<P> The basic number system consists of a dot to represent one, and a bar to represent five . By the Postclassic period a shell symbol represented zero; during the Classic period other glyphs were used . The Maya could write any number from 0 to 19 using a combination of these symbols . The precise value of a numeral was determined by its position; as a numeral shifted upwards, its basic value multiplied by twenty . In this way, the lowest symbol would represent units, the next symbol up would represent multiples of twenty, and the symbol above that would represent multiples of 400, and so on . For example, the number 884 would be written with four dots on the lowest level, four dots on the next level up, and two dots on the next level after that, to give 4x1, plus 4x20, plus 2x400 . Using this system, the Maya were able to record huge numbers . Simple addition could be performed by summing the dots and bars in two columns to give the result in a third column . </P> <P> The Maya calendrical system, in common with other Mesoamerican calendars, had its origins in the Preclassic period . However, it was the Maya that developed the calendar to its maximum sophistication, recording lunar and solar cycles, eclipses and movements of planets with great accuracy . In some cases, the Maya calculations were more accurate than equivalent calculations in the Old World; for example, the Maya solar year was calculated to greater accuracy than the Julian year . The Maya calendar was intrinsically tied to Maya ritual, and it was central to Maya religious practices . The calendar combined a non-repeating Long Count with three interlocking cycles, each measuring a progressively larger period . These were the 260 - day tzolk'in, the 365 - day haab', and the 52 - year Calendar Round, resulting from the combination of the tzolk'in with the haab' . There were also additional calendric cycles, such as an 819 - day cycle associated with the four quadrants of Maya cosmology, governed by four different aspects of the god K'awiil . </P> <P> The basic unit in the Maya calendar was one day, or k'in, and 20 k'in grouped to form a winal . The next unit, instead of being multiplied by 20, as called for by the vigesimal system, was multiplied by 18 in order to provide a rough approximation of the solar year (hence producing 360 days). This 360 - day year was called a tun . Each succeeding level of multiplication followed the vigesimal system . </P> <Table> Long Count periods <Tr> <Th> Period </Th> <Th> Calculation </Th> <Th> Span </Th> <Th> Years (approx .) </Th> </Tr> <Tr> <Td> k'in </Td> <Td> 1 day </Td> <Td> 1 day </Td> <Td> </Td> </Tr> <Tr> <Td> winal </Td> <Td> 1 x 20 </Td> <Td> 20 days </Td> <Td> </Td> </Tr> <Tr> <Td> tun </Td> <Td> 18 x 20 </Td> <Td> 360 days </Td> <Td> 1 year </Td> </Tr> <Tr> <Td> k'atun </Td> <Td> 20 x 18 x 20 </Td> <Td> 7,200 days </Td> <Td> 20 years </Td> </Tr> <Tr> <Td> bak'tun </Td> <Td> 20 x 18 x 20 x 20 </Td> <Td> 144,000 days </Td> <Td> 394 years </Td> </Tr> <Tr> <Td> piktun </Td> <Td> 20 x 18 x 20 x 20 x 20 </Td> <Td> 2,880,000 days </Td> <Td> 7,885 years </Td> </Tr> <Tr> <Td> kalabtun </Td> <Td> 20 x 18 x 20 x 20 x 20 x 20 </Td> <Td> 57,600,000 days </Td> <Td> 157,700 years </Td> </Tr> <Tr> <Td> kinchiltun </Td> <Td> 20 x 18 x 20 x 20 x 20 x 20 x 20 </Td> <Td> 1,152,000,000 days </Td> <Td> 3,154,004 years </Td> </Tr> <Tr> <Td> alawtun </Td> <Td> 20 x 18 x 20 x 20 x 20 x 20 x 20 x 20 </Td> <Td> 23,040,000,000 days </Td> <Td> 63,080,082 years </Td> </Tr> </Table>

When did the mayan civilization began and end