Determining the accuracy of the mayan calendar
Did the Mayas Think a Year Was 365 Days?
Although there were only 365 days in the Haab year, the Mayas were aware that a year is slightly longer than 365 days, and in fact, many of the month-names are associated with the seasons; Yaxkin, for example, means "new or strong sun" and, at the beginning of the Long Count, 1 Yaxkin was the day after the winter solstice, when the sun starts to shine for a longer period of time and higher in the sky. When the Long Count was put into motion, it was started at 188.8.131.52.0, and 0 Yaxkin corresponded with Midwinter Day, as it did at 184.108.40.206.0 back in 3114 B.C.E. The available evidence indicates that the Mayas estimated that a 365-day year precessed through all the seasons twice in 220.127.116.11.0 or 1,101,600 days.
We can therefore derive a value for the Mayan estimate of the year by dividing 1,101,600 by 365, subtracting 2, and taking that number and dividing 1,101,600 by the result, which gives us an answer of 365.242036 days, which is slightly more accurate than the 365.2425 days of the Gregorian calendar.
(This apparent accuracy could, however, be a simple coincidence. The Mayas estimated that a 365-day year precessed through all the seasons twice in 18.104.22.168.0 days. These numbers are only accurate to 2-3 digits. Suppose the 22.214.171.124.0 days had corresponded to 2.001 cycles rather than 2 cycles of the 365-day year, would the Mayas have noticed?)
In ancient times, the Mayans had a tradition of a 360-day year. But by the 4th century B.C.E. they took a different approach than either Europeans or Asians. They maintained three different calendars at the same time. In one of them, they divided a 365-day year into eighteen 20-day months followed by a five-day period that was part of no month. The five-day period was considered to be unlucky.