By Yesica Pineda
The ancient Mayan Pyramid of Kukulkan at Chichén Itzá, Yucatan, Mexico constructed circa 1050 was built during the late Mayan period, The pyramid was used as a calendar: four stairways, each with 91 steps and a platform at the top, making a total of 365, equivalent to the number of days in a calendar year.
The Maya calendar was adopted by the other Mesoamerican nations, such as the Aztecs and the Toltec, which adopted the mechanics of the calendar unaltered but changed the names of the days of the week and the months.
The Maya calendar uses three different dating systems in parallel, the Long Count, the Tzolkin (divine calendar), and the Haab (civil calendar). Of these, only the Haab has a direct relationship to the length of the year.
A typical Mayan date looks like this: 188.8.131.52.6, 3 Cimi 4 Zotz.
184.108.40.206.6 is the Long Count date.
3 Cimi is the Tzolkin date.
4 Zotz is the Haab date.
The tzolkin is a cycle of 260 days and the haab is a cycle of 365 days.
The tzolkin cycle and the haab cycle were combined to produce a cycle of 18,980 days, known as the calendar round. 18,980 days is a little less than 52 solar years.
The “Calendar Round” is like two gears that inter-mesh, one smaller than the other. One of the ‘gears’ is called the tzolkin, or Sacred Round. The other is the haab, or Calendar Round. The smaller wheels together represent the 260-day Sacred Round; the inner wheel, with the numbers one to thirteen, meshes with the glyphs for the 20 day names on the outer wheel. A section of a large wheel represents part of the 365-day year – 18 months of 20 days each (numbered 0-19). The five days remaining at year’s end were considered evil. Any day calculated on these cycles would not repeat for 18,980 days – 52 years.
Thus the Mayas could not simply use a tzolkin/haab date to identify a day within a period of several hundred years because there would be several days within this period with the same tzolkin/haab date, so they used a third dating system which enabled them to identify a day uniquely within a period of 1,872,000 days – approximately 5,125.36 solar years. To do this they used a vigesimal (i.e. based on 20) place-value number system, analogous to our decimal place-value number system.
MAYA VIGESIMAL NUMBER SYSTEM
The Mayas used a pure vigesimal system for counting objects but modified this when counting days. In a pure vigesimal system each place in a number is occupied by a number from 0 to 19, and that number is understood as being multiplied by a power of 20. Thus in such a system:
2.3.4 = 2x20x20 + 3×20 + 4×1 = 864
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