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Astronomy, Calendrics and Mathematics

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The Maya were among the most advanced astronomers of their time.  They used monuments, buildings and wooden implements to make fixed lines of sight for observing celestial bodies. 

Evidence has been found to confirm that they recorded the passage of the sun, moon, and Venus, and that they also measured the changing location of the Pleidaes. They predicted lunar eclipses and computed the length of a tropical year as 365.2420 days.  Modern astronomy, with the use of sophisticated scientific instrumentation, records this year as actually consisting of 365.2422 days and demonstrates that despite their stone tool technology, the Maya were incredibly accurate.  The astronomical data compiled by the Maya were used to develop two calendrical systems that served both practical and religious purposes. These included the Haab or solar calendar, and the Tzolkin or ritual calendar.

The Haab was divided into eighteen months (uinals) of twenty days each.  To this total of 360 days (tun) were added five days (uayeb) that some people suggest were unlucky days.  The tzolkin or sacred almanac was made up of 13 months of 20 days that summed up to 260 days.  When combined, dates in the two systems only reoccurred every 52 years.  This event would mark the completion of a Sacred Round.  To compute time spans longer than the 52 year cycle the Maya developed a system of recording known as the Long Count.  The latter incorporated five segments of time known as Baktun, Katun, Tun, Uinal and Kin.  The Baktun consisted of 144,000 days, the Katun 7,200 days, the Tun 360 days, the Uinal 20 days, and the Kin equivalent to 1 day.

The calendrical calculations of the Maya could not have been made without a sophisticated system of mathematics.  For this they used twenty numerals in what is known as a vigesimal (rather than a decimal) system.   The numbers 1 to 19 were recorded in two ways: as bar and dot symbols where a bar equaled 5 and a dot equaled 1 and by head variant numerals where glyphic symbols of human or god heads represented the actual number.  Another facet of Maya mathematics was the use of zero.  Only two other cultures in the world, the Babylonians and Hindus, are known to have developed the concept of zero independently.  The use of zero and the decimal system of mathematics were only introduced to Europe in the Middle Ages.  The Maya were using their mathematical system long before the birth of Christ.


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