Mayan numerals.

The Pre-Columbian Maya civilization used a vigesimal (base-twenty) numeral system. Image File history File links Maya. ... Image File history File links Maya. ... This article is about different methods of expressing numbers with symbols. ... I like cream cheese, it tastes good on toast. ... For other uses, see Arabic numerals (disambiguation). ... The Eastern Arabic numerals (also called Eastern Arabic numerals, Arabic-Indic numerals, Arabic Eastern Numerals) are the symbols (glyphs) used to represent the Hindu-Arabic numeral system in conjunction with the Arabic alphabet in Egypt, Iran, Pakistan and parts of India, and also in the no longer used Ottoman Turkish... Khmer numerals are the numerals used in the Khmer language of Cambodia. ... India has produced many numeral systems. ... 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). ... The counting rods (Traditional Chinese: , Simplified Chinese: , pinyin: chou2) were used by ancient Chinese before the invention of the abacus. ... The Abjad numerals are a decimal numeral system which was used in the Arabic-speaking world prior to the use of the Hindu-Arabic numerals from the 8th century, and in parallel with the latter until Modern times. ... Cyrillic numerals was a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. ... Note: This article contains special characters. ... The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. ... Greek numerals are a system of representing numbers using letters of the Greek alphabet. ... The Sanskrit alphabetic numerals were created in about A.D. 510 by Āryabhaa. ... Attic numerals were used by ancient Greeks, possibly from the 7th century BC. They were also known as Herodianic numerals because they were first described in a 2nd century manuscript by Herodian. ... 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 in the sun to harden to create a permanent record. ... The Etruscan numerals were used by the ancient Etruscans. ... Roman numerals are a numeral system originating in ancient Rome, adapted from Etruscan numerals. ... During the beginning of the Urnfield culture, around 1200 BC, a series of votive sickles of bronze with marks that have been interpreted as a numeral system, appeared in Central Europe. ... This is a list of numeral system topics, 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 common ratio, called the base or radix of that numeral system. ... The radix (Latin for root), also called base, is the number of various unique symbols (or digits or numerals) a positional numeral system uses to represent numbers. ... For other uses, see Decimal (disambiguation). ... 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 four numeral system. ... 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, base-16, or simply hex, is a numeral system with a radix, or base, of 16, usually written using the symbols 0–9 and A–F, or a–f. ... Base32 is a derivation of Base64 with the following additional properties: The resulting character set is all uppercase, which can often be beneficial when using a case-sensitive filesystem. ... Base64 is a positional notation using a base of 64. ... Ternary or trinary is the base-3 numeral system. ... Nonary is a base 9 numeral system, typically using the digits 0-8, but not the digit 9. ... The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... As there are 24 hours in a day a numbering system based upon 24, and as the base 12 is convenient here some examples of the base 24 (quadrovigesimal) system. ... Base 30 or trigesimal is a positional numeral system using 30 as the radix. ... Base 36 refers to a positional numeral system using 36 as the radix. ... The 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 on the Americas continent. ... This article is about the pre-Columbian Maya civilization. ... The vigesimal or base-20 numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten). ... This article is about different methods of expressing numbers with symbols. ... 20 (twenty) is the natural number following 19 and preceding 21. ... This article is about different methods of expressing numbers with symbols. ...

The numerals are made up of three symbols; zero (shell shape), one (a dot) and five (a bar). For other senses of this word, see zero or 0. ... This article is about the number one. ... Look up five in Wiktionary, the free dictionary. ...

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

		Hi
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. ^[1] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... This article is about different methods of expressing numbers with symbols. ... I like cream cheese, it tastes good on toast. ...

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:
3 + 2 = 5 with apples, a popular choice in textbooks[1] This article is about addition in mathematics. ... Image File history File links No higher resolution available. ...

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 column.

Similarly with subtraction, remove the elements of numeric symbol subtracted from the minuend symbol:
5 - 2 = 3 (verbally, five minus two equals three) An example problem Subtraction is one of the four basic arithmetic operations; it is the inverse of addition. ... In mathematics, subtraction is one of the four basic arithmetic operations. ... Image File history File links No higher resolution available. ...

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 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.^[2] Detail showing three columns of glyphs from 2nd century AD La Mojarra Stela 1. ... Image File history File links MAYA-g-num-0-inc-v1. ... Location within Mexico Country  Mexico Capital Tuxtla Gutiérrez Municipalities 118 Largest City Tuxtla Gutiérrez Government  - Governor Juan José Sabines Guerrero ( PRD)  - Federal Deputies PRI: 7 PRD: 5  - Federal Senators PRI: 1 PRD: 1 PVEM: 1 Area Ranked 8th  - State 74,211 km²  (28,653 sq mi) Population (2005...

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. Indeed, many of the earliest Long Count dates were found within the Olmec heartland - conversely however, as the Olmec civilization had come to an end by the 4th century BCE (several centuries before the earliest known Long Count dates) this would instead imply that zero was not an Olmec discovery. Monument 1, one of the four Olmec colossal heads at La Venta. ...

In the calendar

Detail showing three columns of glyphs from La Mojarra Stela 1. The left column uses Maya numerals to show a Long Count date of 8.5.16.9.9, or 156 CE.

In the "Long Count" portion of the Maya calendar, a variation on the strictly vigesimal numbering is used. 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. This is supposed to be because 360 is roughly the number of days in a year. (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 365.2422 days for the solar year at least since the early Classic era).^{[citation needed]} Subsequent place values return to base-twenty. Image File history File links Download high-resolution version (615x1107, 216 KB) This is a small section of the gylphs carved into La Mojarra Stela 1. ... Image File history File links Download high-resolution version (615x1107, 216 KB) This is a small section of the gylphs carved into La Mojarra Stela 1. ... Inscriptions in the Epi-Olmec script on the right side of La Mojarra Stela 1 Left side image of La Mojarra stela 1 showing a person identified by the name Harvester Mountain Lord La Mojarra Stela 1 is an early Mesoamerican carved monument (stela) dating from the 2nd century CE... 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. ... 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 common ratio, called the base or radix of that numeral system. ... A year (from Old English gÄ“r) is the time between two recurrences of an event related to the orbit of the Earth around the Sun. ... Solar year The period of time required for the earth to make one complete revolution around the sun, measured from one vernal equinox to the next. ...

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