numerals and formed the inspiration for the later Roman Roman numerals are a Numeral system originating in ancient Rome, adapted from Etruscan numerals. Discovery In 1946 a deposit with more than 250 sickles corresponding to the period 1500-1250 BC was discovered in Frankleben (in the region of Merseburg - Querfurt This is a list of Numeral system topics (and "numeric representations" by Wikipedia page A positional notation or place-value notation system is a Numeral system in which each position is related to the next by a Constant multiplier a In mathematical numeral systems, the base or radix is usually the number of unique digits, including zero that a positional Numeral The decimal ( base ten or occasionally denary) Numeral system has ten as its base. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. Quaternary is the base - Numeral system. It uses the digits 0 1 2 and 3 to represent any Real number. The octal Numeral system, or oct for short is the base -8 number system and uses the digits 0 to 7 In Mathematics and Computer science, hexadecimal (also base -, hexa, or hex) is a Numeral system with a Base 32 or duotrigesimal is a Numeral system with 32 as its base The base - system is a Numeral system with 64 as its base It is the largest power-of-two base that can be represented using single printable ASCII The unary numeral system is the bijective base - 1 Numeral system. Ternary or trinary is the base - Numeral system. Analogous to a " Bit " a ternary digit is known as a trit ( Nonary is a base - Numeral system, typically using the digits 0-8 but not the digit 9 The duodecimal system (also known as base -12 or dozenal) is a Numeral system using twelve as its base. The vigesimal or base - numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten The base - system is a Numeral system with 24 as its base There are 24 hours in a day so our time keeping system includes a base-24 component Base 30 or trigesimal is a positional numeral system using 30 as the Radix. Base 36 is a positional numeral system using 36 as the Radix. Sexagesimal ( base-sixty) is a Numeral system with sixty as the base. The pre-Columbian era incorporates all period subdivisions in the history and prehistory of the Americas before the appearance of significant European influences The Maya civilization is a Mesoamerican Civilization, noted for the only known fully developed written language of the Pre-Columbian Americas The vigesimal or base - numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten A numeral system (or system of numeration) is a Mathematical notation for representing numbers of a given set by symbols in a consistent manner "Twenty" redirects here For the village in England, see Twenty Lincolnshire. A numeral system (or system of numeration) is a Mathematical notation for representing numbers of a given set by symbols in a consistent manner

The numerals are made up of three symbols; zero (shell shape), one (a dot) and five (a bar). Mathematics For any number x: x ·1 = 1· x = x (1 is the multiplicative identity This article discusses the number five. For the year 5 AD see 5. For example, nineteen (19) is written as four dots in a horizontal row above three horizontal lines stacked upon each other. 19 ( nineteen) is the Natural number following 18 and preceding 20.

Numbers above 19

400s
20s
1s
	33	429	5125

Numbers after 19 were written vertically up in powers of twenty. For example, thirty-three would be written as one dot above three dots, which are in turn atop two lines. 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 400, another row is started. The number 429 would be written as one dot above one dot above four dots and a bar, or (1×400) + (1×20) + 9 = 429. The powers of twenty are numerals, just as the Hindu-Arabic numeral system uses powers of tens. A numeral system (or system of numeration) is a Mathematical notation for representing numbers of a given set by symbols in a consistent manner The Hindu-Arabic numeral system is a Positional Decimal Numeral system first documented in the ninth century ^[1]

Other than the bar and dot notation, Maya numerals can be illustrated by face type glyphs. The face glyph for a number represents the deity associated with the number. These face number glyphs were rarely used, and are mostly seen only on some of the most elaborate monumental carving.

Addition and Subtraction

Adding and subtracting numbers using Maya numerals is very simple. [1]
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. Addition is the mathematical process of putting things together If four or more bars result, four bars are removed and a dot is added to the next higher column.

Similarly with subtraction, remove the elements of numeric symbol subtracted from the minuend symbol:

If there are not enough dots in a minuend position, a bar is replaced by five dots. Subtraction is one of the four basic Arithmetic operations it is the inverse of Addition, meaning that if we start with any number and add any number and then subtract Subtraction is one of the four basic Arithmetic operations it is the inverse of Addition, meaning that if we start with any number and add any number and then subtract 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 being worked on.

Zero

The Maya/Mesoamerican Long Count calendar required the use of zero as a place-holder within its vigesimal positional numeral system. A shell glyph -- -- was used as a zero symbol for these Long Count dates, the earliest of which (on Stela 2 at Chiapa de Corzo, Chiapas) has a date of 36 BCE. Chiapas is the southernmost state of Mexico, located towards the southeast of the country ^[2]

However, since the eight earliest Long Count dates appear outside the Maya homeland,^[3] it is assumed that the use of zero predated the Maya, and was possibly the invention of the Olmec. The Olmec were an ancient Pre-Columbian people living in the Tropical lowlands of south-central Mexico, in what are roughly the modern-day states 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 BCE, several centuries before the earliest known Long Count dates--which suggests that zero was not an Olmec discovery.

In the calendar

Detail showing three columns of glyphs from La Mojarra Stela 1. La Mojarra Stela 1 is a Mesoamerican carved monument ( Stela) dating from the 2nd century CE The left column uses Maya numerals to show a Long Count date of 8. 5. 16. 9. 7, or 156 CE.

In the "Long Count" portion of the Maya calendar, a variation on the strictly vigesimal numbering is used. The Maya calendar is a system of distinct Calendars and Almanacs used by the Maya civilization of Pre-Columbian Mesoamerica, and by The Long Count changes in the third place value; it is not 20×20 = 400, as would otherwise be expected, but 18×20, so that one dot over two zeros signifies 360. A positional notation or place-value notation system is a Numeral system in which each position is related to the next by a Constant multiplier a This is supposed to be because 360 is roughly the number of days in a year. A year (from Old English gēr) is the time between two recurrences of an event related to the Orbit of the Earth around the Sun (Some hypothesize that this was an early approximation to the number of days in the solar year, although the Maya had a quite accurate calculation of 365. A tropical year (also known as a solar year) is the length of time that the Sun takes to return to the same position in the cycle of seasons as seen from Earth 2422 days for the solar year at least since the early Classic era. ) Subsequent place values return to base-twenty.

In fact, every known example of large numbers 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.

External links

• Maya Mathematics online converter from decimal numeration to Maya numeral notation.
• Anthropomorphic Maya numbers online story of number representations.

Notes

References