The Mayan Long Count Calendar

The Maya were known for their astronomical proficiency. This is demonstrated in the Mayan codices where ritual practices were related to astronomical events/predictions. Whereas Mayan mathematics were based on a vigesimal system, they used a different base when dealing with long periods of time, the Long Count Calendar (LCC), composed of different Long Count Periods: the Tun of 360 days, the Katun of 7200 days and the Baktun of 144000 days. There were two other calendars used in addition to the LCC: a civil year Haab' of 365 days and a religious year Tzolk'in of 260 days. Another cycle was also in use: a 3276-day cycle (combination of the 819-day Kawil cycle and the 4 directions-colors). Based on the hypothesis that Mayan astronomers had a good knowledge of naked-eye astronomy, we propose here an explanation of the origin of the LCC, the Haab', the Tzolk'in and the 3276-day cycle. This study sheds more light on the connection between arithmetic, astronomy and religion in Maya civilization.