Of course, the 365-wheel can be divided into days or into segments of days (20 days, 30 days or whatever). But that does not change the number 365. And just like the 20-wheel and the 13-wheel, the 365-wheel has at least one important marker. At the beginning of a cycle each marker of each wheel is in direct alignment, as indicated by the colored dots in the diagram. The arrows indicate the rotational direction of each wheel.
Suppose we start our count at a certain day of the year (like our January 1). With each day (e.g. at sunrise), each wheel advances one "tooth". After exactly 365 days the big wheel made one complete rotation and its marker is back to its original position. How about the markers of the other two wheels? Since the 20-wheel has to make 18º rotations for each complete rotation of the 365-wheel, its marker shows exactly the additional quarter rotation.
Over the same period of 365 days, the 13-wheel makes 28.07692 (365 ÷ 13) rotations. In other words, its marker makes 28 complete rotations and advances one "tooth". After 2 years of 365 days, the marker of the 20-wheel shows half a rotation (after 36.5 rotations) and the marker of the 13-wheel advances another "tooth" after making 56.1538461538… rotations. Since 0.1538461538 × 13 = 2, the 13-wheel indicates the second year.
After four years, the markers of both the 365 and the 20-wheel are back to their original position and only the 13-wheel suggests that it is the fourth year. That is an important position in the calendar, as it signifies the end of a 4-year period and necessitates the introduction of a leap-day. While in modern times we add a day to our paper calendars (February 29th), the Mayan calendar counted the last day of the 4-year cycle twice; i.e. the 365-wheel was NOT turned on that particular day!
In fact, this could have been the occasion for a religious festival every fourth year on a certain day (e.g. Summer solstice). Apparently, we still have such a festive day: the Olympiad*.
* As the appointed head of the Alexandrian library, the Greek mathematician and astronomer Eratosthenes of Cyrene (3rd century BC) had access to ancient manuscripts, since also the Egyptians utilized a 4-year leap cycle for their Sothic calendar. Owing to his efforts, the 4-year cycle became associated with the Olympic Games. The interesting fact is that these games take place exactly in those years that can be divided by 4 (e.g. 1988, 1992, 1996); similar to the leap years.
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