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.

It is reasonable to assume, but not proven by any evidence, that the normal system in use was a pure base-20 system. (The Maya had however a quite accurate estimation of 365.2422 days for the solar year at least since the early Classic era.) 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.Įvery known example of large numbers in the Maya system uses this 'modified vigesimal' system, with the third position representing multiples of 18×20. Presumably, this is because 360 is roughly the number of days in a year. 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. The 'Long Count' portion of the Maya calendar uses a variation on the strictly vigesimal numerals to show a Long Count date. The left column uses Maya numerals to show a Long Count date of 8.5.16.9.7 or 156 CE. Modified vigesimal system in the Maya calendar Detail showing in the right columns glyphs from La Mojarra Stela 1.

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. If there are not enough dots in a minuend position, a bar is replaced by five dots. Similarly with subtraction, remove the elements of the subtrahend symbol from the minuend symbol: This also means that the value of 1 bar is 5. If four or more bars result, four bars are removed and a dot is added to the next higher row. If five or more dots result from the combination, five dots are removed and replaced by a bar. These face number glyphs were rarely used, and are mostly seen on some of the most elaborate monumental carvings.Īdding and subtracting numbers below 20 using Maya numerals is very simple.Īddition is performed by combining the numeric symbols at each level: The face glyph for a number represents the deity associated with the number. Other than the bar and dot notation, Maya numerals were sometimes illustrated by face type glyphs or pictures. 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. Upon reaching 20 2 or 400, another row is started (20 3 or 8000, then 20 4 or 160,000, and so on). The first dot represents 'one twenty' or '1×20', which is added to three dots and two bars, or thirteen. For example, thirty-three would be written as one dot, above three dots atop two bars. The Maya used powers of twenty, just as the Hindu–Arabic numeral system uses powers of ten. Numbers after 19 were written vertically in powers of twenty. With these three symbols, each of the twenty vigesimal digits could be written. 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. The numerals are made up of three symbols: zero (a shell), one (a dot) and five (a bar). It was a vigesimal (base-20) positional numeral system. The Maya numeral system was the system to represent numbers and calendar dates in the Maya civilization.

Ancient mayan glyphs