Maya numerals
Encyclopedia
Maya Numerals were a vigesimal
Vigesimal
The vigesimal or base 20 numeral system is based on twenty .- Places :...
(base
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
-twenty
20 (number)
20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems....
) numeral system
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
used by the Pre-Columbian
Pre-Columbian
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 American continents, spanning the time of the original settlement in the Upper Paleolithic period to European colonization during...
Maya civilization
Maya civilization
The Maya is a Mesoamerican civilization, noted for the only known fully developed written language of the pre-Columbian Americas, as well as for its art, architecture, and mathematical and astronomical systems. Initially established during the Pre-Classic period The Maya is a Mesoamerican...
.
The numerals are made up of three symbols; zero
0 (number)
0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...
(shell shape), one (a dot) and five (a bar). For example, nineteen
19 (number)
19 is the natural number following 18 and preceding 20. It is a prime number.In English speech, the numbers 19 and 90 are often confused. When carefully enunciated, they differ in which syllable is stressed: 19 vs 90...
(19) is written as four dots in a horizontal row above three horizontal lines stacked upon each other.
Numbers above 19
| 400s |  |
 |
|
| 20s | |
|
 |
| 1s |  |
 |
 |
| 33 | 429 | 5125 |
Numbers after 19 were written vertically 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 20^2 or 400, another row is started. The number 429 would be written as one dot above one dot above four dots and a bar, or (1×20^2) + (1×20^1) + 9 = 429. The powers of twenty are numerals
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
, just as the Hindu-Arabic numeral system
Hindu-Arabic numeral system
The Hindu–Arabic numeral system or Hindu numeral system is a positional decimal numeral system developed between the 1st and 5th centuries by Indian mathematicians, adopted by Persian and Arab mathematicians , and spread to the western world...
uses powers of tens.
Other than the bar and dot notation, Maya numerals can be 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 only on some of the most elaborate monumental carving.
Addition and subtraction
Adding and subtracting numbers below 20 using Maya numerals is very simple.Addition
Addition
Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....
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 column.
Similarly with subtraction
Subtraction
In arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...
, 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 being worked on.
Note that this corresponds almost exactly to traditional addition and subtraction in the common base-10
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
.
Zero
The Maya/Mesoamerican Long Count calendarMesoamerican Long Count calendar
The Mesoamerican Long Count calendar is a non-repeating, vigesimal and base-18 calendar used by several Pre-Columbian Mesoamerican cultures, most notably the Maya. For this reason, it is sometimes known as the Maya 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, ChiapasChiapas
Chiapas officially Estado Libre y Soberano de Chiapas is one of the 31 states that, with the Federal District, comprise the 32 Federal Entities of Mexico. It is divided in 118 municipalities and its capital city is Tuxtla Gutierrez. Other important cites in Chiapas include San Cristóbal de las...
) has a date of 36 BC.
However, since the eight earliest Long Count dates appear outside the Maya homeland, it is assumed that the use of zero predated the Maya, and was possibly the invention of the Olmec
Olmec
The Olmec were the first major Pre-Columbian civilization in Mexico. They lived in the tropical lowlands of south-central Mexico, in the modern-day states of Veracruz and Tabasco....
. 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.
In the calendar
Maya calendar
The Maya calendar is a system of calendars and almanacs used in the Maya civilization of pre-Columbian Mesoamerica, and in many modern Maya communities in highland Guatemala. and in Chiapas....
, a variation on the strictly vigesimal numbering is used. The Long Count changes in the third place value
Positional notation
Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations for its use of the same symbol for the different orders of magnitude...
; 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
Year
A year is the orbital period of the Earth moving around the Sun. For an observer on Earth, this corresponds to the period it takes the Sun to complete one course throughout the zodiac along the ecliptic....
. (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.) 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.